Programs for A300000-A349999

List of integer sequences with links to LODA programs.

A300048 (program): G.f. A(x) satisfies: A(x)^3 = 1 + x*A(x) + x*A(x)^2 + x*A(x)^6.
A300061 (program): Heinz numbers of integer partitions of even numbers.
A300063 (program): Heinz numbers of integer partitions of odd numbers.
A300066 (program): Number of factorizations of the length-n prefix of the Fibonacci word A003849 into a (not strictly) decreasing sequence of finite Fibonacci words.
A300067 (program): Period 6: repeat [0, 0, 0, 1, 2, 2].
A300068 (program): A sequence based on the period 6 sequence A300067.
A300069 (program): Period 6: repeat [0, 0, 0, 1, 2, 1].
A300070 (program): Decimal expansion of the positive member y of a triple (x, y, z) solving a certain historical system of three equations.
A300071 (program): Decimal expansion of the member z of a triple (x, y, z) solving a certain historical system of three equations with positive y.
A300072 (program): Decimal expansion of the positive member -y of a triple (x, y, z) solving a certain historical system of three equations.
A300073 (program): Decimal expansion of the member z of a triple (x, y, z) satisfying a certain historical system of three equations with negative y.
A300074 (program): Decimal expansion of 1/(2*sin(Pi/5)) = A121570/2.
A300075 (program): Period 6: repeat [0, 1, 1, 2, 2, 2].
A300076 (program): A sequence based on the period 6 sequence A300075.
A300077 (program): Decimal expansion of Pi/2 truncated to n places.
A300116 (program): a(n) = Sum_{k=0..n} binomial(2k,k)^3 * binomial(2n-2k,n-k) * 2^(4*(n-k)).
A300126 (program): Number of Motzkin trees that are “uniquely closable skeletons”.
A300147 (program): a(n) = (1/8) * Sum_{d|n} d * A110163(d).
A300154 (program): Consider a spiral on an infinite hexagonal grid. a(n) is the number of cells in the part of the spiral from 1st to n-th cell that are on the same column or diagonal (in any of three directions) as the n-th cell along the spiral, including that cell itself.
A300159 (program): Number of ways of converting one set of lists containing n elements to another set of lists containing n elements by removing the last element from one of the lists and either appending it to an existing list or treating it as a new list.
A300164 (program): Numbers of the form n^2+1 not expressible as j^2+k^2 with j>k>1.
A300177 (program): Number of nX3 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
A300222 (program): In ternary (base-3) representation of n, replace 1’s with 0’s.
A300244 (program): Difference between A005187 and its Möbius transform (A297111).
A300251 (program): Möbius transform of arithmetic derivative (A003415).
A300252 (program): Difference between arithmetic derivative (A003415) and its Möbius transform (A300251).
A300253 (program): GCD of arithmetic derivative (A003415) and its Möbius transform (A300251).
A300254 (program): a(n) = 25*(n + 1)*(4*n + 3)*(5*n + 4)/3.
A300270 (program): a(n) = Sum_{1 <= i <= j <= n} mu(i*j)*floor((n/i)/j)).
A300287 (program): a(n) = floor((1/n) * Sum_{k=1..n} sqrt(k)).
A300290 (program): Period 6: repeat [0, 1, 2, 2, 3, 3].
A300291 (program): Triangle T read by rows: T is used to obtain the denominators of all fractional values for x = cos(phi) and y = sin(phi) with (x, y) on the unit circle for 0 < phi < Pi/2.
A300293 (program): A sequence based on the period 6 sequence A151899.
A300294 (program): Irregular triangle giving the GCD characteristic: t(n, m) = 1 if gcd(n, m) = 1 and zero otherwise, with t(1, 1) = 1 and t(n, m) for n >= 2 and m = 1..(n-1).
A300295 (program): Denominator of (1/3)*n*(n + 2)/((1 + 2*n)*(3 + 2*n)).
A300296 (program): Numerators of n*(5 + 3*n)/(8*(1 + 3*n)*(4 + 3*n)), n >= 0.
A300298 (program): Numerators of r(n) := Sum_{k=0..n-1} 1/Product_{j=0..4} (k + j + 1), for n >= 0, with r(0) = 0.
A300299 (program): Denominators of r(n) := Sum_{k=0..n-1} 1/Product_{j=0..4} (k + j + 1), for n >= 0, with r(0) = 0.
A300303 (program): Squares that are not of the form x^2 + x*y + y^2, where x and y are positive integers.
A300326 (program): Sum of the largest possible permutations that can be written without repetition of digits in each base from binary to n+1.
A300329 (program): Number of solutions to +-1 +- 2 +- 3 +- … +- n == n-1 (mod n).
A300330 (program): a(n) is the product over all prime powers p^e where p^e is the highest power of p dividing n and p-1 does not divide n.
A300344 (program): Number of n X 2 0..1 arrays with every element equal to 1 or 2 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A300401 (program): Array T(n,k) = n*(binomial(k, 2) + 1) + k*(binomial(n, 2) + 1) read by antidiagonals.
A300402 (program): Smallest integer i such that TREE(i) >= n.
A300403 (program): Smallest integer i such that SSCG(i) >= n.
A300404 (program): Smallest integer k such that the largest term in the Goodstein sequence starting at k is > n.
A300409 (program): Number of centered triangular numbers dividing n.
A300410 (program): Number of centered square numbers dividing n.
A300415 (program): Expansion of Product_{k>=2} (1 + x^k)/(1 - x^k).
A300421 (program): Number of n X 2 0..1 arrays with every element equal to 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A300438 (program): Expansion of (1+x)^3/(1-x-2*x^2-x^3+x^4).
A300451 (program): a(n) = (3*n^2 - 3*n + 8)*2^(n - 3).
A300474 (program): Number of partitions of the square resulting from a sequence of n n-sections, each of which divides any part perpendicular to any of the axes.
A300482 (program): a(n) = 2 * Integral_{t>=0} T_n(t/2) * exp(-t) * dt, n>=0, where T_n(x) is n-th Chebyshev polynomial of first kind.
A300483 (program): a(n) = 2 * Integral_{t>=0} T_n((t+1)/2) * exp(-t) * dt, n>=0, where T_n(x) is n-th Chebyshev polynomial of first kind.
A300484 (program): a(n) = 2 * Integral_{t>=0} T_n(t/2+1) * exp(-t) * dt, n>=0, where T_n(x) is n-th Chebyshev polynomial of first kind.
A300485 (program): a(n) = 2 * Integral_{t>=0} T_n((t-1)/2) * exp(-t) * dt, n>=0, where T_n(x) is n-th Chebyshev polynomial of first kind.
A300488 (program): a(n) = n! * [x^n] -exp(n*x)*log(1 - x)/(1 - x).
A300489 (program): a(n) = n! * [x^n] -log(1 - x)/(1 - n*x).
A300490 (program): Expansion of e.g.f. -exp(-x)*log(1 - x)/(1 - x).
A300500 (program): Number of nX2 0..1 arrays with every element equal to 0, 1, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A300518 (program): The greatest prime factor of the squarefree part of n, or 1 if n is square.
A300519 (program): Convolution of n! and n^n.
A300521 (program): Expansion of Product_{k>=1} (1 - x^prime(k))^prime(k).
A300522 (program): a(n) = (5*n + 3)*(5*n + 4)*(5*n + 5)/6.
A300523 (program): a(n) = (5*n + 5)*(5*n + 6)*(5*n + 7)/6.
A300533 (program): Number of nX2 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A300559 (program): a(n) = n*(n+1)!/2 + 1.
A300570 (program): a(n) is the concatenation n in base 2, n-1 in base 2, …, 1 in base 2.
A300571 (program): a(n) is the concatenation n in base 2, n-1 in base 2, …, 0 in base 2.
A300576 (program): Number of nights required in the worst case to find the princess in a castle with n rooms arranged in a line (Castle and princess puzzle).
A300581 (program): Expansion of Product_{k>=1} 1/(1 - 2^(k+1)*x^k).
A300583 (program): Expansion of Product_{k>=1} 1 / (1 - 2*3^k*x^k)).
A300613 (program): Number of partitions of the n-dimensional hypercube resulting from a sequence of n n-sections, each of which divides any part perpendicular to any of the axes.
A300622 (program): Denominators of sequence whose exponential self-convolution yields sequence 1, 2, 3, 5, 7, 11, 13, … (1 with primes).
A300624 (program): Figurate numbers based on the 11-dimensional regular convex polytope called the 11-dimensional cross-polytope, or 11-dimensional hyperoctahedron.
A300656 (program): Triangle read by rows: T(n,k) = 30*k^2*(n-k)^2 + 1; n >= 0, 0 <= k <= n.
A300657 (program): a(n) = Sum_{d|n} sigma(d) mod d.
A300659 (program): Product of digits of n!.
A300662 (program): Expansion of 1/(1 - x - Sum_{k>=2} prime(k-1)*x^k).
A300663 (program): Expansion of 1/(1 - Sum_{k>=1} mu(k)*x^k), where mu() is the Moebius function (A008683).
A300668 (program): a(n) = A000016(2*n).
A300671 (program): Expansion of 1/(1 - Sum_{k>=1} x^prime(k)/(1 - x^prime(k))).
A300672 (program): Expansion of 1/(1 - Sum_{p prime, k>=1} x^(p^k)/(1 - x^(p^k))).
A300707 (program): Decimal expansion of Pi^4/96.
A300709 (program): Decimal expansion of Pi^6/960.
A300711 (program): a(n) = A000367(n)/A001067(n).
A300717 (program): Möbius transform of A003557, n divided by its largest squarefree divisor.
A300718 (program): Möbius transform of A010848, number of numbers k <= n such that at least one prime factor of n is not a prime factor of k.
A300719 (program): Difference between A003557 (n divided by largest squarefree divisor of n) and its Möbius transform.
A300720 (program): Difference between A010848 and its Möbius transform.
A300738 (program): Number of minimal total dominating sets in the n-cycle graph.
A300757 (program): Number of {0,1} n X n matrices with at least one zero row or column.
A300758 (program): a(n) = 2n*(n+1)*(2n+1).
A300763 (program): a(n) = ceiling(n/g^3), where g = (1+sqrt(5))/2 is the golden ratio.
A300778 (program): Number of grid points visible from a corner of an m X n rectangular region on a square grid written as triangle T(m,n), 1 <= n <= m.
A300786 (program): L.g.f.: log(Product_{k>=1} (1 + k*x^k)) = Sum_{n>=1} a(n)*x^n/n.
A300793 (program): a(n) is the n-th derivative of arcsinh(1/x) at x=1 times (-2)^n/sqrt(2) for n >= 1.
A300799 (program): Number of nX3 0..1 arrays with every element equal to 0, 1, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A300820 (program): Length of the longest sequence of consecutive primes in the prime factorization of n. a(1) = 0.
A300826 (program): a(n) = n/A125746(n), where A125746(n) gives the smallest divisor d of n such that the sum which includes d and all smaller divisors is >= n.
A300828 (program): Multiplicative with a(p^2) = 1, a(p^3) = -2 and a(p^e) = 0 when e = 1 or e > 3.
A300836 (program): a(n) is the total number of terms (1-digits) in Zeckendorf representation of all proper divisors of n.
A300837 (program): a(n) is the total number of terms (1-digits) in Zeckendorf representation of all divisors of n.
A300838 (program): Permutation of nonnegative integers: a(n) = A057300(A003188(n)).
A300839 (program): Permutation of nonnegative integers: a(n) = A006068(A057300(n)).
A300843 (program): Number of 4-cycles in the n-transposition graph.
A300846 (program): a(n) = 3*(n - 1)^2*n^3.
A300847 (program): a(n) = 12*binomial(n, 5).
A300850 (program): Number of 6-cycles in the n-odd graph.
A300853 (program): L.g.f.: log(Product_{k>=1} (1 + x^(k^2))) = Sum_{n>=1} a(n)*x^n/n.
A300867 (program): a(n) is the least positive k such that k * n is a Fibbinary number (A003714).
A300889 (program): a(n) is the least positive multiple of n which is a Fibbinary number (A003714).
A300894 (program): L.g.f.: log(Product_{k>=1} (1 + mu(k)^2*x^k)) = Sum_{n>=1} a(n)*x^n/n, where mu() is the Moebius function (A008683).
A300902 (program): a(n) = n! / Product_{p prime < n}.
A300912 (program): Numbers of the form prime(x)*prime(y) where x and y are relatively prime.
A300915 (program): Order of the group PSL(2,Z_n).
A300950 (program): Fixed points of A300948.
A300951 (program): a(n) = Product_{j=1..floor(n/2)} p(j) where p(j) = j if j is prime else 1.
A300975 (program): a(n) = [x^n] Product_{k>=1} 1/(1 - x^(k^3))^n.
A300999 (program): Add to a(n) the first digit of a(n+1) to get a(n+2), with a(1) = 1 and a(2) = 2.
A301270 (program): Number of labeled trees on n vertices containing two fixed non-adjacent edges.
A301271 (program): Expansion of (1-16*x)^(1/8).
A301272 (program): Number of derangements of S_n with exactly one peak.
A301273 (program): Numerator of mean of first n primes.
A301277 (program): Nearest integer to mean of first n primes.
A301291 (program): Expansion of (x^4+3*x^3+x^2+3*x+1) / ((x^2+1)*(x-1)^2).
A301292 (program): Partial sums of A301291.
A301293 (program): Expansion of (x^2+x+1)^2 / ((x^2+1)*(x-1)^2).
A301294 (program): Partial sums of A301293.
A301297 (program): Distance from n to nearest Catalan number.
A301298 (program): Expansion of (1 + 4*x + 4*x^2 + 4*x^3 + x^4)/((1 - x)*(1 - x^3)).
A301299 (program): Coordination sequence for node of type V1 in “krq” 2-D tiling (or net).
A301300 (program): Partial sums of A301299.
A301306 (program): G.f.: Sum_{n>=0} (1 + (1+x)^n)^n * x^n.
A301316 (program): a(n) = ((n-1)! + 1) mod n^2.
A301317 (program): a(n) = (n-1)! + 1 mod n^3.
A301318 (program): a(n) = sqrt(A299921(n)).
A301336 (program): a(n) = total number of 1’s minus total number of 0’s in binary expansions of 0, …, n.
A301337 (program): Number of steps required in the worst case for two knights to find the princess in a castle with n rooms arranged in a line (Castle and princess puzzle).
A301347 (program): a(n) = n^(n-1) + (n-1)!.
A301370 (program): Maximum determinant of an n X n (0,1)-matrix that has exactly 2*n ones.
A301378 (program): a(n) = 10*A007605(n) - 9*A007652(n).
A301383 (program): Expansion of (1 + 3*x - 2*x^2)/(1 - 7*x + 7*x^2 - x^3).
A301402 (program): Number of nX3 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A301417 (program): Sums of positive coefficients in generalized Chebyshev polynomials of the first kind, for a family of 4 data.
A301420 (program): Sums of positive coefficients in generalized Chebyshev polynomials of the first kind, for a family of 5 data.
A301421 (program): Sums of positive coefficients of generalized Chebyshev polynomials of the first kind, for a family of 6 data.
A301424 (program): Sums of positive coefficients of generalized Chebyshev polynomials of the first kind, for a family of 7 data.
A301426 (program): Number of steps required in the worst case for three knights to find the princess in a castle with n rooms arranged in a line (Castle and princess puzzle).
A301438 (program): Number of nX3 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A301451 (program): Numbers congruent to {1, 7} mod 9.
A301454 (program): Number of strictly log-concave permutations of {1,…,n}.
A301458 (program): a(n) = [x^n] Product_{k>=1} 1/(1 - x^(k*(k+1)/2))^n.
A301461 (program): Number of integers less than or equal to n whose largest prime factor is 3.
A301466 (program): a(n) = Sum_{k>=0} binomial(k^3, n)/2^(k+1).
A301468 (program): a(n) = Sum_{k>=0} binomial(k^4, n)/2^(k+1).
A301476 (program): Expansion of (sqrt(8*x^2 - 4*x + 1)*(1 - 4*x))^(-1).
A301477 (program): T(n,k) = Sum_{j=0..n-k} H(n,j)*2^k with H(n,k) = binomial(n,k)* hypergeom([-k/2, 1/2-k/2], [2-k+n], 4), for 0 <= k <= n, triangle read by rows.
A301483 (program): a(n) = floor(a(n-1)/(2^(1/3)-1) with a(1)=1.
A301484 (program): Decimal expansion of J_0(2)/J_1(2) = 1 - 1/(2 - 1/(3 - 1/(4 - …))).
A301500 (program): Number of compositions (ordered partitions) of n into squarefree parts (A005117) such that no two adjacent parts are equal (Carlitz compositions).
A301501 (program): Number of compositions (ordered partitions) of n into prime power parts (A246655) such that no two adjacent parts are equal (Carlitz compositions).
A301502 (program): Number of compositions (ordered partitions) of n into triangular parts (A000217) such that no two adjacent parts are equal (Carlitz compositions).
A301503 (program): Number of compositions (ordered partitions) of n into square parts (A000290) such that no two adjacent parts are equal (Carlitz compositions).
A301516 (program): Numbers n with decimal expansion (d_1, …, d_k) such that the convex hull of the set of points { (i, d_i), i = 1..k } has positive area.
A301523 (program): Integers which can be partitioned into two distinct factorials. 0! and 1! are not considered distinct.
A301560 (program): Matching number of the n-odd graph.
A301571 (program): Number of vertices at distance 2 from a given vertex in the n-Keller graph.
A301587 (program): Positive integers m such that whenever n is in the range of the Euler totient function, so is m*n.
A301593 (program): n can be represented the sum of a(n) distinct factorials. (If there is no such representation, a(n) = 0.)
A301600 (program): a(n) = Primorial(n) / Product_{k prime<n} k.
A301601 (program): Numbers k such that k^6 can be written as a sum of 11 positive 6th powers.
A301616 (program): a(n) = Product_{k=1..n} (k^2+(n-k+1)^2).
A301617 (program): Numbers not divisible by 2, 3 or 5 (A007775) with digital root 1.
A301619 (program): Primes congruent to 65 (mod 192).
A301621 (program): Numbers not divisible by 2, 3 or 5 (A007775) with digital root 2.
A301622 (program): Numbers not divisible by 2, 3 or 5 (A007775) with digital root 4.
A301623 (program): Numbers not divisible by 2, 3 or 5 (A007775) with digital root 5.
A301628 (program): Numbers not divisible by 2, 3 or 5 (A007775) with digital root 7.
A301631 (program): Numerator of population variance of n-th row of Pascal’s triangle.
A301647 (program): a(n) = n^3 - (n mod 2).
A301653 (program): Expansion of x*(1 + 2*x)/((1 - x)*(1 + x)*(1 - x - x^2)).
A301654 (program): Circumference of the n-triangular honeycomb acute knight graph.
A301657 (program): Number of nX3 0..1 arrays with every element equal to 0, 1 or 4 horizontally or vertically adjacent elements, with upper left element zero.
A301658 (program): Number of nX4 0..1 arrays with every element equal to 0, 1 or 4 horizontally or vertically adjacent elements, with upper left element zero.
A301672 (program): Coordination sequence for node of type V2 in “krr” 2-D tiling (or net).
A301673 (program): Partial sums of A301672.
A301676 (program): Coordination sequence for node of type V2 in “krs” 2-D tiling (or net).
A301677 (program): Partial sums of A301676.
A301682 (program): Coordination sequence for node of type V1 in “krg” 2-D tiling (or net).
A301683 (program): Partial sums of A301682.
A301684 (program): Coordination sequence for node of type V2 in “krg” 2-D tiling (or net).
A301685 (program): Partial sums of A301684.
A301686 (program): Coordination sequence for node of type V1 in “krh” 2-D tiling (or net).
A301687 (program): Partial sums of A301686.
A301688 (program): Coordination sequence for node of type V2 in “krh” 2-D tiling (or net).
A301689 (program): Partial sums of A301688.
A301694 (program): Expansion of (1 + 5*x + 4*x^2 + 5*x^3 + x^4)/((1 - x)*(1 - x^3)).
A301695 (program): Expansion of (1 + 5*x + 4*x^2 + 5*x^3 + x^4)/((1 - x)^2*(1 - x^3)).
A301696 (program): Partial sums of A219529.
A301697 (program): Coordination sequence for node of type V2 in “krj” 2-D tiling (or net).
A301698 (program): Partial sums of A301697.
A301699 (program): Generating function = g(g(x)), where g(x) = g.f. of Jacobsthal numbers A001045.
A301702 (program): a(n) = [x^n] Product_{k>=0} 1/(1 - x^(2^k))^n.
A301707 (program): a(n) = n * Sum_{k prime<=n} k.
A301708 (program): Coordination sequence for node of type V1 in “krc” 2-D tiling (or net).
A301709 (program): Partial sums of A301708.
A301710 (program): Coordination sequence for node of type V2 in “krc” 2-D tiling (or net).
A301711 (program): Partial sums of A301710.
A301712 (program): Coordination sequence for node of type V1 in “usm” 2-D tiling (or net).
A301713 (program): Partial sums of A301712.
A301714 (program): Coordination sequence for node of type V2 in “usm” 2-D tiling (or net).
A301715 (program): Partial sums of A301714.
A301716 (program): Coordination sequence for node of type V1 in “kre” 2-D tiling (or net).
A301717 (program): Partial sums of A301716.
A301718 (program): Coordination sequence for node of type V2 in “kre” 2-D tiling (or net).
A301719 (program): Partial sums of A301718.
A301720 (program): Coordination sequence for node of type V1 in “krb” 2-D tiling (or net).
A301721 (program): Partial sums of A301720.
A301722 (program): Coordination sequence for node of type V2 in “krb” 2-D tiling (or net).
A301723 (program): Partial sums of A301722.
A301724 (program): Coordination sequence for node of type V1 in “kra” 2-D tiling (or net).
A301725 (program): Partial sums of A301724.
A301726 (program): Coordination sequence for node of type V2 in “kra” 2-D tiling (or net).
A301727 (program): Partial sums of A301726.
A301728 (program): a(0)=1; thereafter, a(n) = 2n-1 if n == 0 (mod 3), (5n+1)/3 if n == 1 (mod 3), (5n+2)/3 if n == 2 (mod 3).
A301729 (program): a(0)=1; thereafter positive numbers that are congruent to {0, 1, 3, 5} mod 6.
A301730 (program): Expansion of (x^8-x^7+x^6+5*x^5+4*x^4+3*x^3+5*x^2+5*x+1)/(x^6-x^5-x+1).
A301739 (program): The number of trees with 4 nodes labeled by positive integers, where each tree’s label sum is n.
A301741 (program): a(n) = n! * [x^n] exp((n + 1)*x + x^2/2).
A301747 (program): Expansion of Product_{k>=1} (1/(1 - x^k))^(sigma_0(k)^2).
A301752 (program): Clique covering number of the n-triangular grid graph.
A301755 (program): Decimal expansion of 3/8.
A301758 (program): Clique covering number of the n X n fiveleaper graph.
A301764 (program): Number of ways to choose a constant rooted partition of each part in a constant rooted partition of n such that the flattened sequence is also constant.
A301772 (program): Number of odd chordless cycles in the n-antiprism graph.
A301773 (program): Number of odd chordless cycles in the 2n-Moebius ladder graph.
A301774 (program): Number of odd chordless cycles in the (2n+1)-prism graph.
A301775 (program): Number of odd chordless cycles in the (2n+1)-web graph.
A301779 (program): Number of nX3 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.
A301786 (program): Number of nX4 0..1 arrays with every element equal to 0 or 1 horizontally or antidiagonally adjacent elements, with upper left element zero.
A301787 (program): Number of nX5 0..1 arrays with every element equal to 0 or 1 horizontally or antidiagonally adjacent elements, with upper left element zero.
A301788 (program): Number of nX6 0..1 arrays with every element equal to 0 or 1 horizontally or antidiagonally adjacent elements, with upper left element zero.
A301789 (program): Number of n X 7 0..1 arrays with every element equal to 0 or 1 horizontally or antidiagonally adjacent elements, with upper left element zero.
A301791 (program): Number of 2Xn 0..1 arrays with every element equal to 0 or 1 horizontally or antidiagonally adjacent elements, with upper left element zero.
A301792 (program): Number of 3Xn 0..1 arrays with every element equal to 0 or 1 horizontally or antidiagonally adjacent elements, with upper left element zero.
A301797 (program): a(n) = (4^prime(n) - 1)/3.
A301809 (program): Group the natural numbers such that the first group is (1) then (2),(3),(4,5),(6,7,8),… with the n-th group containing F(n) sequential terms where F(n) is the n-th Fibonacci number (A000045(n)). Sequence gives the sum of terms in the n-th group.
A301812 (program): Numbers of the form p^2 - 1 where p is a prime of the form 3*k-1 (A003627).
A301819 (program): Number of nX4 0..1 arrays with every element equal to 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.
A301836 (program): Number of n X 3 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.
A301848 (program): Number of states generated by morphism during inflation stage of paper-folding sequence.
A301849 (program): The Pagoda sequence: a sequence with isolated zeros in number-wall over finite fields.
A301862 (program): Decimal expansion of the probability of intersection of 2 random chords in a circle, where each chord is selected by a random point within the circle and a random direction.
A301875 (program): Expansion of Product_{k>=1} 1/(1 - x^k)^A007434(k).
A301877 (program): Group the natural numbers into groups (1),(2),(3),(4),(5,6),(7,8,9),… so that the n-th group contains N(n) terms, where N(n) is the Narayana’s cows sequence (A000930). Sequence contains the sum of the terms in the n-th group.
A301879 (program): Number of nX3 0..1 arrays with every element equal to 0, 1 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.
A301885 (program): Number of 2Xn 0..1 arrays with every element equal to 0, 1 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.
A301895 (program): a(n) = (number of 1’s in binary expansion of n)^(number of 0’s in binary expansion of n).
A301898 (program): a(n) = (2*n + 1)! if n is even, a(n) = 2*(2*n + 1)! if n is odd.
A301902 (program): Number of n X 3 0..1 arrays with every element equal to 0, 2 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.
A301917 (program): a(n) is the least k for which A301916(n) divides 3^k + 1.
A301919 (program): a(n) is the least value of k for which A301918(n) divides 3^k+3.
A301926 (program): a(n+3) = a(n) + 24*n + 32, a(0)=0, a(1)=3, a(2)=13.
A301941 (program): a(n) is the smallest positive integer k such that n + k divides n^2 + k, or 0 if no such k exists.
A301946 (program): Number of nX3 0..1 arrays with every element equal to 1, 2 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.
A301959 (program): Number of nX3 0..1 arrays with every element equal to 0, 1 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
A301960 (program): Number of nX4 0..1 arrays with every element equal to 0, 1 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
A301965 (program): Number of 3Xn 0..1 arrays with every element equal to 0, 1 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
A301972 (program): a(n) = n*(n^2 - 2*n + 4)*binomial(2*n,n)/((n + 1)*(n + 2)).
A301973 (program): a(n) = (n^2 - 3*n + 6)*binomial(n+2,3)/4.
A301975 (program): Numbers whose abundance is divisible by its number of divisors.
A301977 (program): a(n) is the number of distinct positive numbers whose binary digits appear in order but not necessarily as consecutive digits in the binary representation of n.
A301985 (program): a(n) = n^2 + 2329n + 1697.
A301990 (program): a(n) = 8*(n-1)*a(n-1) + Product_{k=0..n-2} (2*k-1) with a(1) = 1.
A301992 (program): a(n) = 8*(n-2)*(2*n-5)*a(n-1) + ((n-2)/9)*Product_{k=0..n-2} (2*k-3)^2 with a(1) = 0.
A301994 (program): Number of n X 3 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
A301995 (program): Number of nX4 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
A302006 (program): Number of nX4 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.
A302017 (program): Expansion of 1/(1 - x*Product_{k>=1} (1 + x^(2*k-1))).
A302018 (program): Expansion of 1/(1 - x*(1 + theta_3(x))/2), where theta_3() is the Jacobi theta function.
A302019 (program): Expansion of 1/(1 - x*Sum_{k>=0} x^(k^3)).
A302020 (program): Expansion of 1/(1 - x*Product_{k>=1} (1 + x^(2*k))/(1 - x^(2*k-1))).
A302028 (program): Permutation of nonnegative integers: a(0) = 0; for n >= 1, a(n) = 1+A057889(A057889(n)-1), where A057889 is a bijective bit-reverse.
A302033 (program): a(n) = A019565(A003188(n)).
A302047 (program): a(n) = 1 if n = prime(k)*prime(2+k) for some k, otherwise 0.
A302048 (program): a(n) = 1 if n = p^2 for some prime p, otherwise 0. Characteristic function of squares of primes (A001248).
A302049 (program): a(n) = 1 if n = prime(k)*prime(1+k) for some k, otherwise 0.
A302054 (program): a(n) is the sum of prime divisors of A302033(n).
A302056 (program): Numbers k such that the coefficient of x^k in the expansion of Product_{j>=1} (1 - x^j)^4 is zero.
A302058 (program): Numbers that are not square pyramidal numbers.
A302064 (program): Number of nX3 0..1 arrays with every element equal to 0, 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
A302076 (program): Number of nX3 0..1 arrays with every element equal to 0, 1, 3 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
A302092 (program): Product of n-th Bell number and n-th Bell number written backwards.
A302110 (program): Let d be the list of A000005(n) = tau(n) divisors of n. Then a(n) is the largest k such that Sum_{i=1..#d-k} d_i > n.
A302113 (program): a(n) = (4/(2*n-3))*(2*(n-1)*(2*n-1)*a(n-1) + (-1)^n*Product_{k=0..n-1} (2*k+1)) with a(0) = 0.
A302114 (program): a(n) = 8*(n-1)*(2*n-3)*a(n-1) + ((-1)^n)*(n-1)*Product_{k=0..n-3} (2*k+1)^2 with a(0) = 0.
A302115 (program): a(n) = 16*(n-1)*a(n-1) + ((-1)^n)*(4/3)*Product_{k=0..n-1} (2*k-3) with a(0) = 0.
A302116 (program): a(n) = 16*(n-1)*((2*n-3)*a(n-1) + (((-1)^n)/9)*Product_{k=0..n-1} (2*k-3)^2) with a(0) = 0.
A302117 (program): a(n) = 4*(n-1)*a(n-1) - (1/3)*Product_{k=0..n-1} (2*k-3), with a(0) = 0.
A302126 (program): Interleaved Fibonacci and Lucas numbers.
A302129 (program): Number of unlabeled uniform connected hypergraphs of weight n.
A302138 (program): Period of Kronecker symbol modulo n.
A302141 (program): Multiplicative order of 16 mod 2n+1.
A302146 (program): Number of nX3 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
A302156 (program): a(n) = Product_{k=1..n} prime(k+1)^(n-k+1).
A302165 (program): Number of 3Xn 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
A302178 (program): The number of 3D walks of semilength n in a quadrant returning to the origin.
A302180 (program): Number of 3D walks of type aad.
A302181 (program): Number of 3D walks of type abb.
A302183 (program): Number of 3D walks of type abd.
A302184 (program): Number of 3D walks of type abe.
A302186 (program): Number of 3D walks of type ace.
A302188 (program): Number of 3D walks of type bce.
A302189 (program): Hurwitz inverse of squares [1,4,9,16,…].
A302190 (program): Hurwitz logarithm of natural numbers 1,2,3,4,5,…
A302195 (program): Hurwitz inverse of triangular numbers [1,3,6,10,15,…].
A302203 (program): a(n) = floor(sin(n)) + 1.
A302231 (program): Number of pairs of Goldbach partitions of 2n, (p,q) and (s,t) with p < s <= t < q such that s = p + 2 and t = q - 2.
A302234 (program): Expansion of Product_{k>=1} (1 - x^k)/(1 - x^prime(k)).
A302240 (program): Triangle T(n,k) of the numbers of k-matchings in the n-pan graph (0 <= k <= ceiling(n/2).
A302242 (program): Total weight of the n-th multiset multisystem. Totally additive with a(prime(n)) = Omega(n).
A302243 (program): Total weight of the n-th twice-odd-factored multiset partition.
A302245 (program): Maximum remainder of p*q divided by p+q with 0 < p <= q <= n.
A302253 (program): Positions of 3 in A190436.
A302254 (program): Exponent of the group of the Gaussian integers in a reduced system modulo (1+i)^n.
A302255 (program): Total domination number of the n-antiprism graph.
A302266 (program): Number of 2Xn 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
A302279 (program): Number of 2 X n 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
A302286 (program): a(n) = [x^n] 1/(1 - n*x - x/(1 - n*x - x/(1 - n*x - x/(1 - n*x - x/(1 - …))))), a continued fraction.
A302298 (program): Wiener index of the graph of nodes (i,j) of the square lattice such that abs(i) + abs(j) <= n.
A302302 (program): Number of triples (i,j,k) such that i+j+k > 0 with -n <= i,j,k <= n.
A302323 (program): Number of 2Xn 0..1 arrays with every element equal to 0, 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
A302329 (program): a(0)=1, a(1)=61; for n>1, a(n) = 62*a(n-1) - a(n-2).
A302330 (program): a(0)=1, a(1)=97; for n>1, a(n) = 98*a(n-1) - a(n-2).
A302331 (program): a(0)=1, a(1)=141; for n>1, a(n) = 142*a(n-1) - a(n-2).
A302332 (program): a(0)=1, a(1)=193; for n>1, a(n) = 194*a(n-1) - a(n-2).
A302334 (program): A weighted smoothing applied to the primes as a data set: a(n) = floor(A007443(2n-1)/2^(2n-2)), where A007443 is binomial transform of primes.
A302338 (program): a(n) = 3*n + 2^v(n) where v(n) denotes the 2-adic valuation of n.
A302339 (program): Triangle read by rows: T(n,k) = number of linear operators T on an n-dimensional vector space over GF(2) such that U is invariant under T for some given k-dimensional subspace U.
A302341 (program): Triameter of the n X n knight graph.
A302342 (program): Cumulative sums of the bits in the binary representation of Pi.
A302352 (program): a(n) = Sum_{k=0..n} k^4*binomial(2*n-k,n).
A302353 (program): a(n) = Sum_{k=0..n} k^n*binomial(2*n-k,n).
A302354 (program): Expansion of (Sum_{i>=1} x^prime(i))*(Sum_{j>=0} x^(j^3)).
A302368 (program): Number of 2Xn 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
A302390 (program): Triameter of the n-cube-connected cycle graph.
A302391 (program): Number of partitions of 2n into two parts with at least one nonsquarefree part.
A302392 (program): Number of odd parts in the partitions of 3n into 3 parts.
A302393 (program): Number of even parts in the partitions of 3n into 3 parts.
A302397 (program): Expansion of e.g.f. 1/(1 + x*exp(x)).
A302398 (program): a(n) = n! * [x^n] 1/(1 + x*exp(n*x)).
A302402 (program): Total domination number of the n-ladder graph.
A302404 (program): Total domination number of the n-Moebius ladder.
A302405 (program): Total domination number of the n-prism graph.
A302406 (program): Total domination number of the n X n torus grid graph.
A302433 (program): a(n) is the sum of the nonmiddle divisors of n.
A302436 (program): a(n) is the number of ways of writing the binary expansion of n as a concatenation of nonempty substrings with Hamming weight at most 1.
A302445 (program): Triangle read by rows: row n gives primes of form k^2 + n - k for 0 < k < n.
A302451 (program): a(n) = [x^n] Product_{k>=0} (1 + n*x^(2^k)).
A302479 (program): Number of partitions of n into two distinct nonprime parts.
A302480 (program): Number of partitions of n into two parts with the smaller part nonprime and the larger part prime.
A302481 (program): Number of partitions of n into two parts with the smaller part prime and the larger part nonprime.
A302483 (program): Number of FF-equivalence classes of Łukasiewicz paths. Łukasiewicz paths are P-equivalent iff the positions of pattern P are identical in these paths.
A302488 (program): Total domination number of the n X n grid graph.
A302491 (program): Prime numbers of squarefree index.
A302493 (program): Prime numbers of prime-power index.
A302505 (program): Numbers whose prime indices are squarefree and have disjoint prime indices.
A302506 (program): Number of total dominating sets in the n-pan graph.
A302507 (program): a(n) = 4*(3^n-1).
A302521 (program): Odd numbers whose prime indices are squarefree and have disjoint prime indices. Numbers n such that the n-th multiset multisystem is a set partition.
A302534 (program): Squarefree numbers whose prime indices are also squarefree and have disjoint prime indices.
A302537 (program): a(n) = (n^2 + 13*n + 2)/2.
A302542 (program): Expansion of e.g.f. arctan(x)/cos(x) (odd powers only).
A302543 (program): Expansion of e.g.f. arctanh(x)/cos(x) (odd powers only).
A302546 (program): a(n) = Sum_{k = 1…n} 2^binomial(n, k).
A302549 (program): Expansion of Sum_{k>=1} (-1 + Product_{j>=1} 1/(1 - x^(k*j))^j).
A302550 (program): Expansion of Sum_{k>=1} (-1 + Product_{j>=1} (1 + x^(k*j))^j).
A302553 (program): Hyper-4 powers that are not hyper-5 powers.
A302557 (program): Expansion of 1/(2 - Sum_{k>=0} k!*x^k/(1 + x)^(k+1)).
A302560 (program): Partial sums of icosahedral numbers (A006564).
A302562 (program): Partial sums of A092181.
A302563 (program): Numbers whose digital root is equal to their number of digits.
A302564 (program): a(n) is the greatest prime p such that (2*n+1-p)/2 is prime.
A302576 (program): Numbers k such that k/10 + 1 is a square.
A302581 (program): a(n) = n! * [x^n] -exp(-n*x)*log(1 - x).
A302582 (program): a(n) = n! * [x^n] log(1 + x)/(1 - x)^n.
A302583 (program): a(n) = ((n + 1)^n - (n - 1)^n)/2.
A302584 (program): a(n) = n! * [x^n] exp(n*x)/cos(x).
A302585 (program): a(n) = n! * [x^n] exp(n*x)/cosh(x).
A302586 (program): a(n) = n! * [x^n] exp(n*x)*tan(x).
A302587 (program): a(n) = n! * [x^n] exp(n*x)*tanh(x).
A302588 (program): a(n) = a(n-3) + 7*(n-2), a(0)=1, a(1)=2, a(2)=4.
A302603 (program): Number of total dominating sets in the wheel graph on n nodes.
A302604 (program): Number of partitions of n into two parts such that the positive difference of the parts is squarefree.
A302608 (program): a(n) = n! * [x^n] exp(n*x)*arctan(x).
A302609 (program): a(n) = n! * [x^n] exp(n*x)*arctanh(x).
A302611 (program): Expansion of e.g.f. -log(1 - x)*arctanh(x).
A302612 (program): a(n) = (n+1)*(n^4-4*n^3+11*n^2-8*n+12)/12.
A302642 (program): Number of partitions of n into two parts such that the positive difference of the parts is semiprime.
A302643 (program): Number of partitions of n into two parts such that the positive difference of the parts is a squarefree semiprime.
A302647 (program): a(n) = (2*n^2*(n^2 - 3) - (2*n^2 + 1)*(-1)^n + 1)/64.
A302650 (program): Number of minimal total dominating sets in the n-barbell graph.
A302653 (program): Number of minimum total dominating sets in the n-cycle graph.
A302654 (program): Number of minimum total dominating sets in the n-path graph.
A302655 (program): Number of minimal total dominating sets in the n-path graph.
A302658 (program): Number of minimal total dominating sets in the wheel graph on n nodes.
A302660 (program): a(n) = (prime(n) mod 9) + (prime(n) mod 10).
A302675 (program): Number of nX3 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
A302689 (program): a(n) = 4 + 2^n - 4*n.
A302697 (program): Odd numbers whose prime indices are relatively prime. Heinz numbers of integer partitions with no 1’s and with relatively prime parts.
A302707 (program): Number of factors of Chebyshev polynomial S(2*n+1, x) (A049310) over the integers. Factorization is into the minimal integer polynomials C (A187360).
A302709 (program): a(n) = Trinomial(2*n+1, 4) = (1/6)*n*(2*n + 1)*(2*n^2 + 9*n + 1), n >= 0.
A302710 (program): a(n) = trinomial(2*n, 4) = (1/6)*n*(2*n - 1)*(2*n^2 + 7*n - 3).
A302733 (program): a(n) = 4*n*(2*n-1)*a(n-1) + (4/9)*n*Product_{k=0..n} (2*k-3)^2, with a(0) = 0.
A302734 (program): Number of paths in the n-path complement graph.
A302747 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = -2*T(n-1,k) + 3*T(n-2,k-1) for 0 <= k <= floor(n/2); T(n,k)=0 for n or k < 0.
A302748 (program): Half thrice the previous number, rounded down, plus 1, starting with 6.
A302749 (program): Number of maximal matchings in the n-path complement graph.
A302750 (program): Number of maximum matchings in the n-path complement graph.
A302757 (program): a(n) is the smallest number whose greedy representation as a sum of terms of A126684 uses n terms.
A302758 (program): a(n) = n^2*(n*(4*n + 3) + 3*n*(-1)^n - 4)/96.
A302761 (program): Number of total dominating sets in the n-barbell graph.
A302764 (program): Pascal-like triangle with A000012 as the left border and A080956 as the right border.
A302766 (program): a(n) = n*((4*n + 1)*(7*n - 4) + 15*n*(-1)^n)/48.
A302769 (program): a(n) = 2*((2*n-1)*a(n-1) - (n-2)!), with a(1) = 4, n > 1.
A302770 (program): a(n) = (4*n-2)*((n-1)*a(n-1) + ((n-2)!)^2), with a(1) = 0, n > 1.
A302773 (program): Numerators of (3*n + 2)/12.
A302774 (program): a(n) is the position of the first term in A303762 that has prime(n) as one of its prime factors.
A302776 (program): a(1) = 1; for n>1, a(n) = n/(largest Fermi-Dirac factor of n).
A302777 (program): a(n) = 1 if n is of the form p^(2^k) where p is prime and k >= 0, otherwise 0.
A302778 (program): Number of “Fermi-Dirac primes” (A050376) <= n.
A302792 (program): a(1) = 1; for n>1, a(n) = n/(smallest Fermi-Dirac factor of n).
A302794 (program): Permutation of nonnegative integers: a(0) = 0; for n >= 1, a(n) = 1+A193231(A193231(n)-1), where A193231(n) is blue code of n.
A302826 (program): a(n) is number of primes of form k^2 + n - k for 0 < k < n.
A302829 (program): a(n) is the number of lattice points in a Cartesian grid between a circle of radius n and an inscribed square whose vertices lie on the coordinate axes.
A302830 (program): Expansion of (1/(1 - x))*Product_{k>=1} 1/(1 - k*x^k).
A302831 (program): Expansion of (1/(1 - x))*Product_{k>=1} (1 + k*x^k).
A302832 (program): Expansion of (1/(1 - x))*Product_{k>=1} (1 + x^k)^k.
A302833 (program): Expansion of (1/(1 - x))*Product_{k>=1} 1/(1 - x^(k^2)).
A302834 (program): Expansion of (1/(1 - x))*Product_{k>=1} 1/(1 - x^(k^3)).
A302835 (program): Expansion of (1/(1 - x))*Product_{k>=1} 1/(1 - x^(k*(k+1)/2)).
A302852 (program): Permutation of nonnegative integers: a(0) = 0; for n >= 1, a(n) = 1+A225901(A225901(n)-1))
A302855 (program): Expansion of ((1 + 2 * Sum_{k>=1} q^(k^2))^16 - 1) / 32.
A302856 (program): Number of ways of writing n as a sum of 32 squares.
A302857 (program): Expansion of ((1 + 2 * Sum_{k>=1} q^(k^2))^32 - 1) / 64.
A302860 (program): a(n) = [x^n] theta_3(x)^n/(1 - x), where theta_3() is the Jacobi theta function.
A302865 (program): a(n) = (4*n+2)*a(n-1) + (-1)^(n+1)*4*((n-1)!), with a(0) = 8, n > 0.
A302866 (program): a(n) = 2*(n*(2*n+1)*b(n-1) + (-1)^(n-1)*(2*n+1)*((n-1)!)^2), with a(0) = 0, n > 1.
A302906 (program): a(0) = 0; for n > 0, a(n) = a(n-1) + 5*n + 4.
A302909 (program): Determinant of n X n matrix whose main diagonal consists of the first n 5-gonal numbers and all other elements are 1’s.
A302910 (program): Determinant of n X n matrix whose main diagonal consists of the first n 6-gonal numbers and all other elements are 1’s.
A302911 (program): Determinant of n X n matrix whose main diagonal consists of the first n 7-gonal numbers and all other elements are 1’s.
A302912 (program): Determinant of n X n matrix whose main diagonal consists of the first n 8-gonal numbers and all other elements are 1’s.
A302913 (program): Determinant of n X n matrix whose main diagonal consists of the first n 9-gonal numbers and all other elements are 1’s.
A302914 (program): Determinant of n X n matrix whose main diagonal consists of the first n 10-gonal numbers and all other elements are 1’s.
A302918 (program): Number of nonequivalent minimal total dominating sets in the n-cycle graph up to rotation.
A302930 (program): Maximum number of 6’s possible in an infinite Minesweeper grid with n mines.
A302931 (program): Maximum number of 7’s possible in an infinite Minesweeper grid with n mines.
A302938 (program): Lexicographically first sequence of distinct terms such that the sum of any two terms is not a term of the sequence, and the sum of any two digits is not a digit of the sequence.
A302941 (program): Number of total dominating sets in the 2n-crossed prism graph.
A302942 (program): a(n) = (2^n-1)^2*(2^n + 2).
A302944 (program): a(n) = 4*((2*n-1)*a(n-1) + (-1)^n*(n-2)!), with a(1) = 8, n > 1.
A302945 (program): a(n) = 4*(2*n+1)(n*a(n-1) + (-1)^(n-1)*((n-1)!)^2), with a(0) = 0, n > 0.
A302946 (program): Number of minimal (and minimum) total dominating sets in the 2n-crossed prism graph.
A302974 (program): a(n) = numerator of tau(n)^n / n^tau(n).
A302975 (program): a(n) = denominator of tau(n)^n / n^tau(n).
A302976 (program): a(n) = tau(n)^n mod n^tau(n).
A302978 (program): Chromatic invariant of the n-path complement graph.
A302980 (program): Size of the smallest square Minesweeper grid that allows each number from 0 to 8 to appear exactly n times.
A302989 (program): a(n) = n^n + n*n + n.
A302999 (program): a(n) = Product_{k=1..n} (Fibonacci(k+2) - 1).
A303003 (program): Total domination number of the n X n queen graph.
A303005 (program): Number of dominating sets in the n-pan graph.
A303007 (program): Expansion of (1-240*x)^(1/8).
A303051 (program): Number of partitions of n into two distinct parts (p,q) such that p, q and p+q are all squarefree.
A303052 (program): Total area of all squares with squarefree side length |s - t|, such that n = s + t, and s < t, where s and t are positive integers.
A303054 (program): Number of minimum total dominating sets in the n-ladder graph.
A303055 (program): Expansion of (1-504*x)^(1/12).
A303070 (program): a(n) = [x^n] (1/(1 - x))*Product_{k>=1} 1/(1 - x^k)^n.
A303071 (program): a(n) = [x^n] (1/(1 - x))*Product_{k>=1} (1 + x^k)^n.
A303072 (program): Number of minimal total dominating sets in the n-ladder graph.
A303073 (program): L.g.f.: log(1 + Sum_{k>=1} prime(k)*x^k) = Sum_{n>=1} a(n)*x^n/n.
A303074 (program): Expansion of Product_{n>=1} (1 + (9*x)^n)^(1/3).
A303108 (program): a(n) = (2*n-1)*a(n-1) - (n-2)!, with a(1) = 2, n > 1.
A303109 (program): a(n) = n*(2*n-1)*a(n-1) + ((n-1)!)^2, with a(0) = 0, n > 0.
A303120 (program): Total area of all rectangles of size p X q such that p + q = n^2 and p <= q.
A303124 (program): Expansion of Product_{n>=1} (1 + (16*x)^n)^(1/4).
A303125 (program): Expansion of Product_{n>=1} (1 + (25*x)^n)^(1/5).
A303130 (program): Expansion of Product_{n>=1} (1 + (9*x)^n)^(-1/3).
A303131 (program): Expansion of Product_{n>=1} (1 + (16*x)^n)^(-1/4).
A303132 (program): Expansion of Product_{n>=1} (1 + (25*x)^n)^(-1/5).
A303135 (program): Expansion of Product_{n>=1} (1 - (16*x)^n)^(-1/4).
A303152 (program): Expansion of Product_{n>=1} (1 - (9*x)^n)^(1/3).
A303165 (program): Sum of the squarefree differences |q-p| of the parts in the partitions of n into two distinct parts (p,q) where p < q.
A303205 (program): Number of rectangles with squarefree area and dimensions p and |q-p| such that n = p + q and p < q.
A303211 (program): Number of minimum total dominating sets in the n X n rook graph.
A303212 (program): Number of minimum total dominating sets in the n X n rook complement graph.
A303221 (program): Total area of all rectangles with dimensions p and p + q such that p and q are both squarefree, n = p + q and p <= q.
A303222 (program): Total volume of all rectangular prisms with dimensions p, q and (p + q)/2 such that p and q are squarefree, n = p + q and p <= q.
A303223 (program): Sum of the perimeters of the family of rectangles with dimensions p and q such that |q - p| is prime, n = p + q and p < q.
A303224 (program): a(0)=0, a(1)=1; for n>1, a(n) = n*a(n-1) - 3*a(n-2).
A303226 (program): Number of minimal total dominating sets in the n-gear graph.
A303259 (program): Number of ordered rooted trees with n non-root nodes such that the maximal outdegree equals ceiling(n/2).
A303260 (program): Determinant of n X n matrix A[i,j] = (j - i - 1 mod n) + [i=j], i.e., the circulant having (n, 0, 1, …, n-2) as first row.
A303269 (program): Sum of squares of odd digits minus sum of squares of even digits of n.
A303272 (program): Multiples of 1852.
A303273 (program): Array T(n,k) = binomial(n, 2) + k*n + 1 read by antidiagonals.
A303276 (program): Decimal expansion of the value of 1 US gallon in liters.
A303277 (program): If n = Product (p_j^k_j) then a(n) = (Sum (k_j))^(Sum (p_j)).
A303278 (program): If n = Product_j p_j^k_j where the p_j are distinct primes then a(n) = (Product_j k_j)^(Product_j p_j).
A303279 (program): Expansion of (1/(1 - x)^2) * Sum_{p prime, k>=1} x^(p^k)/(1 - x^(p^k)).
A303281 (program): Expansion of (x/(1 - x)) * (d/dx) Sum_{p prime, k>=1} x^(p^k)/(1 - x^(p^k)).
A303295 (program): a(n) is the maximum water retention of a height-3 length-n number parallelogram with maximum water area.
A303296 (program): Digital roots of fourth powers A000583.
A303298 (program): Generalized 21-gonal (or icosihenagonal) numbers: m*(19*m - 17)/2 with m = 0, +1, -1, +2, -2, +3, -3, …
A303299 (program): Generalized 22-gonal (or icosidigonal) numbers: m*(10*m - 9) with m = 0, +1, -1, +2, -2, +3, -3, …
A303302 (program): a(n) = 34*n^2.
A303303 (program): Generalized 23-gonal (or icositrigonal) numbers: m*(21*m - 19)/2 with m = 0, +1, -1, +2, -2, +3, -3, …
A303304 (program): Generalized 25-gonal (or icosipentagonal) numbers: m*(23*m - 21)/2 with m = 0, +1, -1, +2, -2, +3, -3, …
A303305 (program): Generalized 17-gonal (or heptadecagonal) numbers: m*(15*m - 13)/2 with m = 0, +1, -1, +2, -2, +3, -3, …
A303306 (program): Expansion of Product_{n>=1} ((1 - (2*x)^n)/(1 + (2*x)^n))^(1/2).
A303307 (program): Expansion of Product_{n>=1} ((1 + (2*x)^n)/(1 - (2*x)^n))^(1/2).
A303331 (program): a(n) is the minimum size of a square integer grid allowing all triples of n points to form triangles of different areas.
A303336 (program): Number of rectangles with semiprime area and dimensions p,q where n = p+q and p <= q.
A303337 (program): Number of rectangles with semiprime area and dimensions (p) X (p+q) such that n = p+q, p < q.
A303342 (program): Expansion of Product_{k>=1} ((1 + (9*x)^k) / (1 - (9*x)^k))^(1/3).
A303361 (program): Expansion of Product_{n>=1} ((1 + (4*x)^n)/(1 - (4*x)^n))^(1/4).
A303365 (program): Number of integer partitions of the n-th squarefree number using squarefree numbers.
A303370 (program): Least integer k such that (k+1)^k >= n.
A303381 (program): Expansion of Product_{n>=1} ((1 + (8*x)^n)/(1 - (8*x)^n))^(1/8).
A303383 (program): Total volume of all cubes with side length q such that n = p + q and p <= q.
A303384 (program): Total area of all rectangles with dimensions s and t where s | t, n = s + t and s <= t.
A303385 (program): Total area of all rectangles with dimensions s and t such that s | t, n = s + t and s < t.
A303394 (program): Expansion of Product_{n>=1} ((1 - (4*x)^n)/(1 + (4*x)^n))^(1/4).
A303395 (program): Expansion of Product_{n>=1} ((1 - (8*x)^n)/(1 + (8*x)^n))^(1/8).
A303416 (program): Number of n X 3 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
A303427 (program): Interleaved Lucas and Fibonacci numbers.
A303449 (program): Denominator of (2*n+1)/(2^(2*n+1)-1).
A303479 (program): Total volume of the family of rectangular prisms with dimensions p, q, and |q - p| where p divides q, n = p + q and p < q.
A303481 (program): Total volume of the family of rectangular prisms with dimensions p, q and p + q where p divides q, n = p + q and p < q.
A303486 (program): a(n) = n! * [x^n] 1/(1 - 3*x)^(n/3).
A303487 (program): a(n) = n! * [x^n] 1/(1 - 4*x)^(n/4).
A303488 (program): a(n) = n! * [x^n] 1/(1 - 5*x)^(n/5).
A303489 (program): Square array A(n,k), n >= 0, k >= 1, read by antidiagonals: A(n,k) = n! * [x^n] 1/(1 - k*x)^(n/k).
A303500 (program): The smallest positive even integer that can be written with n digits in base 3/2.
A303502 (program): Integers k such that the digits of k together with a single supplementary digit could be reordered to form a base-10 palindrome number.
A303505 (program): Number of odd chordless cycles in the n-triangular (Johnson) graph.
A303506 (program): G.f.: Sum_{n>=1} (-1)^(n-1) * x^(n^2)/(1 - x^n)^n.
A303534 (program): Amount by which n exceeds the largest binary palindrome less than or equal to n.
A303536 (program): Number of terms in greedy partition of n into binary palindromes.
A303537 (program): Expansion of ((1 + 4*x)/(1 - 4*x))^(1/4).
A303538 (program): Expansion of ((1 + 8*x)/(1 - 8*x))^(1/8).
A303554 (program): Union of the prime powers (p^k, p prime, k >= 0) and numbers that are the product of 2 or more distinct primes.
A303555 (program): Triangle read by rows: T(n,k) = 2^(n-k)*prime(k)#, 1 <= k <= n, where prime(k)# is the product of first k primes.
A303557 (program): a(0) = 1; a(n) = 2^(n-1)*prime(n)#, where prime(n)# is the product of first n primes.
A303565 (program): a(n) = [x^n] (Sum_{k=0..n} k!*x^k)/(Sum_{k=0..n} k!*(-x)^k).
A303566 (program): a(n) = [x^n] (Sum_{k=0..n} (k+1)!*x^k)/(Sum_{k=0..n} (k+1)!*(-x)^k).
A303577 (program): Break up the list of values of the divisor function d(k) into nondecreasing runs; sequence gives lengths of successive runs.
A303578 (program): List of starts of nondecreasing runs of values of d(n) (the divisor function A000005(n)).
A303581 (program): Add i (>= 0) to the i-th block of terms in the Thue-Morse sequence A010060.
A303586 (program): Number of partitions of n that contain no isolated singletons.
A303587 (program): Number of partitions of n that contain exactly one isolated singleton.
A303588 (program): Number of partitions of n that contain exactly two isolated singletons.
A303589 (program): Floor(n*alpha)-1, where alpha is the number with continued fraction expansion [1;1,2,3,4,5,…] (A247844).
A303590 (program): Floor(n*beta)-1, where 1/alpha+1/beta=1, alpha being the number with continued fraction expansion [1;1,2,3,4,5,…] (A247844).
A303602 (program): a(n) = Sum_{k = 0..n} k*binomial(2*n+1, k).
A303603 (program): a(n) is the maximum distance between primes in Goldbach partitions of 2n, or 2n if there are no Goldbach partitions of 2n.
A303609 (program): a(n) = 2*n^3 + 9*n^2 + 9*n.
A303611 (program): a(n) = (-1 - (-2)^(n-2)) mod 2^n.
A303617 (program): Decimal expansion of Sum_{k >= 0} 2^(2*k+1)/Product_{i = 0..k} (2*i+1).
A303631 (program): Number of nX3 0..1 arrays with every element unequal to 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.
A303644 (program): a(n) is the number of lattice points in a Cartesian grid between a square of side length 2*n, centered at the origin, and its inscribed circle. The sides of the square are parallel to the coordinate axes.
A303647 (program): a(n) = ceiling(a(n-1)/(2^(1/3)-1)+1), a(1)=1.
A303649 (program): Number of involutions of [n] having exactly one peak.
A303658 (program): Decimal expansion of the alternating sum of the reciprocals of the triangular numbers.
A303663 (program): Expansion of (1/(1 - x))*Product_{k>=1} (1 - x^prime(k))/(1 - x^k).
A303665 (program): Expansion of 1/((1 - x)*(1 - Sum_{k>=1} x^prime(k))).
A303666 (program): Expansion of 1/((1 - x)*(1 - Sum_{k>=0} x^(2^k))).
A303667 (program): Expansion of 2/((1 - x)*(3 - theta_3(x))), where theta_3() is the Jacobi theta function.
A303668 (program): Expansion of 1/((1 - x)*(2 - theta_2(sqrt(x))/(2*x^(1/8)))), where theta_2() is the Jacobi theta function.
A303677 (program): Number of nX2 0..1 arrays with every element unequal to 0, 1 or 3 king-move adjacent elements, with upper left element zero.
A303692 (program): a(n) = n^2*(2*n - 3 - (-1)^n)/4.
A303699 (program): Triangle read by rows in which row n gives coefficients of polynomial f_n(x) of degree less than n that satisfies Integral_{x=0..1} g(t - x) * f_n(x) dx = g(t) for any polynomial g(x) of degree less than n.
A303700 (program): Triangle read by rows in which row n gives coefficients of polynomial f_n(x)/(n+1) of degree less than n that satisfies Integral_{x=0..1} g(t - x) * f_n(x) dx = g(t) for any polynomial g(x) of degree less than n.
A303707 (program): Number of factorizations of n using elements of A007916 (numbers that are not perfect powers).
A303714 (program): Number of nX3 0..1 arrays with every element unequal to 0, 1 or 5 king-move adjacent elements, with upper left element zero.
A303730 (program): Number of noncrossing path sets on n nodes with each path having at least two nodes.
A303735 (program): a(n) is the metric dimension of the n-dimensional hypercube.
A303739 (program): Numbers k such that 9*k^2 + 3*k + 1 (A082040) is prime.
A303740 (program): Primes of the form 9*k^2 + 3*k + 1 (A082040).
A303749 (program): First differences of A302774; Number of terms in A303762 that have prime(n) as their largest prime factor (A006530).
A303760 (program): Divisor-or-multiple permutation of squarefree numbers: a(0) = 1, and for n >= 1, a(n) is either the least divisor of a(n-1) not already present in the sequence, or (if all divisors already used), a(n-1) * {the least prime p such that p does not divide a(n-1) and p*a(n-1) is not already present}.
A303767 (program): May code of n: a(0) = 0, and for n > 0, if n = 2^k, a(n) = n + a(n-1), otherwise, when n = 2^k + r (with 0 < r < 2^k), then a(n) = 2^k + a(r-1); see comments for equivalent alternative descriptions.
A303768 (program): Inverse permutation to A303767.
A303781 (program): a(2) = 1; for n <> 2, a(n) = gcd(n, A000005(n)), where A000005(n) = number of divisors of n.
A303787 (program): a(n) = Sum_{i=0..m} d(i)*4^i, where Sum_{i=0..m} d(i)*5^i is the base-5 representation of n.
A303788 (program): a(n) = Sum_{i=0..m} d(i)*5^i, where Sum_{i=0..m} d(i)*6^i is the base-6 representation of n.
A303789 (program): a(n) = Sum_{i=0..m} d(i)*6^i, where Sum_{i=0..m} d(i)*7^i is the base-7 representation of n.
A303802 (program): Number of n X 2 0..1 arrays with every element unequal to 0, 1, 3 or 4 king-move adjacent elements, with upper left element zero.
A303812 (program): Generalized 28-gonal (or icosioctagonal) numbers: m*(13*m - 12) with m = 0, +1, -1, +2, -2, +3, -3, …
A303813 (program): Generalized 19-gonal (or enneadecagonal) numbers: m*(17*m - 15)/2 with m = 0, +1, -1, +2, -2, +3, -3, …
A303814 (program): Generalized 24-gonal (or icositetragonal) numbers: m*(11*m - 10) with m = 0, +1, -1, +2, -2, +3, -3, …
A303815 (program): Generalized 29-gonal (or icosienneagonal) numbers: m*(27*m - 25)/2 with m = 0, +1, -1, +2, -2, +3, -3, …
A303816 (program): Decimal expansion of 2700/17.
A303817 (program): Decimal expansion of 360/17.
A303834 (program): Number of total dominating sets in the n-gear graph.
A303846 (program): Total domination number of the n-halved cube graph.
A303872 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = -T(n-1,k) + 2 T(n-1,k-1) for k = 0,1,…,n; T(n,k)=0 for n or k < 0.
A303873 (program): Total area of the family of squares with side length n such that n = p + q, p divides q and p < q.
A303878 (program): Consider the representation of some integer (>1) as the sum of distinct unit fraction (<1). The sum of these denominators is least.
A303901 (program): Triangle read by rows of coefficients in expansion of (3-2x)^n, where n is a nonnegative integer.
A303902 (program): Expansion of (1 - x^2)*Product_{k>=2} (1 + x^k)^k.
A303904 (program): Expansion of (1/(1 - x))*Product_{k>=1} (1 + x^(k^3)).
A303906 (program): Expansion of Product_{k>=2} 1/(1 - x^(k*(k+1)/2)).
A303908 (program): Expansion of 1/(2 + x - theta_2(sqrt(x))/(2*x^(1/8))), where theta_2() is the Jacobi theta function.
A303909 (program): Expansion of 2*(1 - x)/(3 - theta_3(x)), where theta_3() is the Jacobi theta function.
A303915 (program): a(n) = lambda(n)*E(n), where lambda(n) = A008836(n) and E(n) = A005361(n).
A303916 (program): Constant term in the expansion of (Sum_{k=0..n} k*(x^k + x^(-k)))^3.
A303921 (program): Main diagonal of triangle A303920: a(n) = A303920(n,n) for n>=0.
A303941 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = 3*T(n-1,k) - 2*T(n-2,k-1) for k = 0..floor(n/2); T(n,k)=0 for n or k < 0. Triangle of coefficients of Fermat polynomials.
A303943 (program): Expansion of 1/(1 - x/(1 - 1^2*x/(1 - 2^2*x/(1 - 3^2*x/(1 - 4^2*x/(1 - …)))))), a continued fraction.
A303952 (program): a(n) is the number of monic polynomials P(z) of degree n over the complex numbers such that P(z) divides P(z^2).
A303963 (program): Number of nX2 0..1 arrays with every element unequal to 0, 1, 3 or 5 king-move adjacent elements, with upper left element zero.
A303972 (program): Total volume of all cubes with side length n which can be split such that n = p + q, p divides q and p < q.
A303973 (program): Total volume of all rectangular prisms with dimensions (p,p,q) such that n = p + q, p divides q and p < q.
A303975 (program): Number of distinct prime factors in the product of prime indices of n.
A303977 (program): Number of inequivalent solutions to problem discussed in A286874.
A303986 (program): Triangle of derivatives of the Niven polynomials evaluated at 0.
A303987 (program): Triangle read by rows: T(n, k) = (binomial(n,k)*binomial(n+k,k))^2 = A063007(n, k)^2, for n >= 0, k = 0..n.
A303990 (program): Triangle, read by rows: n^k * k^n, for n >= 1 and k = 1..n.
A303991 (program): Row sums of triangle A303990.
A304001 (program): Number of permutations of [n] whose up-down signature has a nonnegative total sum.
A304004 (program): Number of n X 2 0..1 arrays with every element unequal to 0, 2, 3 or 5 king-move adjacent elements, with upper left element zero.
A304011 (program): Number of same-sized pairs of subsets of set of n numbers that might have the same sum.
A304023 (program): a(n) is the smallest integer with n digits in base 3/2 expressed in base 3/2.
A304024 (program): a(n) is the largest integer with n digits in base 3/2.
A304025 (program): a(n) is the largest integer that can be written with n digits in base 3/2.
A304035 (program): a(n) is the number of lattice points inside a square bounded by the lines x=-n/sqrt(2), x=n/sqrt(2), y=-n/sqrt(2), y=n/sqrt(2).
A304037 (program): If n = Product (p_j^k_j) then a(n) = Sum (pi(p_j)^k_j), where pi() = A000720.
A304041 (program): Number of inequivalent solutions to problem in A054961.
A304066 (program): a(n) = Sum_{k=1..n} k*floor(n/prime(k)).
A304091 (program): a(n) is the number of the proper divisors of n that are Lucas numbers (A000032, with 2 included).
A304092 (program): Number of Lucas numbers (A000032: 2, 1, 3, 4, 7, 11, …) dividing n.
A304093 (program): a(n) is the number of the proper divisors of n that are Lucas numbers (A000204, with 2 excluded).
A304094 (program): Number of Lucas numbers (A000204: 1, 3, 4, 7, 11, … excluding 2) that divide n
A304095 (program): a(n) is the number of the proper divisors of n that are Lucas numbers larger than 3 (4, 7, 11, 18, …).
A304096 (program): Number of Lucas numbers larger than 3 (4, 7, 11, 18, …) that divide n.
A304100 (program): a(n) = A003602(A048679(n)).
A304126 (program): a(n) = (6*n)!*(4*n)!/((2*n)!*(3*n)!*(5*n)!).
A304128 (program): Number of nX3 0..1 arrays with every element unequal to 0, 1, 3 or 6 king-move adjacent elements, with upper left element zero.
A304157 (program): a(n) is the first Zagreb index of the linear phenylene G[n], defined pictorially in the Darafsheh reference.
A304158 (program): a(n) is the second Zagreb index of the linear phenylene G[n], defined pictorially in the Darafsheh reference (Fig. 3).
A304159 (program): a(n) = 2*n^3 - 4*n^2 + 6*n - 2 (n>=1).
A304160 (program): a(n) = n^4 - 3*n^3 + 6*n^2 - 5*n + 2 (n >= 1).
A304161 (program): a(n) = 2*n^3 - 4*n^2 + 10*n - 2 (n>=1).
A304162 (program): a(n) = n^4 - 3*n^3 + 9*n^2 - 7*n + 5 (n>=1).
A304163 (program): a(n) = 9*n^2 - 3*n + 1 with n>0.
A304164 (program): a(n) = 27*n^2 - 21*n + 6 (n>=1).
A304165 (program): a(n) = 324*n^2 - 336*n + 102 (n >= 1).
A304166 (program): a(n) = 972*n^2 - 1224*n + 414 with n > 0.
A304167 (program): a(n) = 3^n - 2^(n-1) + 2 (n>=1).
A304168 (program): a(n) = 2*3^n - 2^(n-1) (n>=1).
A304169 (program): a(n) = 16*3^n + 2^(n+1) - 26 (n>=1).
A304170 (program): a(n) = 32*3^n + 18*2^n - 116 (n>=1).
A304171 (program): a(n) = 87*2^n - 38 (n>=0).
A304172 (program): a(n) = 99*2^n - 45 (n>=0).
A304180 (program): If n = Product (p_j^k_j) then a(n) = max{p_j}^max{k_j}.
A304182 (program): Number of primitive inequivalent mirror-symmetric sublattices of rectangular lattice of index n.
A304183 (program): Number of primitive inequivalent oblique sublattices of rectangular lattice of index n.
A304205 (program): Numbers k such that 24*k + 6 is congruent to 0 (mod 49).
A304207 (program): a(1)=17; for n>1, a(n) = (a(n-1)^2 - 1)/2 if n is even, a(n-1) + 1 if n is odd.
A304214 (program): Smallest k > 0 such that 2^(p-1) (mod p^2) < k*p for p = prime(n).
A304216 (program): Number of nX3 0..1 arrays with every element unequal to 0, 1, 3 or 8 king-move adjacent elements, with upper left element zero.
A304225 (program): Number of nX3 0..1 arrays with every element unequal to 0, 1, 2 or 7 king-move adjacent elements, with upper left element zero.
A304236 (program): Triangle T(n,k) = T(n-1,k) + 3*T(n-2,k-1) for k = 0..floor(n/2), with T(0,0) = 1, T(n,k) = 0 for n or k < 0, read by rows.
A304249 (program): Triangle T(n,k) = 3*T(n-1,k) + T(n-2,k-1) for k = 0..floor(n/2), with T(0,0) = 1 and T(n,k) = 0 for n < 0 or k < 0, read by rows.
A304251 (program): If n = Product (p_j^k_j) then a(n) = Sum (prime(p_j)^k_j).
A304252 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = T(n-1,k) + 6*T(n-2,k-1) for k = 0..floor(n/2); T(n,k)=0 for n or k < 0.
A304255 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = 6*T(n-1,k) + T(n-2,k-1) for k = 0..floor(n/2); T(n,k)=0 for n or k < 0.
A304265 (program): Number of nX3 0..1 arrays with every element unequal to 0, 1, 5 or 8 king-move adjacent elements, with upper left element zero.
A304272 (program): The largest even integer that can be written with n digits in base 3/2.
A304273 (program): The concatenation of the first n terms is the smallest positive even number with n digits when written in base 3/2 (cf. A024629).
A304274 (program): The concatenation of the first n elements is the largest positive even number with n digits when written in base 3/2.
A304275 (program): Sum_{k=1..n} gcd(k,n) / cos(Pi*k/n)^2 for odd n.
A304293 (program): Number of points of a Koblitz curve E: y^2 + x*y = x^3 + a*x^2 + 1 over a field with 2^n elements.
A304326 (program): Number of ways to write n as a product of a number that is not a perfect power and a squarefree number.
A304327 (program): Number of ways to write n as a product of a perfect power and a squarefree number.
A304330 (program): T(n, k) = Sum_{j=0..k} (-1)^j*binomial(2*k, j)*(k - j)^(2*n), triangle read by rows, n >= 0 and 0 <= k <= n.
A304335 (program): Sum of digits of (2*n-1)!!.
A304337 (program): Lexicographically earliest fractal-like sequence such that the erasure of all pairs of contiguous terms of opposite parity leaves the sequence unchanged.
A304349 (program): Number of nX2 0..1 arrays with every element unequal to 0, 1, 3, 4 or 5 king-move adjacent elements, with upper left element zero.
A304357 (program): Antidiagonal sums of the first quadrant of array A(k,m) = F_k(m), F_k(m) being the k-th Fibonacci polynomial evaluated at m.
A304364 (program): Numbers k such that A304362(k) = Sum_{d|k, d = 1 or not a perfect power} mu(k/d) = 0.
A304366 (program): Numbers n with additive persistence = 1.
A304367 (program): Numbers n with additive persistence = 2.
A304368 (program): Numbers n with additive persistence = 3.
A304370 (program): Number of function calls of the first kind required to compute ack(3,n), where ack denotes the Ackermann function.
A304371 (program): Number of function calls of the second kind required to compute ack(3,n), where ack denotes the Ackermann function.
A304373 (program): Numbers n with additive persistence = 4.
A304374 (program): a(n) = 9*n^2 + 21*n - 6 (n>=1).
A304375 (program): a(n) = 27*n^2/2 + 45*n/2 - 12 (n>=1).
A304376 (program): a(n) = 60*2^n - 48 (n>=1).
A304377 (program): a(n) = 102*2^n - 96 (n>=1).
A304378 (program): a(n) = 4*(n - 1)*(16*n - 23) for n >= 1.
A304379 (program): a(n) = 256n^2 - 828n + 656 (n>=1).
A304380 (program): a(n) = 36*n^2 - 4*n (n>=1).
A304381 (program): a(n) = 54*n^2 - 26*n + 4 (n>=1).
A304383 (program): a(n) = 36*2^n - 5 (n>=1).
A304384 (program): a(n) = 168*2^n - 26 (n>=1).
A304385 (program): a(n) = 192*2^n - 31 (n>=1).
A304387 (program): a(n) = 27*2^n - 5.
A304388 (program): a(n) = 144*2^n - 20 (n>=1).
A304389 (program): a(n) = 126*2^n - 22 (n>=1).
A304404 (program): If n = Product (p_j^k_j) then a(n) = Product (n/p_j^k_j).
A304407 (program): If n = Product (p_j^k_j) then a(n) = Product ((p_j - 1)*k_j).
A304408 (program): If n = Product (p_j^k_j) then a(n) = Product ((p_j - 1)*(k_j + 1)).
A304409 (program): If n = Product (p_j^k_j) then a(n) = Product (p_j*(k_j + 1)).
A304411 (program): If n = Product (p_j^k_j) then a(n) = Product ((p_j + 1)*k_j).
A304412 (program): If n = Product (p_j^k_j) then a(n) = Product ((p_j + 1)*(k_j + 1)).
A304421 (program): Number of nX2 0..1 arrays with every element unequal to 1, 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.
A304438 (program): Coefficient of s(y) in p(|y|), where s is Schur functions, p is power-sum symmetric functions, y is the integer partition with Heinz number n, and |y| = Sum y_i.
A304439 (program): Add to n the sum of its odd digits minus the sum of its even digits.
A304440 (program): Add to n the sum of its even digits minus the sum of its odd digits.
A304443 (program): Coefficient of x^n in Product_{k>=1} (1+x^k)^(2*n).
A304444 (program): Coefficient of x^n in Product_{k>=1} 1/(1-x^k)^(2*n).
A304445 (program): Coefficient of x^n in Product_{k>=1} (1+x^k)^(n^2).
A304446 (program): Coefficient of x^n in Product_{k>=1} 1/(1-x^k)^(n^2).
A304447 (program): Coefficient of x^n in Product_{k>=1} ((1+x^k)/(1-x^k))^(2*n).
A304448 (program): Coefficient of x^n in Product_{k>=1} ((1+x^k)/(1-x^k))^(n^2).
A304449 (program): Numbers that are either squarefree or a perfect power.
A304453 (program): An expanded binary notation for n: the normal binary expansion for n is expanded by mapping each 1 to 10 and retaining the existing 0’s.
A304455 (program): Number of steps in the reduction to a multiset of size 1 of the multiset of prime factors of n, obtained by repeatedly taking the multiset of multiplicities.
A304459 (program): Coefficient of x^n in Product_{k>=1} (1+x^k)^(n^3).
A304461 (program): Coefficient of x^n in Product_{k>=1} ((1+x^k)/(1-x^k))^(n^3).
A304480 (program): a(n) is the least m such that lambda(k) >= n for all k >= m where lambda is A002322, the Carmichael lambda function.
A304483 (program): a(n) = pi(n)*pi(2n), where pi is A000720: the prime counting function.
A304484 (program): a(n) = A033270(n)*A033270(2n), where A033270 counts the odd primes.
A304487 (program): a(n) = (3 + 2*n - 3*n^2 + 4*n^3 - 3*((-1 + n) mod 2))/6.
A304491 (program): Last or deepest exponent in the power-tower for n.
A304497 (program): Solution (a(n)) of the system of complementary equations defined in Comments.
A304498 (program): Solution (b(n)) of the system of complementary equations defined in Comments.
A304501 (program): Solution (b(n)) of the system of complementary equations defined in Comments.
A304503 (program): a(n) = 3*(n+1)*(9*n+4).
A304504 (program): a(n) = 3*(3*n+1)*(9*n+8)/2.
A304505 (program): a(n) = 4*(n+1)*(9*n+4).
A304506 (program): a(n) = 2*(3*n+1)*(9*n+8).
A304507 (program): a(n) = 5*(n+1)*(9*n+4).
A304508 (program): a(n) = 5*(3*n+1)*(9*n+8)/2 (n>=0).
A304509 (program): a(n) = 63*2^n - 39 (n>=1).
A304510 (program): a(n) = 69*2^n - 42 (n>=1).
A304511 (program): a(n) = 318*2^n - 186 (n>=1).
A304512 (program): a(n) = 366*2^n - 204 (n >= 1).
A304513 (program): a(n) = 57*2^(n-1) - 38 (n >= 1).
A304514 (program): a(n) = 33*2^n - 45 (n>=1).
A304515 (program): a(n) = 159*2^n - 222 (n>=1).
A304516 (program): a(n) = 192*2^n - 273 (n>=1).
A304517 (program): a(n) = 16*2^n - 11 (n>=1).
A304518 (program): a(n) = 68*2^n - 50 (n>=1).
A304519 (program): a(n) = 72*2^n -56 (n>=1).
A304569 (program): Triangle read by rows: T(n,k) = 1 if k | n^e with e >= 0, otherwise T(n,k) = 0 (1 <= k <= n).
A304573 (program): Number of non-perfect powers (A007916) less than n and relatively prime to n.
A304575 (program): a(n) = Sum_{d|n} #{k < d, k squarefree and relatively prime to d}.
A304577 (program): Period 21: repeat (0,0,0,0,1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1).
A304578 (program): a(n) = (n^2 + 1) * 5^n + (n^2 + 2) * 3^n.
A304579 (program): a(n) = (n^2 + 1)*(n^2 + 2).
A304583 (program): Period length 18: repeat 1,8,3,6,5,4,7,2,9,0,9,2,7,4,5,6,3,8.
A304584 (program): A linear mapping a(n) = x + d*n of pairs of nonnegative integers (x,d), where the pairs are enumerated by antidiagonals.
A304585 (program): A linear mapping a(n) = x + d*n of pairs of nonnegative integers (x,d), where the pairs are enumerated by meandering antidiagonals.
A304588 (program): Length of shortest prefix of the Thue-Morse word (A010060) such that some length-n block appears twice.
A304605 (program): a(n) = 48*2^n + 26 (n>=1).
A304606 (program): a(n) = 54*2^n + 28 (n >= 1).
A304607 (program): a(n) = 252*2^n + 140 (n>=1).
A304608 (program): a(n) = 288*2^n + 178 (n >= 1).
A304609 (program): a(n) = 114*n - 20.
A304610 (program): a(n) = 157*n - 40 (n>=1).
A304611 (program): a(n) = 155*n - 38.
A304612 (program): a(n) = 75*2^n - 38.
A304613 (program): a(n) = 87*2^n - 45.
A304614 (program): a(n) = 420*2^n - 222.
A304615 (program): a(n) = 507*2^n - 273.
A304616 (program): a(n) = 81*n^2 - 69*n + 24.
A304617 (program): a(n) = 324*n^2 - 564*n + 321 (n>=1).
A304618 (program): a(n) = 108*n^2 - 228*n + 114 (n>=2).
A304619 (program): a(n) = 324*n^2 - 804*n + 468 (n>=2).
A304620 (program): Expansion of (1/(1 - x)) * Sum_{k>=0} x^(2*k) / Product_{j=1..2*k} (1 - x^j).
A304625 (program): a(n) = [x^n] Product_{k>=1} ((1 - x^(n*k))/(1 - x^k))^n.
A304626 (program): a(n) = [x^n] Product_{k>=1} ((1 + x^k)/(1 + x^(n*k)))^n.
A304627 (program): a(n) = [x^n] Product_{k>=1} (1 + x^k)*(1 - x^(n*k))/((1 - x^k)*(1 + x^(n*k))).
A304630 (program): Expansion of (1/(1 - x))*Product_{k>=1} (1 - x^(3*k))/(1 - x^k).
A304631 (program): Expansion of (1/(1 - x))*Product_{k>=1} (1 + x^(2*k-1)).
A304633 (program): Expansion of 2/((1 - x)*(3 + 2*x - theta_3(x))), where theta_3() is the Jacobi theta function.
A304634 (program): Numbers n with prime omicron 2, meaning A304465(n) = 2.
A304635 (program): Triangle T(n,j) read by rows: the number of j-faces in the hypersimplicial decomposition of the unit cube of n dimensions.
A304651 (program): Number of coprime pairs (x,y) with x^2 + y^2 <= n.
A304653 (program): a(n) = (-1)^Omega(n) if n is not a perfect power > 1, and 0 otherwise.
A304656 (program): Decimal expansion of Pi*sqrt(3).
A304659 (program): a(n) = n*(n + 1)*(16*n - 1)/6.
A304660 (program): A run-length describing inverse to A181819. The multiplicity of prime(k) in a(n) is the k-th smallest prime index of n, which is A112798(n,k).
A304685 (program): a(n) = A000699(n) (mod 3).
A304690 (program): Primes p > 5 such that no polygonal number P_s(k) (with s >= 3, k >= 5 ) is equal to p - 1.
A304710 (program): Number of partitions of 2n whose Ferrers-Young diagram cannot be tiled with dominoes.
A304723 (program): a(n) = 5^(n-1)*(3^n - 1)/2.
A304725 (program): a(n) = n^4 + 8*n^3 + 20*n^2 + 16*n + 2.
A304726 (program): a(n) = n^4 + 4*n^2 + 3.
A304727 (program): a(0) = 0, a(1) = 1, a(n) = n! * a(n-1) + a(n-2).
A304747 (program): May code shown in binary: a(n) = A007088(A303767(n)).
A304759 (program): Binary encoding of 1-digits in ternary representation of A048673(n).
A304809 (program): Solution (a(n)) of the complementary equation a(n) = b(2n) + b(4n) ; see Comments.
A304810 (program): Solution (b(n)) of the complementary equation a(n) = b(2n) + b(4n) ; see Comments.
A304817 (program): Number of divisors of n that are either 1 or not a perfect power.
A304819 (program): Dirichlet convolution of r with zeta, where r(n) = (-1)^Omega(n) if n is 1 or not a perfect power and r(n) = 0 otherwise.
A304824 (program): Convolution of central binomial coefficients and partition numbers.
A304825 (program): Sum of binomial(Y(2,p), 2) over the partitions p of n, where Y(2,p) is the number of part sizes with multiplicity 2 or greater in p.
A304826 (program): a(n) = 32*7^n/21 - 8/3, n>=1.
A304827 (program): a(n) = 52*7^n/21 - 16/3 (n>=1).
A304828 (program): a(n) = 344*7^n/21 - 128/3 (n>=1).
A304829 (program): a(n) = 4024*7^n/147 - 256/3 (n >= 2).
A304830 (program): a(n) = 102*2^n - 108 (n>=1).
A304831 (program): a(n) = 123*2^n - 135.
A304832 (program): a(n) = n^2 + 25*n - 34 (n >=2).
A304833 (program): a(n) = 3*n^2 + 38*n - 76 (n>=2).
A304834 (program): a(n) = 36*n^2 - 8*n - 2 (n >=1).
A304835 (program): a(n) = 108*n^2 - 104*n + 20 (n>=1).
A304836 (program): a(n) = 27*n^2 - 51*n + 24, n>=1.
A304837 (program): a(n) = 6*(n - 1)*(81*n - 104) for n >= 1.
A304838 (program): a(n) = 1944*n^2 - 5016*n + 3138 (n >= 1).
A304839 (program): a(n) = 61*n - 38 (n>=1).
A304840 (program): a(n) = 52*n - 2 (n>=1).
A304841 (program): a(n) = 67*n - 10 (n>=1).
A304866 (program): E.g.f. A(x) satisfies: Sum_{n>=0} (n*x - A(x))^n / n! = 1.
A304870 (program): L.g.f.: log(Product_{k>=1} (1 + x^k)^(k^k)) = Sum_{n>=1} a(n)*x^n/n.
A304887 (program): Number of non-isomorphic blobs of weight n.
A304902 (program): Let (P,<) be the strict partial order on the subsets of {1,2,…,n} ordered by their cardinality. Then a(n) is the number of paths of any length from {} to {1,2,…,n}.
A304906 (program): L.g.f.: log(Product_{k>=1} (1 + x^(k^3))) = Sum_{n>=1} a(n)*x^n/n.
A304907 (program): Expansion of x * (d/dx) 1/(1 - Sum_{k>=1} x^k/(1 + x^k)).
A304908 (program): Expansion of x * (d/dx) 1/(1 - Sum_{k>=0} x^(2^k)).
A304909 (program): Expansion of x * (d/dx) Product_{k>=0} 1/(1 - x^(2^k)).
A304915 (program): Expansion of ((1 + 16*x)/(1 - 16*x))^(1/16).
A304917 (program): a(n) = prime(n)^n - primorial(n - 1).
A304933 (program): a(0) = 0, a(1) = 1 and a(n) = 2*a(n-1)/(n-1) + 16*a(n-2) for n > 1.
A304934 (program): a(0) = 0, a(1) = 1 and a(n) = 2*a(n-1)/(n-1) + 64*a(n-2) for n > 1.
A304936 (program): a(n) = [x^n] 1/(1 - n*x/(1 - x - n*x/(1 - x - n*x/(1 - x - n*x/(1 - x - n*x/(1 - …)))))), a continued fraction.
A304939 (program): Number of labeled nonempty hypertrees (connected antichains with no cycles) spanning some subset of {1,…,n} without singleton edges.
A304940 (program): Expansion of ((1 + 4*x)/(1 - 4*x))^(1/2).
A304941 (program): Expansion of ((1 + 4*x)/(1 - 4*x))^(3/4).
A304944 (program): a(0) = 0, a(1) = 1 and a(n) = 6*a(n-1)/(n-1) + 16*a(n-2) for n > 1.
A304960 (program): Number of business cards required to build an origami level n Mosely snowflake sponge.
A304963 (program): Expansion of 1/(1 - Sum_{i>=1, j>=1, k>=1} x^(i*j*k)).
A304964 (program): Expansion of 1/(1 - Sum_{i>=1, j>=1, k>=1, l>=1} x^(i*j*k*l)).
A304968 (program): Number of labeled hypertrees spanning some subset of {1,…,n}, with singleton edges allowed.
A304973 (program): Number of achiral color patterns (set partitions) for a row or loop of length n using exactly 3 colors (sets).
A304974 (program): Number of achiral color patterns (set partitions) for a row or loop of length n using exactly 4 colors (sets).
A304979 (program): The nonzero terms of the cogrowth sequence of (Z/5Z)^*2 = <x|x^5=1> * <y|y^5=1> with respect to the generating set {(x,1), (1,y)}.
A304980 (program): a(n) = 4^n * (1 - 4^n) * Bernoulli(2*n) / (2*n) + EulerE(2*n).
A304990 (program): Squares of number of partitions into distinct parts.
A304991 (program): a(n) = A000041(n) * A000009(n).
A304993 (program): a(n) = n*(n + 1)*(7*n + 5)/6.
A304995 (program): Expansion of (1 + 6*x + 6*x^2 + 6*x^3 + x^4 + 6*x^5)/((1 - x)*(1 + x^4)).
A305004 (program): Number of labeled hypertrees (connected acyclic antichains) spanning some subset of {1,…,n} without singleton edges.
A305006 (program): Numerators of coefficients in expansion of Sum_{k>=1} x^k/(k*(1 + x^k)).
A305007 (program): Denominators of coefficients in expansion of Sum_{k>=1} x^k/(k*(1 + x^k)).
A305029 (program): Period 10 sequence [ 0, 2, 2, 2, 2, 0, -2, -2, -2, -2, …] except a(0) = 1.
A305031 (program): Expansion of ((1 + 2*x)/(1 - 2*x))^(3/2).
A305032 (program): a(0) = 0, a(1) = 1 and a(n) = 6*a(n-1)/(n-1) + 4*a(n-2) for n > 1.
A305035 (program): Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 6 or 7 king-move adjacent elements, with upper left element zero.
A305049 (program): Expansion of 1/(1 - Sum_{k>=1} tau_k(k)*x^k), where tau_k(k) = number of ordered k-factorizations of k (A163767).
A305051 (program): a(n) = n! * [x^n] exp(exp(x) - 1)/(1 - x)^n.
A305060 (program): a(n) = 18*2^n + 10.
A305061 (program): a(n) = 20*2^n + 14.
A305062 (program): a(n) = 96*2^n + 80.
A305063 (program): a(n) = 110*2^n + 118.
A305064 (program): a(n) = 42*2^n - 20.
A305065 (program): a(n) = 48*2^n - 24.
A305066 (program): a(n) = 234*2^n - 120.
A305067 (program): a(n) = 282*2^n - 150.
A305068 (program): a(n) = 54*n - 18 (n>=1).
A305069 (program): a(n) = 117*n - 72 (n>=1).
A305070 (program): a(n) = 378*n^2 - 54*n (n>=1).
A305071 (program): a(n) = 972*n^2 - 270*n (n>=1).
A305072 (program): a(n) = 144*n^2 - 24*n (n>=1).
A305073 (program): a(n) = 288*n^2 - 96*n (n>=1).
A305074 (program): a(n) = 20*n - 8 (n>=1).
A305075 (program): a(n) = 32*n - 24 (n>=1).
A305077 (program): Partial sums of absolute values of A076191.
A305078 (program): Heinz numbers of connected integer partitions.
A305098 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = -T(n-1,k) + 2 T(n-2,k-1) for k = 0..floor(n/2); T(n,k)=0 for n or k < 0.
A305117 (program): a(n) = A304651(n)/4.
A305127 (program): Expansion of e.g.f. Product_{k>=1} 1/(1 - x^k)^(sigma(k)/k), where sigma(k) is the sum of the divisors of k.
A305133 (program): E.g.f.: (1-x) / (exp(-x) - x).
A305151 (program): a(n) = (2n+1) - A294673(n), the amount by which A294673 is less than the maximum possible for n.
A305152 (program): Expansion of Sum_{k>0} x^(k^2) / (1 + x^k).
A305153 (program): a(n) = 30*2^n + 12.
A305154 (program): a(n) = 36*2^n + 9.
A305155 (program): a(n) = 28*2^n - 15.
A305156 (program): a(n) = 136*2^n - 78 (n>=0).
A305157 (program): a(n) = 164*2^n - 99.
A305158 (program): a(n) = 21*2^n - 15.
A305159 (program): a(n) = 102*2^n - 78.
A305160 (program): a(n) = 123*2^n - 99.
A305163 (program): a(n) = 24*2^n - 18.
A305164 (program): a(n) = 28*2^n - 22.
A305165 (program): a(n) = 136*2^n - 112.
A305166 (program): a(n) = 164*2^n - 140.
A305168 (program): Number of non-isomorphic graphs on 4n vertices whose edges are the union of two n-edge matchings.
A305185 (program): a(n) minimizes the maximum norm of elements in a complete residue system of Eisenstein integers modulo n.
A305189 (program): a(n) = 1*2 + 3 + 4*5 + 6 + 7*8 + 9 + 10*11 + 12 + … + (up to n).
A305215 (program): a(n) is the number of numbers whose largest prime power factor equals A000961(n).
A305233 (program): Smallest k such that binomial(k, floor(k/2)) >= n.
A305237 (program): Numbers n such that n, n+1 and n+2 all have primitive roots.
A305258 (program): List of y-coordinates of a point moving in a smooth counterclockwise spiral rotated by Pi/4.
A305259 (program): x-coordinates of a point moving counterclockwise on concentric squares of grid points rotated by Pi/4 with side length m*sqrt(2), m=1,2,…, with jump to next square on the positive x-axis.
A305261 (program): a(n) = 120*2^n - 108.
A305262 (program): a(n) = 140*2^n - 127.
A305263 (program): a(n) = 680*2^n - 622.
A305264 (program): a(n) = 836*2^n - 771.
A305265 (program): a(n) = 12*2^n + 62.
A305266 (program): a(n) = 14*2^n + 73.
A305267 (program): a(n) = 68*2^n + 358.
A305268 (program): a(n) = 82*2^n + 440.
A305269 (program): a(n) = 120*2^n - 95.
A305270 (program): a(n) = 140*2^n - 112.
A305271 (program): a(n) = 680*2^n - 548.
A305272 (program): a(n) = 836*2^n - 676.
A305276 (program): Expansion of e.g.f. 1/(1 + LambertW(-x/(1 - x))).
A305290 (program): Numbers k such that 4*k + 1 is a perfect cube, sorted by absolute values.
A305291 (program): Numbers k such that 4*k + 3 is a perfect cube, sorted by absolute values.
A305292 (program): Numbers k such that k-1 is a square and k+1 is a triangular number.
A305295 (program): Binary encoding of 1-digits in ternary representation of A245612(n).
A305304 (program): Expansion of e.g.f. 1/(1 + LambertW(-x/(1 + x))).
A305306 (program): Expansion of e.g.f. 1/(1 + log(1 - x)/(1 - x)).
A305307 (program): Expansion of e.g.f. 1/(1 - log(1 + x)/(1 - x)).
A305315 (program): a(n) = sqrt(5*b(n)^2 - 4), with b(n) = A134493(n) = Fibonacci(6*n+1), n >= 0.
A305316 (program): a(n) = sqrt(5*b(n)^2 - 4) with b(n) = Fibonacci(6*n+5) = A134497(n).
A305318 (program): Numbers k such that A071866(k)=3.
A305322 (program): Repdigit numbers that are divisible by 3.
A305326 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+1) + 1/(x+2) = 1.
A305327 (program): Decimal expansion of the middle x such that 1/x + 1/(x+1) + 1/(x+2) = 1.
A305328 (program): Decimal expansion of the least x such that 1/x + 1/(x+1) + 1/(x+2) = 1 (negated).
A305373 (program): a(n) = A003144(n) + A003145(n).
A305374 (program): First differences of A140101.
A305377 (program): Tribonacci representation of primes, written in base 10.
A305378 (program): Tribonacci representation of 2n+1, written in base 10.
A305379 (program): Tribonacci representation of primes, written in base 2.
A305385 (program): Indicator function of A140100.
A305386 (program): Indicator function of A140101.
A305387 (program): Indicator function of A140102.
A305388 (program): Indicator function of A140103.
A305390 (program): A ternary tribonacci sequence: define the morphism f: 1 -> 2, 2 -> 3, 3 -> 1,2,3; let S[k] be result of applying f k times to 1, for k =- 0,1,2,…; sequence gives limit S[3k+1] as k -> oo.
A305391 (program): A ternary tribonacci sequence: define the morphism f: 1 -> 2, 2 -> 3, 3 -> 1,2,3; let S[k] be result of applying f k times to 1, for k =- 0,1,2,…; sequence gives limit S[3k+2] as k -> oo.
A305392 (program): First differences of A140100.
A305393 (program): First differences of A140102.
A305394 (program): First differences of A140103.
A305395 (program): Records in A073053.
A305396 (program): Records in A171797.
A305397 (program): Largest diameter of a lattice polygon.
A305401 (program): Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where A(n,k) is Sum_{j=0..floor(n/2)} ((n-j)!/j!)*binomial(n-j,j)*k^(n-2*j).
A305404 (program): Expansion of Sum_{k>=0} (2*k - 1)!!*x^k/Product_{j=1..k} (1 - j*x).
A305412 (program): a(n) = F(n)*F(n+1) + F(n+2), where F = A000045 (Fibonacci numbers).
A305413 (program): a(n) = Fibonacci(11*n)/89.
A305426 (program): Number of proper divisors of n of the form 2^k - 1 for k >= 1.
A305435 (program): Number of proper divisors of n of the form 2^k + 1 for k >= 0.
A305436 (program): Number of divisors of n of the form 2^k + 1 for k >= 0.
A305444 (program): a(n) = Product_{p is odd and prime and divisor of n} (p - 2).
A305459 (program): a(0) = 1, a(1) = 3, a(n) = 3*n*a(n-1) + a(n-2).
A305460 (program): a(0) = 1, a(1) = 3, a(n) = 3*n*a(n-1) + 2*a(n-2).
A305461 (program): The number of one-digit numbers, k, in base n such that k^2 and k^3 end in the same digit.
A305465 (program): a(n) = Sum_{k=0..floor(n/2)} ((n-k)!/k!)*binomial(n-k,k)*n^(n-2*k).
A305466 (program): Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where A(n,k) is Sum_{j=0..floor(n/2)} ((n-j)!/j!)*binomial(n-j,j)*k^(n-2*j)*(-1)^j.
A305467 (program): a(n) = Sum_{k=0..floor(n/2)} ((n-k)!/k!)*binomial(n-k,k)*n^(n-2*k)*(-1)^k.
A305471 (program): a(0) = 1, a(1) = 3, a(n) = 3*n*a(n-1) - a(n-2).
A305472 (program): a(0) = 1, a(1) = 3, a(n) = 3*n*a(n-1) - 2*a(n-2).
A305490 (program): Fixed point of the morphism 0->120, 1->110, 2->100.
A305491 (program): a(n) = numerator(r(n)) where r(n) = (((1/2)*(sqrt(3) + 1))^n - ((1/2)*(sqrt(3) - 1))^n * cos(Pi*n))/sqrt(3).
A305492 (program): a(n) = ((1 + y)^n - (1 - y)^n)/y with y = sqrt(8).
A305495 (program): Positions of 0 in the fixed point of the morphism 0->120, 1->110, 2->100 applied to 1 (as in A305490).
A305496 (program): Positions of 2 in the fixed point of the morphism 0->120, 1->110, 2->100 applied to 1 (as in A305490).
A305497 (program): The largest positive even integer that can be represented with n digits in base 3/2.
A305498 (program): The smallest positive even integer that can be represented with n digits in base 3/2.
A305499 (program): Square array A(n,k), n > 0 and k > 0, read by antidiagonals, with initial values A(1,k) = k and recurrence equations A(n+1,k) = A(n,k) for 0 < k <= n and A(n+1,k) = A(n,k) - A000035(n+k) for 0 < n < k.
A305503 (program): Largest cardinality of subsets A of {0,1,…,n-1} with |A + A| > |A - A|.
A305532 (program): Expansion of 1/(1 - x/(1 - 1*2*x/(1 - 2*3*x/(1 - 3*4*x/(1 - 4*5*x/(1 - …)))))), a continued fraction.
A305533 (program): Expansion of 1/(1 - x/(1 - 1*x/(1 - 3*x/(1 - 6*x/(1 - 10*x/(1 - … - (k*(k + 1)/2)*x/(1 - …))))))), a continued fraction.
A305535 (program): Expansion of 1/(1 - x/(1 - 2*x/(1 - 2*x/(1 - 4*x/(1 - 4*x/(1 - 6*x/(1 - 6*x/(1 - …)))))))), a continued fraction.
A305536 (program): Expansion of 1/(1 - x/(1 - x - 1*x/(1 - x - 2*x/(1 - x - 3*x/(1 - x - 4*x/(1 - …)))))), a continued fraction.
A305539 (program): a(n) is a generalized pentagonal number such that 2*a(n) is also a generalized pentagonal number.
A305548 (program): a(n) = 27*n.
A305549 (program): Crystal ball sequence for the lattice C_6.
A305559 (program): [0, -1, -1] together with A000290.
A305561 (program): Expansion of 2*x*(1 - 2*x)/(1 + 2*x - 8*x^2 - sqrt(1 - 4*x^2)).
A305573 (program): Number of (1,1) pairs occurring at depth 3n of the Fibonacci tree.
A305574 (program): Number of primitive (1,1) pairs in the Fibonacci tree at depth 3n.
A305581 (program): Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 7 or 8 king-move adjacent elements, with upper left element zero.
A305608 (program): Expansion of 1/2 * (((1 + 4*x)/(1 - 4*x))^(1/4) - 1).
A305609 (program): Expansion of 1/2 * (((1 + 8*x)/(1 - 8*x))^(1/8) - 1).
A305612 (program): Expansion of 1/2 * (((1 + 2*x)/(1 - 2*x))^(3/2) - 1).
A305615 (program): Next term is the largest earlier term that would not create a repetition of an earlier subsequence of length 2, if such a number exists; otherwise it is the smallest nonnegative number not yet in the sequence.
A305623 (program): Number of chiral pairs of rows of n colors with exactly 3 different colors.
A305624 (program): Number of chiral pairs of rows of n colors with exactly 4 different colors.
A305625 (program): Number of chiral pairs of rows of n colors with exactly 5 different colors.
A305626 (program): Number of chiral pairs of rows of n colors with exactly 6 different colors.
A305627 (program): a(n) = (2^n / n!) * (2^1 - 1) * (2^2 - 1) * … * (2^n - 1).
A305630 (program): Expansion of Product_{r = 1 or not a perfect power} 1/(1 - x^r).
A305634 (program): Even numbers that are not perfect powers.
A305635 (program): 1 and odd numbers that are not perfect powers.
A305650 (program): a(n) = -1/3 * (u^n-1)*(v^n-1) with u = 1+sqrt(3), v = 1-sqrt(3).
A305658 (program): Powers of 3 in base 3/2.
A305659 (program): Powers of 2 in base 3/2.
A305693 (program): a(n) = binomial(4*n, 2*n) - 4*n*binomial(2*n-2, n-1).
A305714 (program): Number of finite sequences of positive integers of length n that are polydivisible and strictly pandigital.
A305716 (program): Order of rowmotion on the divisor lattice for n.
A305721 (program): Crystal ball sequence for the lattice C_7.
A305722 (program): Crystal ball sequence for the lattice C_8.
A305723 (program): Crystal ball sequence for the lattice C_9.
A305724 (program): Crystal ball sequence for the lattice C_10.
A305728 (program): Numbers of the form 216*p^3, where p is a Pythagorean prime (A002144).
A305730 (program): a(n) is the total displacement of all letters in all permutations of n letters with no fixed points.
A305739 (program): a(n) = n!*T(n) - 1, where T(n) is the n-th triangular number.
A305747 (program): Let c be the n-th composite number; then a(n) is the smallest divisor of c such that a(n) >= sqrt(c).
A305748 (program): Distance of a prime number from the average of the next two consecutive prime numbers.
A305750 (program): Number of achiral color patterns (set partitions) in a row or cycle of length n with 4 or fewer colors (subsets).
A305753 (program): A base-3/2 sorted Fibonacci sequence that starts with a(0) = 0 and a(1) = 1. The terms are interpreted as numbers written in base 3/2. To get a(n+2), add a(n) and a(n+1), write the result in base 3/2 and sort the “digits” into increasing order, omitting all zeros.
A305762 (program): a(0) = 24, a(n) = 2^(max(0, min(3, p - 1))) * 3^(max(0, min(1, q - 1))) where n = 2^p * 3^q * 5^r * … .
A305800 (program): Filter sequence for a(prime) = constant sequences.
A305801 (program): Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = 0 if n is an odd prime, with f(n) = n for all other n.
A305818 (program): Number of proper divisors d of n such that 2d+1 is a prime.
A305833 (program): Triangle read by rows: T(0,0)=1; T(n,k) = 4*T(n-1,k) + T(n-2,k-1) for k = 0..floor(n/2); T(n,k)=0 for n or k < 0.
A305834 (program): Triangle read by rows: T(0,0)= 1; T(n,k)= T(n-1,k) + 4*T(n-2,k-1) for k = 0..floor(n/2); T(n,k)=0 for n or k < 0.
A305837 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = 5*T(n-1,k) + T(n-2,k-1) for k = 0..floor(n/2); T(n,k)=0 for n or k < 0.
A305838 (program): Triangle read by rows: T(0,0)= 1; T(n,k)= T(n-1,k) + 5*T(n-2,k-1) for k = 0..floor(n/2); T(n,k)=0 for n or k < 0.
A305841 (program): Product_{n>=1} (1 + x^n)^a(n) = g.f. of A001970 (partitions of partitions).
A305847 (program): Solution a() of the complementary equation a(n) + b(n) = 5*n, where a(1) = 1. See Comments.
A305848 (program): Solution b() of the complementary equation a(n) + b(n) = 5n, where a(1) = 1. See Comments.
A305849 (program): Positions of 2 in the difference sequence of A305847.
A305859 (program): Numbers that are congruent to {1, 3, 11} mod 12.
A305861 (program): a(n) = 32*3^n - 2^(n+5) + 5.
A305862 (program): a(n) = 384*4^n - 576*3^n + 220*2^n - 14.
A305877 (program): Numbers in base 3 reversed.
A305878 (program): For any number n >= 0: apply the map 0 -> “0”, 1 -> “01”, 2 -> “011” to the ternary representation of n and interpret the result as a binary string.
A305880 (program): A base 3/2 reverse sorted Fibonacci sequence that starts with terms 2211 and 2211. The terms are interpreted as numbers written in base 3/2. To get a(n+2), add a(n) and a(n+1), write the result in base 3/2 and sort the digits into decreasing order, omitting all zeros.
A305889 (program): a(n) = 3*a(n-2) + a(n-4), a(0)=a(1)=0, a(2)=1, a(3)=2.
A305890 (program): Filter sequence for all such sequences b, for which b(A176997(k)) = constant for all k > 1, where A176997 is the union of odd primes and Fermat pseudoprimes.
A305897 (program): Lexicographically earliest infinite sequence such that a(i) = a(j) => A348717(i) = A348717(j), for all i, j >= 1.
A305900 (program): Filter sequence for a(primes > 3) = constant sequences.
A305930 (program): Number of digits ‘0’ in 3^n (in base 10).
A305931 (program): Powers of 3 having at least one digit ‘0’ in their decimal representation.
A305980 (program): Filter sequence for a(Squarefree numbers > 1) = constant sequences.
A305989 (program): Numbers in binary reversed.
A305990 (program): E.g.f.: (1+x) / (exp(-x) - x).
A305991 (program): Expansion of (1-27*x)^(1/9).
A305994 (program): a(n) = ((A000265(3*n + 1) + 1) mod 4)/2.
A306006 (program): Number of non-isomorphic intersecting set-systems of weight n.
A306007 (program): Number of non-isomorphic intersecting antichains of weight n.
A306008 (program): Number of non-isomorphic intersecting set-systems of weight n with no singletons.
A306020 (program): a(n) is the number of set-systems using nonempty subsets of {1,…,n} in which all sets have the same size.
A306021 (program): Number of set-systems spanning {1,…,n} in which all sets have the same size.
A306038 (program): Expansion of e.g.f. (1 + x)/(1 - log(1 + x)).
A306069 (program): Partial sums of A286324: Sum_{k=1..n} bd(k) where bd(k) is the number of bi-unitary divisors of k.
A306102 (program): Numbers that are the difference of two positive squares in at least two ways.
A306103 (program): Numbers that are the difference of two positive squares in at least three ways.
A306104 (program): Numbers that are the difference of two positive squares in at least four ways.
A306145 (program): Expansion of (1/(1 - x)) * Sum_{k>=0} x^(2*k+1) / Product_{j=1..2*k+1} (1 - x^j).
A306150 (program): Row sums of A306015.
A306156 (program): Inverse Weigh transform of 2^n.
A306157 (program): Inverse Weigh transform of 3^n.
A306158 (program): Inverse Weigh transform of 4^n.
A306159 (program): Inverse Weigh transform of 5^n.
A306174 (program): a(n) = (prime(n)^6 - 1)/504.
A306183 (program): The coefficients of x in the reduction of x^2 -> x + 1 for the polynomial p(n,x) = Product_{k=1..n} (x+k).
A306184 (program): a(n) = (2n+1)!! mod (2n)!! where k!! = A006882(k).
A306185 (program): a(n) = (2n+1)!! + (2n)!! where k!! = A006882(k).
A306190 (program): a(n) = p^2 - p - 1 where p = prime(n), the n-th prime.
A306192 (program): a(n) = (n - 1)*prime(n + 1).
A306193 (program): a(n) = Product_{k=0..n} (1 + n!/k!).
A306198 (program): Multiplicative with a(p^e) = p^(e-1)*(p^2 - p - 1).
A306199 (program): Numbers k having the property that tau(4*k) < tau(3*k) where tau = A000005.
A306210 (program): T(n,k) = binomial(n + k, n) - binomial(n + floor(k/2), n) + 1, square array read by descending antidiagonals (n >= 0, k >= 0).
A306237 (program): a(n) = primorial prime(n)#/prime(n - 1).
A306246 (program): a(1) = 1, a(2) = 2, and for any n > 2, a(n) = o(n-1) + o(n-2) where o(k) is the number of occurrences of a(k) among a(1), …, a(k).
A306251 (program): Ordinal transform of A306246.
A306258 (program): a(n) = floor(n^2/4)*n!.
A306262 (program): Difference between maximum and minimum sum of products of successive pairs in permutations of [n].
A306264 (program): a(n) = 1 + d*a(n/d); a(1)=0. If n has only one prime divisor, then d=n, otherwise d is the greatest proper unitary divisor of n.
A306266 (program): Number of reciprocally monophyletic coalescence sequences for 2n lineages, n each in 2 species.
A306276 (program): a(0) = a(1) = a(2) = a(3) = 1; thereafter a(n) = a(n-2) + a(n-3) + a(n-4).
A306277 (program): Numbers congruent to 1 or 8 mod 10.
A306278 (program): Numbers congruent to 2 or 11 mod 14.
A306279 (program): Numbers congruent to 3 or 18 mod 22.
A306280 (program): a(n) = Sum_{k=0..n} binomial(n,k)*binomial(n^2+k,k).
A306285 (program): Numbers congruent to 4 or 21 mod 26.
A306286 (program): a(n) is the product of the positions of the ones in the binary expansion of n (the most significant bit having position 1).
A306289 (program): The smallest prime factor of numbers greater than 1 and coprime to 6.
A306290 (program): a(n) = 1/(Integral_{x=0..1} (x^3 - x^4)^n dx).
A306292 (program): Number of asymmetric Dyck paths of semilength n.
A306295 (program): Maximal number of coalescent histories among non-matching pairs consisting of a caterpillar gene tree and a caterpillar species tree with n+2 leaves.
A306298 (program): Numbers k such that k^2-1 is divisible by exactly two distinct primes.
A306300 (program): Discriminant D of real quadratic number field Q(sqrt(D)) associated with fundamental discriminant d = A003658(n).
A306307 (program): Numbers that are divisible by the number of their nontrivial divisors.
A306312 (program): Number of terms of the set of divisors of n that are not the product of any other two distinct divisors.
A306323 (program): Break up the Kolakoski sequence A000002 into pieces by inserting a space between every pair of equal terms; sequence gives lengths of successive pieces.
A306326 (program): The q-analogs T(q; n,k) of the rascal-triangle, here q = 2.
A306329 (program): If n = Product (p_j^k_j) then a(n) = Product (p_j)^Sum (k_j).
A306331 (program): Numbers congruent to 6 or 31 mod 38.
A306344 (program): The q-analogs T(q; n,k) of the rascal-triangle, here q = 3.
A306354 (program): a(n) = gcd(n, A101337(n)).
A306357 (program): Number of nonempty subsets of {1, …, n} containing no three cyclically successive elements.
A306358 (program): Odd numbers which are the sum of two squares in two or more different ways.
A306362 (program): Prime numbers in A317298.
A306366 (program): For any sequence s of positive integers without infinitely many consecutive equal terms, let T(s) be the sequence obtained by replacing each run, say of k consecutive t’s, with a run of t consecutive k’s; this sequence corresponds to T(K) (where K denotes the Kolakoski sequence A000002).
A306367 (program): a(n) = numerator of (n^2 + 2)/(n + 2).
A306368 (program): a(n) = numerator of (n + 3)*(n + 4)/((n + 1)*(n + 2)).
A306369 (program): a(n) = A000010(n) + A069359(n).
A306376 (program): Sum of the 2 X 2 minors in the n X n Pascal matrix.
A306377 (program): a(n) = n^(n+1) - Sum_{k=1..n-1} k^(k+1).
A306379 (program): Dirichlet convolution of psi(n) with itself.
A306380 (program): Squares of the form 5*k^2 + 5.
A306388 (program): a(n) is a decimal number k having a length n binary expansion which encodes, from left to right at digit j, the coprimality (0) or non-coprimality (1) of j to n, for 1 < j <= n, except for the first digit, which is always 1.
A306389 (program): Partial sums of (k-th digit of decimal expansion of Pi multiplied by (-1)^k).
A306390 (program): Size of one subtree in the unlabeled binary rooted tree shape of size n whose leaf-labeled trees have the largest number of coalescence sequences.
A306392 (program): a(n) = 2^n with 1’s and 2’s swapped.
A306408 (program): a(n) = Sum_{d|n} (-1)^omega(n/d) * d.
A306409 (program): a(n) = -Sum_{0<=i<j<=n} (-1)^(i+j) * (i+j)!/(i!*j!).
A306411 (program): a(n) = phi(n^6) = n^5*phi(n).
A306412 (program): a(n) = phi(n^8) = n^7*phi(n).
A306419 (program): Number of set partitions of {1, …, n} whose blocks are all singletons and pairs, not including {1, n} or {i, i + 1} for any i.
A306423 (program): Number of coalescent histories for pseudocaterpillar gene trees G and caterpillar species trees S.
A306433 (program): Number of partitions of n into 2 distinct prime powers (not including 1).
A306436 (program): The nonnegative integers, the ten successive digits being swapped by pairs.
A306444 (program): A(n,k) = binomial((2*k+1)*n+2, k*n+1)/((2*k+1)*n+2), square array A(n,k) read by antidiagonals, for n >= 0, k >= 0.
A306447 (program): Number of (undirected) Hamiltonian cycles in the n-antiprism graph.
A306455 (program): Total number of covered falling diagonals in all n X n permutation matrices.
A306458 (program): a(n) = A001694(n)/A007947(A001694(n)), the powerful numbers divided by their squarefree kernel.
A306472 (program): a(n) = 37*27^n.
A306473 (program): a(n) is the maximum number of distinct palindromic not necessarily contiguous subwords over all binary words of length n.
A306476 (program): Numbers k, with sigma(k) >= 3k and sigma(k) divisible by 3, that are not in A204830.
A306480 (program): Numbers k such that A054404(k) is not floor(k/e - 1/(2*e) + 1/2).
A306486 (program): Number of squares in the interval [e^(n-1), e^n).
A306490 (program): Numbers k such that sigma(k) - k - 2 is prime.
A306495 (program): Expansion of e.g.f. (2-exp(-x))*exp(x)/(x-1)^2.
A306496 (program): Number of (undirected) Hamiltonian cycles in the n-crown graph.
A306504 (program): Expansion of 1/(x^6+2*x^5-x^4-4*x^3-x^2-2*x+1).
A306509 (program): a(n) is the number of divisors of the sum of digits of n.
A306511 (program): Number of permutations p of [n] having at least one index i with |p(i)-i| = 1.
A306519 (program): Expansion of 2/(1 + 2*x + sqrt(1 - 4*x*(1 + x))).
A306534 (program): Square array A(n,k), n >= 0, k >= 1, read by antidiagonals: A(n,k) = Sum_{j=0..n} floor(n/k^j).
A306535 (program): Number of permutations p of [2n] having no index i with |p(i)-i| = n.
A306545 (program): Number of permutations p of [2n+2] such that min_{j=1..2n+2} |p(j)-j| = n;
A306546 (program): Modified Collatz Map such that odd numbers are treated the same, but even numbers have all factors of 2 removed.
A306549 (program): a(n) is the product of the positions of the zeros in the binary expansion of n (the most significant bit having position 1).
A306556 (program): Integers that appear as (unreduced) numerators of segment endpoints when a ternary Cantor set is created.
A306561 (program): Square numbers that are also central polygonal numbers (i.e., square numbers found in the Lazy Caterer’s sequence).
A306562 (program): a(n) = 1 + 2 - 3 - 4 + 5 + 6 + 7 - 8 - 9 - 10 - 11 + 12 + 13 + 14 + 15 + … + (+-1)*n, where, after the 1st summand there is one plus, two minuses, three plusses, etc.
A306577 (program): Last odd number reached by n before 1 through Collatz iteration, where a(n) = 1 when no other odd number is reached, or -1 if 1 is never reached.
A306591 (program): a(n) is the denominator of 1/2 - 1/(prime(n)+1), where prime(n) is the n-th prime.
A306609 (program): a(n) = Sum_{k=0..n} k*binomial(4*n+2,2*k)
A306610 (program): a(n) = (2*cos(Pi/15))^(-n) + (2*cos(7*Pi/15))^(-n) + (2*cos(11*Pi/15))^(-n) + (2*cos(13*Pi/15))^(-n), for n >= 1.
A306623 (program): Expansion of e.g.f. exp(Sum_{k=1..8} x^k).
A306624 (program): Expansion of e.g.f. exp(Sum_{k=1..9} x^k).
A306628 (program): Expansion of e.g.f. log(Sum_{k>=0} (k*x)^k).
A306637 (program): a(n) = Fibonacci(n) * A128834(n).
A306642 (program): a(n) = Sum_{k=0..n} (3*n)!/(k! * (n-k)!)^3.
A306653 (program): a(n) = Sum_{m=1..n} Sum_{k=1..n} [k divides n]*[n/k divides m]*A008683(n/k)*n/k*[k divides m + 2^p]*A008683(k)*k, where p can be a positive integer: 1,2,3,4,5,…
A306656 (program): Number of ways to fill a 3D matrix with n distinct values.
A306671 (program): a(n) = gcd(tau(n), pod(n)) where tau(k) = the number of the divisors of k (A000005) and pod(k) = the product of the divisors of k (A007955).
A306672 (program): Partial sums of the even Lucas numbers (A014448).
A306674 (program): Number of distinct non-similar obtuse triangles with integer sides and length of largest side <= n.
A306675 (program): Number of permutations p of [2n] having at least one index i with |p(i)-i| = n.
A306680 (program): Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. ((1-x)^(k-1))/((1-x)^k-x^(k+1)).
A306682 (program): a(n) = gcd(sigma(n), pod(n)) where sigma(k) = the sum of the divisors of k (A000203) and pod(k) = the product of the divisors of k (A007955).
A306683 (program): Integers k for which the base-phi representation of k does not include 1 or phi.
A306684 (program): Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of 2/(1 - x + sqrt(1 - 2*x + (1-4*k)*x^2)).
A306694 (program): a(n) is the denominator of log(A014963(n))/log(n) if n > 1 and a(1) = 1.
A306695 (program): a(n) = gcd(n, psi(n)).
A306696 (program): Lexicographically earliest sequence of nonnegative terms such that for any n > 0 and k > 0, if a(n) >= a(n+k), then a(n+2*k) <> a(n+k).
A306705 (program): a(n) = Product_{d|n} d*tau(d), where tau(k) = the number of the divisors of k (A000005).
A306712 (program): Decimal expansion of 3*sqrt(3)/Pi.
A306713 (program): Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of g.f. 1/(1-x^k-x^(k+1)).
A306721 (program): a(n) = Sum_{k=0..n} binomial(k, 7*(n-k)).
A306736 (program): Exponential infinitary highly composite numbers: where the number of exponential infinitary divisors (A307848) increases to record.
A306752 (program): a(n) = Sum_{k=0..n} binomial(k, 8*(n-k)).
A306753 (program): a(n) = Sum_{k=0..n} binomial(k, 9*(n-k)).
A306755 (program): a(n) = a(n-6) + a(n-7) with a(0)=7, a(1)=…=a(5)=0, a(6)=6.
A306756 (program): a(n) = a(n-7) + a(n-8) with a(0)=8, a(1)=…=a(6)=0, a(7)=7.
A306764 (program): a(n) is a sequence of period 12: repeat [1, 1, 6, 2, 1, 3, 2, 2, 3, 1, 2, 6].
A306770 (program): Decimal expansion of Sum_{k>=0} 1/(k! + (k+1)! + (k+2)!).
A306771 (program): Numbers m such that m = i + j = i * k and phi(m) = phi(i) + phi(j) = phi(i) * phi(k) for some i, j, k, where phi is the Euler totient function A000010.
A306775 (program): Partial sums of A060648: sum of the inverse Moebius transform of the Dedekind psi function from 1 to n.
A306780 (program): Decimal expansion of the constant S_1 - S_2 = Sum_{j>=1} (-1)^(j+1)*(prime(j)!/prime(j + 1)!).
A306789 (program): a(n) = Product_{k=0..n} binomial(n + k, n).
A306807 (program): An irregular fractal sequence: underline a(n) iff the absolute difference |a(n-1) - a(n)| is prime; all underlined terms rebuild the starting sequence.
A306809 (program): Binomial transform of the continued fraction expansion of e.
A306810 (program): Inverse binomial transform of the continued fraction expansion of e.
A306811 (program): Decimal expansion of Pi/(Pi - 1) = 1 + 1/Pi + 1/Pi^2 + … .
A306821 (program): Inverse binomial transform of the “original” Bernoulli numbers [A164555(n)/A027642(n)] with 1 and 1/2 swapped. Denominators.
A306825 (program): Primitive part of A001353(n).
A306829 (program): a(1) = 1; a(n+1) is the smallest k > a(n) such that 2^k == 2^a(n) (mod a(n)).
A306843 (program): a(n) = Sum_{d|n} binomial(n,d)^3.
A306846 (program): Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of g.f. ((1-x)^(k-1))/((1-x)^k-x^k).
A306847 (program): a(n) = Sum_{k=0..floor(n/6)} binomial(n,6*k).
A306848 (program): Product of first n odd nonprimes, a(n) = Product_{k=1..n) A071904(k).
A306852 (program): a(n) = Sum_{k=0..floor(n/7)} binomial(n,7*k).
A306858 (program): Decimal expansion of 1 - 1/(1*3) + 1/(1*3*5) - 1/(1*3*5*7) + …
A306859 (program): a(n) = Sum_{k=0..floor(n/8)} binomial(n,8*k).
A306860 (program): a(n) = Sum_{k=0..floor(n/9)} binomial(n,9*k).
A306863 (program): a(n) is the number of primes between the n-th and (n+1)-st odd composite numbers.
A306878 (program): Number of 0 < k < n such that n-k and n+k are both nonprimes.
A306890 (program): a(n) is the number of prime digits used in writing out all primes up to and including the n-th prime.
A306896 (program): a(n) = Sum_{d|n} (2^d + 2*(-1)^d)*phi(n/d).
A306897 (program): a(n) = A306896(n)/6.
A306898 (program): a(n) = Sum_{d|n} 2^d*phi(2*n/d).
A306905 (program): a(n) = A306898(n)/2.
A306915 (program): Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of g.f. 1/((1-x)^k-x^k).
A306921 (program): Number of ways of breaking the binary expansion of n into consecutive blocks with no leading zeros.
A306927 (program): a(n) = A001615(n) - n.
A306939 (program): Expansion of 1/((1 - x)^9 - x^9).
A306940 (program): Expansion of 1/((1 - x)^6 + x^6).
A306941 (program): Expansion of 1/((1 - x)^8 + x^8).
A306942 (program): Expansion of 1/((1 - x)^9 + x^9).
A306943 (program): Trajectory of 5 under repeated application of x -> A306938(x).
A306948 (program): Expansion of e.g.f. (1 + x)*log(1 + x)*exp(x).
A306957 (program): a(n) = n!*binomial(10,n).
A306958 (program): If the decimal expansion of n is d_1 … d_k, a(n) = Sum d_i!*binomial(10,d_i).
A306960 (program): Trajectory of 1 under repeated application of x -> A306958(x).
A306961 (program): Trajectory of 3 under repeated application of x -> A306958(x).
A306962 (program): Trajectory of 4 under repeated application of x -> A306958(x).
A306964 (program): Trajectory of 2 under repeated application of x -> A306958(x).
A306965 (program): If the decimal expansion of n is d_1 … d_k, a(n) = Sum binomial(10,d_i).
A306966 (program): Decimal expansion of t+t^2, where t is the tribonacci constant, the real root of x^3 - x^2 - x - 1.
A306967 (program): a(n) is the first Zagreb index of the Fibonacci cube Gamma(n).
A306988 (program): a(n) = Sum_{k=1..n} binomial(n,k)*phi(k), where phi is the Euler totient function.
A307000 (program): Number of unitary rings with additive group (Z/nZ)^2. Equivalently, number of unitary commutative rings with additive group (Z/nZ)^2.
A307001 (program): Odd numbers > 1 not of the form (3n*k - n - k + 1)/2 where n and k are odd numbers > 1.
A307005 (program): Expansion of e.g.f. (2*exp(x)-2*x-x^2)/(2-2*x-x^2).
A307006 (program): Expansion of e.g.f. (2*exp(x)-1-2*x-x^2)/(1-x-x^2).
A307011 (program): First coordinate in a redundant hexagonal coordinate system of the points of a counterclockwise spiral on an hexagonal grid. Second and third coordinates are given in A307012 and A345978.
A307012 (program): Second coordinate in a redundant hexagonal coordinate system of the points of a counterclockwise spiral on an hexagonal grid. First and third coordinates are given in A307011 and A345978.
A307013 (program): Third coordinate (asymmetric variant) in a redundant hexagonal coordinate system of the points of a counterclockwise spiral on an hexagonal grid. First and second coordinates are given in A307011 and A307012.
A307018 (program): Total number of parts of size 3 in the partitions of n into parts of size 2 and 3.
A307027 (program): Number of (undirected) paths in the complete bipartite graph K_{m,n} (triangle read by rows with m = 1..n and n = 1..).
A307035 (program): a(n) is the unique integer k such that A108951(k) = n!.
A307037 (program): The unitary analog of the alternating sum-of-divisors function (A206369).
A307040 (program): a(n) = Sum_{k=0..floor(n/6)} (-1)^k*binomial(n,6*k).
A307041 (program): a(n) = Sum_{k=0..floor(n/7)} (-1)^k*binomial(n,7*k).
A307044 (program): a(n) = Sum_{k=0..floor(n/8)} (-1)^k*binomial(n,8*k).
A307045 (program): a(n) = Sum_{k=0..floor(n/9)} (-1)^k*binomial(n,9*k).
A307047 (program): Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of g.f. 1/((1+x)^k-x^k).
A307055 (program): Even k such that psi(m) = k has no solution, where psi is the Dedekind psi function A001615.
A307059 (program): Expansion of 1/(2 - Product_{k>=1} (1 - x^k)).
A307062 (program): Expansion of 1/(2 - Product_{k>=1} (1 + x^k)^k).
A307063 (program): Expansion of 1/(2 - Product_{k>=1} (1 + k*x^k)).
A307064 (program): Expansion of 1 - 1/Sum_{k>=0} k!!*x^k.
A307066 (program): a(n) = exp(-1) * Sum_{k>=0} (n*k + 1)^n/k!.
A307073 (program): Expansion of 1/(1 - Sum_{k>=1} mu(k)^2*x^k/(1 - x^k)^2).
A307075 (program): Expansion of 1/(1 - Sum_{k>=1} mu(k)*x^k*(1 + x^k)/(1 - x^k)^3).
A307076 (program): Expansion of 1/(1 - Sum_{k>=1} lambda(k)*x^k), where lambda() is the Liouville function (A008836).
A307078 (program): Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of g.f. ((1-x)^(k-2))/((1-x)^k-x^k).
A307086 (program): Decimal expansion of 4*(5 - sqrt(5)*log(phi))/25, where phi is the golden ratio (A001622).
A307089 (program): Expansion of (1 - x)^4/((1 - x)^6 + x^6).
A307091 (program): a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(n,2*k)^2.
A307093 (program): a(n) = Sum_{k=0..n} (-1)^k * binomial(n,k^2).
A307094 (program): a(n) = Sum_{k=0..n} (-1)^k * binomial(n^2,k^2).
A307096 (program): Positive integers m such that for any positive integer k the last k bits of the binary expansion of m is not a multiple of 3.
A307100 (program): a(n) = Sum_{d|n} (tau(d)*pod(d)) where tau(k) = the number of divisors of k (A000005) and pod(k) = the product of the divisors of k (A007955).
A307101 (program): a(n) = Product_{d|n} (tau(d)*pod(d)) where tau(k) = the number of divisors of k (A000005) and pod(k) = the product of the divisors of k (A007955).
A307118 (program): a(1) = 0; for n>1, a(n) = dr(n-1) + dr(n) + dr(n+1), where dr(n) is the number of nontrivial divisors of n (A070824).
A307119 (program): a(1) = 1, for n>1, a(n) = dp(n-1) + dp(n) + dp(n+1), where dp(n) is the number of divisors of n less than n (A032741).
A307120 (program): a(1) = 3, for n>1, a(n) = A000005(n-1) + A000005(n) + A000005(n+1).
A307124 (program): a(n) is twice the square of the product of the first n primes each decreased by one.
A307135 (program): E.g.f. A(x) satisfies: d/dx A(x) = 1 + A(x*exp(-x)).
A307136 (program): a(n) = ceiling(2*sqrt(A000037(n))), n >= 1.
A307138 (program): State complexity profile of R-Lambda_24 version of Leech lattice.
A307152 (program): a(n) = floor((A002144(n)+19)/24).
A307158 (program): a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(n,3*k)^2.
A307163 (program): Minimum number of intercalates in a diagonal Latin square of order n.
A307168 (program): First class of all proper positive solutions x1(n) = a(n) of the Pell equation x^2 - 7*y^2 = 9.
A307169 (program): First class of all proper positive solutions y1(n) = a(n) of the Pell equation x^2 - 7*y^2 = 9.
A307172 (program): Second class of all proper positive solutions x2(n) of the Pell equation x^2 - 7*y^2 = 9.
A307173 (program): Second class of all proper positive solutions y2(n) = a(n) of the Pell equation x^2 - 7*y^2 = 9.
A307178 (program): Decimal expansion of coth(1/2).
A307182 (program): Crossing number of the n-crown graph (conjectured).
A307201 (program): Coordination sequence for trivalent node of type alpha in the first Moore pentagonal tiling.
A307202 (program): Coordination sequence for trivalent node of type alpha’ in the first Moore pentagonal tiling.
A307229 (program): Decimal expansion of (3*exp(1/2) - 1)/2.
A307233 (program): a(n) = Product_{k=1..n} (k^2 + k + 1) mod n.
A307240 (program): a(0) = 1; a(n) = Sum_{k=1..n} -lambda(k+1)*a(n-k), where lambda() is the Liouville function (A008836).
A307241 (program): a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k+1)*d(k+1)*a(n-k), where d() is the number of divisors (A000005).
A307242 (program): a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k+1)*sigma_2(k+1)*a(n-k), where sigma_2() is the sum of squares of divisors (A001157).
A307248 (program): a(n) is the number of n X n binary matrices (over the reals) with at least one row and column full of 1’s where the row index equals the column index.
A307253 (program): Number of triangles larger than size=1 in a matchstick-made hexagon with side length n.
A307258 (program): Expansion of (1/(1 + x)) * Product_{k>=1} 1/(1 - k*x^k/(1 + x)^k).
A307259 (program): Expansion of (1/(1 - x)) * Product_{k>=1} (1 + k*x^k/(1 - x)^k).
A307260 (program): Expansion of (1/(1 + x)) * Product_{k>=1} (1 + k*x^k/(1 + x)^k).
A307262 (program): Expansion of Product_{k>=1} (1 + k*x^k/(1 - x)^k).
A307264 (program): Expansion of (1/(1 - x)) * Product_{k>=1} 1/(1 + (-x)^k/(1 - x)^k).
A307265 (program): Expansion of Product_{k>=1} 1/(1 + (-x)^k/(1 - x)^k).
A307268 (program): Partial sums of the Lucas numbers of the form L(3n+2) (A163063).
A307271 (program): Partial sums of A307201.
A307272 (program): Partial sums of A307202.
A307294 (program): If n is even, a(n) = A000201(n/2+1), otherwise a(n) = A000201((n-1)/2+1) + 1.
A307295 (program): If n is even, a(n) = A001950(n/2+1), otherwise a(n) = A001950((n-1)/2+1) + 1.
A307304 (program): Number of inequivalent ways of placing 2 nonattacking rooks on n X n board up to rotations and reflections of the board.
A307310 (program): Expansion of Product_{k>=1} (1 - x^k/(1 - x)^k).
A307313 (program): a(n) is the denominator of n/2^(length of the binary representation of n).
A307314 (program): Number of divisors d of 2n such that adding d to 2n in binary requires no carries.
A307342 (program): Products of four primes, except fourth powers of primes.
A307346 (program): Number of uniquely sorted permutations of [2n+1] that avoid the patterns 231 and 4123.
A307349 (program): a(n) = Sum_{i=1..n} Sum_{j=1..n} (-1)^(i+j) * (i+j)!/(2!*i!*j!).
A307354 (program): a(n) = Sum_{0<=i<=j<=n} (-1)^(i+j) * (i+j)!/(i!*j!).
A307364 (program): Expansion of 1/(1 - Sum_{k>=1} prime(k)#*x^k), where prime(k)# is the product of first k primes (A002110).
A307368 (program): a(n) is the minimal positive integer such that 2*a(n)*prime(n)-1 equals another prime.
A307371 (program): Numbers k such that the digits of sqrt(k) begin with k.
A307373 (program): Heinz numbers of integer partitions with at least three parts, the third of which is 2.
A307374 (program): G.f. A(x) satisfies: A(x) = 1 + x - x^2*A(x)^2.
A307376 (program): a(n) = 1/n! * Sum_{k=0..n} (2*n+k)!/((n-k)!*k!*2^k).
A307386 (program): Heinz numbers of integer partitions with Durfee square of length 3.
A307389 (program): a(n) is the number of elements in the species of orbit polytopes in dimension n.
A307390 (program): Primes p such that 2*p-1 is not prime.
A307393 (program): Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of g.f. ((1-x)^(k-4))/((1-x)^k-x^k).
A307395 (program): Expansion of 1/((1 - x) * ((1 - x)^3 + x^3)).
A307408 (program): a(n) = (A001222(n) - 1)*A001221(n) + 2.
A307409 (program): a(n) = (A001222(n) - 1)*A001221(n).
A307413 (program): G.f. A(x) satisfies: A(x) = 1 + x*A(x)/(1 - x*A(x) - 2*x^2*A(x)^2).
A307420 (program): Dirichlet g.f.: zeta(2*s) * zeta(3*s) / zeta(s).
A307421 (program): Dirichlet g.f.: zeta(s) * zeta(3*s) / zeta(2*s).
A307423 (program): Dirichlet g.f.: zeta(2*s) / zeta(3*s).
A307424 (program): Dirichlet g.f.: zeta(3*s) / zeta(2*s).
A307425 (program): Dirichlet g.f.: zeta(s) / (zeta(2*s) * zeta(3*s)).
A307427 (program): Dirichlet g.f.: zeta(3*s) / (zeta(s) * zeta(2*s)).
A307428 (program): Dirichlet g.f.: zeta(2*s) / (zeta(s) * zeta(3*s)).
A307430 (program): Dirichlet g.f.: zeta(s) / zeta(4*s).
A307433 (program): A special version of Pascal’s triangle where only powers of 2 are permitted.
A307445 (program): Dirichlet g.f.: 1 / (zeta(s) * zeta(2*s)).
A307460 (program): Expansion of Product_{k>=1} (1-x^k)^((-1)^k*k^2).
A307462 (program): Expansion of Product_{k>=1} (1+x^k)^((-1)^k*k^2).
A307464 (program): Number of Catalan words of length n avoiding the pattern 000.
A307465 (program): Number of Catalan words of length n avoiding the pattern 110.
A307466 (program): Number of Catalan words of length n avoiding the pattern 210.
A307467 (program): The number of points, corresponding to the first n primes, and placed on the unit circle according to an algorithm using the data from A077218 (in the spirit of Ulam’s spiral, and described in the COMMENTS section below), which lie on the closed arc of the unit circle from 0 to 45 degrees.
A307469 (program): a(n) = 2*a(n-1) + 6*a(n-2) for n >= 2, a(0) = 1, a(1) = 5.
A307484 (program): Expansion of Product_{k>=1} 1/(1+x^k)^((-1)^k*k^2).
A307485 (program): A permutation of the nonnegative integers: one odd, two even, four odd, eight even, etc.; extended to nonnegative integer with a(0) = 0.
A307489 (program): G.f. A(x) satisfies: A(x) = 1/(1 - 2*x*A(x) - x*A(x)/(1 - x*A(x)/(1 - x*A(x)/(1 - …)))), a continued fraction.
A307490 (program): G.f. A(x) satisfies: A(x) = 1/(1 - x*A(x) - x^2*A(x)^2/(1 - x^2*A(x)^2/(1 - x^2*A(x)^2/(1 - …)))), a continued fraction.
A307495 (program): Expansion of Sum_{k>=0} k!*((1 - sqrt(1 - 4*x))/2)^k.
A307500 (program): Expansion of Product_{k>=1} 1/(1 - (x*(1 - x))^k).
A307508 (program): Primes p for which the continued fraction expansion of sqrt(p) does not have a 1 in the second position.
A307513 (program): Beatty sequence for 1/log(2).
A307515 (program): Heinz numbers of integer partitions with Durfee square of length > 2.
A307516 (program): Numbers whose maximum prime index and minimum prime index differ by more than 1.
A307517 (program): Numbers with at least two not necessarily distinct prime factors less than the largest prime factor.
A307520 (program): Expansion of Product_{k>=1} ((1 - x)^k - x^k)/((1 - x)^k + x^k).
A307521 (program): Expansion of Product_{k>=1} ((1 + x)^k + x^k)/((1 + x)^k - x^k).
A307522 (program): Expansion of Product_{k>=1} ((1 + x)^k - x^k)/((1 + x)^k + x^k).
A307533 (program): Primes p such that p+2 has exactly two distinct prime factors.
A307539 (program): Heinz numbers of square integer partitions, where the Heinz number of an integer partition (y_1,…,y_k) is prime(y_1)*…*prime(y_k).
A307548 (program): Expansion of Product_{k>=1} (1 - (x/(1+x))^k).
A307557 (program): Number of Motzkin meanders of length n with no level steps at odd level.
A307559 (program): a(n) = floor(n/3)*(n - floor(n/3))*(n - floor(n/3) - 1).
A307561 (program): Numbers k such that both 6*k - 1 and 6*k + 5 are prime.
A307562 (program): Numbers k such that both 6*k + 1 and 6*k + 7 are prime.
A307563 (program): Numbers k such that both 6k - 1 and 6k + 7 are prime.
A307574 (program): Expansion of Product_{k>=1} (1 - (x/(1-x))^k)^k.
A307593 (program): Expansion of e.g.f. (sec(x) + tan(x))*exp(x)/(1 - x).
A307594 (program): Expansion of e.g.f. (sec(x) + tan(x))*exp(-x)/(1 - x).
A307597 (program): Number of partitions of n into 2 distinct positive triangular numbers.
A307607 (program): a(n) = 1 + Sum_{d|n, d > 1} d^2*a(n/d).
A307612 (program): Partial sums of the permutation A307485: one odd, two even, four odd, eight even, etc.
A307613 (program): Inverse of the permutation A307485: one odd, two even, four odd, eight even, etc; extended with a(0) = 0.
A307614 (program): Number of partitions of the n-th triangular number into consecutive positive triangular numbers.
A307618 (program): A Calabi-Yau period integral: a(n) = C(4*n,2*n)*C(2*n,n)^3.
A307621 (program): Number of cycles in the n-dipyramidal graph.
A307627 (program): Primes p such that 2 is a primitive root modulo p while 8 is not.
A307628 (program): Primes p such that 2 is a primitive root modulo p while 32 is not.
A307641 (program): Triangle T(i,j=1..i) read by rows which contain the naturally ordered prime-or-one factorization of the row number i.
A307642 (program): a(n) = n!*Sum_{i=1..n} (Sum_{j=1..i} (i/j)).
A307645 (program): Numbers that are the sum of a positive triangular number and a positive cube.
A307646 (program): Numbers that are the sum of a prime number and a nonnegative cube.
A307647 (program): Numbers that are the sum of a prime number and a positive cube.
A307648 (program): G.f. A(x) satisfies: 1/(1 - x) = A(x)*A(x^2)^2*A(x^3)^3*A(x^4)^4* … *A(x^k)^k* …
A307654 (program): a(n) = Product_{p|n, p prime} (1 - p^p).
A307656 (program): G.f. A(x) satisfies: (1 - x) = A(x)*A(x^2)^2*A(x^3)^3*A(x^4)^4* … *A(x^k)^k* …
A307660 (program): E.g.f. A(x) satisfies: A(x) = exp(-x) * A(x^2)*A(x^3)*A(x^4)* … *A(x^k)* …
A307662 (program): Triangle T(i,j=1..i) read by rows which contain the naturally ordered divisors-or-ones of the row number i.
A307663 (program): a(n) = (n-1)!*(Sum_{i=1..n} Sum_{j=1..i} binomial(i,j)*i/j).
A307665 (program): A(n,k) = Sum_{j=0..floor(n/k)} binomial(2*n,k*j+n), square array A(n,k) read by antidiagonals, for n >= 0, k >= 1.
A307666 (program): Number of partitions of n into consecutive positive triangular numbers.
A307673 (program): Partial sums of A108754.
A307677 (program): a(0) = a(1) = a(2) = a(3) = 1; thereafter a(n) = a(n-1) + a(n-2) + a(n-4).
A307678 (program): G.f. A(x) satisfies: A(x) = 1 + x*A(x)^3/(1 - x).
A307679 (program): Expansion of e.g.f. Product_{k>=1} 1/(1 - x^k/(1 - x)^k)^(1/k).
A307681 (program): Difference between the number of diagonals and the number of sides for a convex n-gon.
A307682 (program): Products of four primes, two of which are distinct.
A307686 (program): Sum of the smallest side lengths of all integer-sided triangles with perimeter n.
A307688 (program): a(n) = 2*a(n-1)-2*a(n-2)+a(n-3)+2*a(n-4) with a(0)=a(1)=0, a(2)=2, a(3)=3.
A307692 (program): g values of Triphosian primes.
A307695 (program): Expansion of 1/(sqrt(1-4*x)*sqrt(1-16*x)).
A307702 (program): Clique covering number of the n-Sierpinski tetrahedron graph.
A307704 (program): Expansion of (1/(1 - x)) * Sum_{k>=1} (-x)^k/(1 - (-x)^k).
A307707 (program): Lexicographically earliest sequence starting with a(1) = 0 such that a(n) is the number of pairs of contiguous terms whose sum is a(n).
A307716 (program): Denominator of the barycenter of first n primes defined as a(n) = denominator(Sum_{i=1..n} (i*prime(i)) / Sum_{i=1..n} prime(i)).
A307726 (program): Number of partitions of n into 2 prime powers (not including 1).
A307742 (program): Quasi-logarithm A064097(n) of von Mangoldt’s exponential function A014963(n).
A307743 (program): a(n) = Sum_{k=1..n} A307742(k).
A307753 (program): Number of palindromic pentagonal numbers of length n whose index is also palindromic.
A307766 (program): Number of palindromic hexagonal numbers of length n whose index is also palindromic.
A307768 (program): Number of n-step random walks on a line starting from the origin and returning to it at least once.
A307778 (program): a(1) = 1; a(n+1) = Sum_{d|n} (-1)^(d+1)*a(d).
A307779 (program): a(1) = 1; a(n+1) = Sum_{d|n, n/d odd} a(d).
A307788 (program): Number of valid hook configurations of permutations of [n] that avoid the patterns 231 and 321.
A307789 (program): Number of valid hook configurations of permutations of [n] that avoid the patterns 231 and 1243.
A307791 (program): Number of palindromic heptagonal numbers of length n whose index is also palindromic.
A307800 (program): Binomial transform of least common multiple sequence (A003418), starting with a(1).
A307802 (program): Number of palindromic octagonal numbers of length n whose index is also palindromic.
A307803 (program): Inverse binomial transform of least common multiple sequence.
A307805 (program): a(n) = first position of prime(n) in A023503.
A307808 (program): Number of palindromic nonagonal numbers of length n whose index is also palindromic.
A307810 (program): Expansion of 1/AGM(1-64*x, sqrt((1-16*x)*(1-256*x))).
A307811 (program): Expansion of 1/AGM(1-45*x, sqrt((1-25*x)*(1-81*x))).
A307813 (program): a(n) = (5/32)*4^n - floor((n^2 + 1)/2)*2^(n - 2).
A307826 (program): The number of integers r such that all primes above a certain value have the form primorial(n)*q +- r.
A307832 (program): Number of palindromic decagonal (10-gonal) numbers of length n whose index is also palindromic.
A307844 (program): Constant term in the expansion of (n/x + 1 + n*x)^n.
A307845 (program): Exponential unitary highly composite numbers: where the number of exponential unitary divisors (A278908) increases to a record.
A307847 (program): Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of 1/sqrt(1 - 2*x + (1-4*k^2)*x^2).
A307848 (program): The number of exponential infinitary divisors of n.
A307849 (program): Number of ways to pay n dollars using Canadian coins, that is: nickels (5 cents), dimes (10 cents), quarters (25 cents), loonies (100 cents or $1 coins) and toonies ($2 coins).
A307855 (program): Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of 1/sqrt(1 - 2*x + (1-4*k)*x^2).
A307860 (program): Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of 1/sqrt(1 - 2*x + (1+4*k)*x^2).
A307862 (program): Coefficient of x^n in (1 + x - n*x^2)^n.
A307872 (program): Sum of the smallest parts in the partitions of n into 3 parts.
A307876 (program): a(n) is the smallest m such that there are prime(n) Pythagorean triangles with a leg (not hypotenuse) of length m, or -1 if no such m exists.
A307878 (program): Expansion of e.g.f. exp(3*x)*(sec(x) + tan(x)).
A307879 (program): Expansion of e.g.f. exp(4*x)*(sec(x) + tan(x)).
A307883 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of 1/sqrt(1 - 2*(k+1)*x + ((k-1)*x)^2).
A307884 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of 1/sqrt(1 + 2*(k-1)*x + ((k+1)*x)^2).
A307885 (program): Coefficient of x^n in (1 - (n-1)*x - n*x^2)^n.
A307889 (program): G.f. A(x) satisfies: A(x) = 1 + x*A(x^2)/(1 - x)^2.
A307892 (program): a(n) = lcm(tau(n), pod(n)) / n, where tau(k) = the number of divisors of k (A000005) and pod(n) = the product of divisors of k (A007955).
A307893 (program): a(n) = lcm(sigma(n), pod(n)) / n, where sigma (k) = the sum of divisors of k (A000203) and pod(n) = the product of divisors of k (A007955).
A307895 (program): Numbers whose prime exponents, starting from the largest prime factor through to the smallest, form an initial interval of positive integers.
A307897 (program): Dimensions of space of harmonic polynomials of each degree invariant under the icosahedral rotation group.
A307898 (program): Expansion of 1/(1 - x * Sum_{k>=1} prime(k)*x^k).
A307899 (program): Expansion of 1/(1 + x * Sum_{k>=1} prime(k)*x^k).
A307901 (program): Expansion of 1/(1 - x * theta_4(x)), where theta_4() is the Jacobi theta function.
A307904 (program): Coefficient of x^n in (1 + x + n*x^3)^n.
A307906 (program): Coefficient of x^n in 1/(n+1) * (1 + x + n*x^2)^(n+1).
A307907 (program): a(n) is the greatest k such that p^k <= n for any prime factor p of n.
A307908 (program): a(n) is the least k such that p^k >= n for any prime factor p of n.
A307911 (program): Coefficient of x^n in expansion of (1 - n*x - n*x^2)^n.
A307912 (program): a(n) = n - 1 - pi(2*n-1) + pi(n), where pi is the prime counting function.
A307913 (program): Numbers without the decimal digits 3, 6 and 9.
A307921 (program): Number of (undirected) paths in the n-book graph.
A307923 (program): Number of (undirected) Hamiltonian cycles in the n-cocktail party graph.
A307935 (program): Number of (undirected) Hamiltonian paths in the n-cocktail party graph.
A307939 (program): Number of (undirected) Hamiltonian paths in the n-dipyramidal graph.
A307946 (program): Coefficient of x^n in 1/(n+1) * (1 - n*x - n*x^2)^(n+1).
A307947 (program): Coefficient of x^n in 1/(n+1) * (1 + x - n*x^2)^(n+1).
A307966 (program): Sum of the largest side lengths of all integer-sided triangles with perimeter n.
A307969 (program): Coefficient of x^n in 1/(n+1) * (1 - 2*x - 2*x^2)^(n+1).
A307985 (program): Number of integer-sided triangles with perimeter n and sides a, b, and c such that a <= b <= c and b|n.
A307989 (program): a(n) = n - pi(2*n) + pi(n-1), where pi is the prime counting function.
A307993 (program): G.f. A(x) satisfies: A(x) = x + x^2 + x^3 * (1 + A(x) + A(x^2) + A(x^3) + …).
A307994 (program): G.f. A(x) satisfies: A(x) = x + x^2 + x^3 + x^4 * (1 + A(x) + A(x^2) + A(x^3) + …).
A307995 (program): G.f. A(x) satisfies: A(x) = x + x^2 + x^3 + x^4 + x^5 * (1 + A(x) + A(x^2) + A(x^3) + …).
A307996 (program): Expansion of e.g.f. exp(1 - exp(x)*(1 - 2*x)).
A307997 (program): a(n) is the sum of A023896(k) over the totatives of n.
A308003 (program): A modified Sisyphus function: a(n) = concatenation of (number of even digits in n) (number of digits in n) (number of odd digits in n).
A308005 (program): A modified Sisyphus function: a(n) = concatenation of (number of odd digits in n) (number of digits in n) (number of even digits in n).
A308025 (program): a(n) = n*(2*n - 3 - (-1)^n)*(5*n - 2 + (-1)^n)/16.
A308026 (program): a(n) = n*(2*n - 3 - (-1)^n)*(11*n + (-1)^n)/24.
A308034 (program): Number of partitions of n into 3 parts with at least 1 part that is a nondivisor of n.
A308035 (program): Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of 2/(1 - x + sqrt(1 - 2*x + (1+4*k)*x^2)).
A308036 (program): Coefficient of x^n in 1/(n+1) * (1 + x - 3*x^2)^(n+1).
A308038 (program): a(n) = Sum_{i=1..floor((n-1)/2)} i * (n-i)^2.
A308044 (program): a(n) = 2*prevprime(2*n-1) - 2*n, where prevprime(n) is the largest prime < n.
A308046 (program): a(n) = 2*nextprime(n - 1) - 2*n, where nextprime(n) is the smallest prime > n.
A308047 (program): Sum of subgroup indices of dihedral group, Sum_{H <= D(n)} [D(n):H].
A308048 (program): a(n) = n - nextprime(ceiling(n/2) - 1), where nextprime(n) is the smallest prime > n.
A308050 (program): a(n) = n - prevprime(n - 1), where prevprime(n) is the largest prime < n.
A308052 (program): a(n) = nextprime(ceiling(n/2)-1), where nextprime(n) is the smallest prime > n.
A308066 (program): Number of triangles with perimeter n whose side lengths are even.
A308067 (program): Number of integer-sided triangles with perimeter n whose longest side length is odd.
A308068 (program): Number of integer-sided triangles with perimeter n whose longest side length is even.
A308077 (program): G.f. A(x) satisfies: A(x) = x - A(x^2) + A(x^3) - A(x^4) + A(x^5) - A(x^6) + …
A308084 (program): a(n) = n*(n-1)*d(n)/4, where d(n)=A000005(n) is the number of divisors of n.
A308089 (program): Sum of the perimeters of all integer-sided triangles with perimeter n.
A308090 (program): a(n) = gcd(2^n + n!, 3^n + n!, n+1).
A308095 (program): a(n) is the sum of sigma (i.e., A000203) over the totatives of n.
A308096 (program): Take all the integer-sided triangles with perimeter n and sides a, b, and c such that a <= b <= c. a(n) is the sum of all the b’s.
A308102 (program): Sum of the perimeters of all integer-sided scalene triangles with perimeter n.
A308107 (program): Sum of the smallest side lengths of all integer-sided scalene triangles with perimeter n.
A308108 (program): Sum of the largest side lengths of all integer-sided scalene triangles with perimeter n.
A308109 (program): Take all the integer-sided triangles with perimeter n and sides a, b, and c such that a < b < c. a(n) is the sum of all the b’s.
A308123 (program): Sum of the perimeters of all integer-sided isosceles triangles with perimeter n.
A308124 (program): a(n) = (2 + 7*4^n)/3.
A308135 (program): Sum of non-coreful divisors of n.
A308136 (program): Number of (undirected) Hamiltonian paths in the 2n-crossed prism graph.
A308137 (program): Number of (undirected) Hamiltonian paths on the n-prism graph.
A308149 (program): Positive integers with Collatz trajectories that do not include the number 5.
A308150 (program): Numbers k such that sigma(k) mod k is prime, where sigma = A000203.
A308158 (program): Sum of the smallest side lengths of all integer-sided isosceles triangles with perimeter n.
A308159 (program): Sum of the largest sides of all integer-sided isosceles triangles with perimeter n.
A308160 (program): Take all the integer-sided isosceles triangles with perimeter n and sides a, b, and c such that a <= b <= c. a(n) is the sum of all the b’s.
A308166 (program): Number of integer-sided triangles with perimeter n such that the smallest side divides the largest.
A308167 (program): Number of integer-sided triangles with perimeter n and sides a, b, and c such that a <= b <= c and a|b.
A308169 (program): Numbers k such that A023896(k) mod A000203(k) is prime.
A308183 (program): S_oo, where S_1 = bc, S_n = S_{n-1} a^n S_{n-1} for n > 1, over the alphabet {a,b,c} = {0,1,2}.
A308184 (program): S_oo, where S_1 = bc, S_n = S_{n-1} a^n S_{n-1} for n > 1, over the alphabet {a,b,c} = {1,2,3}.
A308185 (program): Fixed point (beginning with a) of the morphism a -> abab, b -> b, over the alphabet {a,b} = {0,1}.
A308186 (program): Fixed point (beginning with a) of the morphism a -> abab, b -> b, over the alphabet {a,b} = {1,2}.
A308187 (program): Fixed point (beginning with a) of the morphism a -> aab, b -> b, over the alphabet {a,b} = {0,1}.
A308188 (program): Fixed point (beginning with a) of the morphism a -> aab, b -> b, over the alphabet {a,b} = {1,2}.
A308189 (program): Numbers of the form t_n or t_n + t_{n+1} where {t_n} are the tribonacci numbers A000073.
A308196 (program): Partial sums of A063808.
A308197 (program): Numbers m such that the tribonacci representation of m (A278038) ends in an even number of 0’s.
A308198 (program): Numbers m such that the tribonacci representation of m (A278038) ends in an odd number of 0’s.
A308199 (program): The tribonacci representation of a(n) is obtained by appending 0,0 to the tribonacci representation of n (cf. A278038).
A308200 (program): The tribonacci representation of a(n) is obtained by appending 0,0,0 to the tribonacci representation of n (cf. A278038).
A308215 (program): a(n) is the multiplicative inverse of A001844(n+1) modulo A001844(n); where A001844 is the sequence of centered square numbers.
A308217 (program): a(n) is the multiplicative inverse of A001844(n) modulo A001844(n+1); where A001844 is the sequence of centered square numbers.
A308222 (program): Numbers that are the perimeter of a primitive Heronian isosceles triangle.
A308230 (program): Irregular triangle: row n shows the alternating sums of partitions of n when the parts are arranged in nonincreasing order and the partitions are arranged lexicographically from [n] to [1,1,1,…,1].
A308259 (program): a(n) is equal to the sum of the factorials of the digits of a(n-1), initial term is 3.
A308265 (program): Sum of the largest parts in the partitions of n into 3 parts.
A308266 (program): Sum of the middle parts in the partitions of n into 3 parts.
A308281 (program): The third power of the unsigned Lah triangular matrix A105278.
A308282 (program): The fifth power of the unsigned Lah triangular matrix A105278.
A308287 (program): Length 20 arithmetic progression of primes (PAP-20).
A308303 (program): Number of integer-sided triangles with perimeter n and at least one even side length.
A308305 (program): a(n) = s(n,n) + s(n,n-1) + s(n,n-2), where s(n,k) are the unsigned Stirling numbers of the first kind (see A132393).
A308313 (program): a(n) = Sum_{k=1..n} (-1)^(n-k) * k^n * floor(n/k).
A308320 (program): Decimal expansion of 2^(-7/4); exact length of the A4 paper size measured in meters according to the ISO 216 standard.
A308321 (program): Decimal expansion of 2^(-9/4); exact width of the A4 paper size measured in meters according to the ISO 216 standard.
A308329 (program): Even moments of the trace of elements of the binary icosahedral group.
A308341 (program): Hypotenuses of primitive Pythagorean triangles two sides of which are Pythagorean primes.
A308344 (program): a(n) = (A001359(n+1)^2 - 1)/24, where A001359 = lesser of twin primes; or: pentagonal numbers (A000326) whose indices are twin ranks (A002822).
A308346 (program): Expansion of e.g.f. 1/(1 - x)^log(1 - x).
A308347 (program): n-th digit in the base-6 expansion of 1/n.
A308351 (program): For n >= 2, a(n) = n*u(n-1) + n*(n-1)*u(n-2), where u = A292932; a(1)=1.
A308352 (program): Number of k-ary quasitrivial semigroups that have no neutral element on an n-element set.
A308354 (program): Number of (2k+1)-ary quasitrivial semigroups that have two neutral elements on an n-element set.
A308355 (program): Limiting row sequence of the array A128628.
A308357 (program): Smallest k such that k! can be represented as the sum of the n-th powers of two or more distinct primes; or -1 if no such k exists.
A308358 (program): Beatty sequence for sqrt(3)/4.
A308361 (program): The largest codimension of a cyclically covering subspace in GF(2)^n.
A308364 (program): a(0) = 0, a(3n) = a(n), a(3n+1) = a(n)*3 + 1, a(3n-1) = a(n)*3 - 1.
A308366 (program): Expansion of Sum_{k>=1} (-1)^(k+1)*k*x^k/(1 - k*x^k).
A308367 (program): Expansion of Sum_{k>=1} x^k/(1 + k*x^k).
A308375 (program): Digital sum of composite numbers.
A308381 (program): Expansion of e.g.f. exp(Sum_{k>=1} x^(k^2)*(2 + x^(k^2))/(2*k^2)).
A308385 (program): a(n) is the last square visited by fers moves on a spirally numbered (2n-1) X (2n-1) board, moving to the lowest available unvisited square at each step.
A308392 (program): Expansion of e.g.f. exp(x + 2 * Sum_{k>=1} x^(2^k)/2^k).
A308396 (program): Expansion of e.g.f. exp(-Sum_{k>=1} x^(k^2)/k^2).
A308399 (program): Expansion of 1 / Sum_{k=-oo..oo} (-x)^(k*(4*k + 1)).
A308401 (program): Number of bracelets (turnover necklaces) of length n that have no reflection symmetry and consist of 6 white beads and n-6 black beads.
A308416 (program): Values of m for which 2*p + m cannot be a square when p is a prime.
A308417 (program): Expansion of e.g.f. exp(x*(1 + x + x^2)/(1 - x^2)^2).
A308418 (program): Expansion of e.g.f. exp(x*(1 + 3*x + 6*x^2 + 3*x^3 + x^4)/(1 - x^2)^3).
A308422 (program): a(n) = n^2 if n odd, 3*n^2/4 if n even.
A308432 (program): Given n cards in a stack numbered from 1 to n with 1 at the top, repeat the following process: first remove the card that is in the middle (at position (size of the stack)/2, rounding up), then move the card that is at the bottom of the stack to the top. This process is repeated until there is only one card left. a(n) is the number of the last remaining card.
A308434 (program): n! + n!!.
A308435 (program): Peak- and valleyless Motzkin meanders.
A308436 (program): Expansion of 1/((1-2*x)*(1-4*x)*(1-8*x)*(1-16*x)*(1-32*x)).
A308439 (program): a(n) is the smallest prime factor of 1 + the product of primes indexed by the binary digits of n.
A308443 (program): Expansion of e.g.f. Product_{k>=1} 1/(1 - x^k)^(psi(k)/k), where psi() is the Dedekind psi function (A001615).
A308445 (program): a(0) = 1; a(n) = Sum_{k=1..n} gcd(n,k)*a(n-k).
A308457 (program): Expansion of e.g.f. (1/(1 - x)) * Product_{k>=2} 1/(1 - x^k)^(phi(k)/2), where phi() is the Euler totient function (A000010).
A308462 (program): Expansion of e.g.f. exp(Sum_{k>=1} psi(k)*x^k/k), where psi() is the Dedekind psi function (A001615).
A308464 (program): Squarefree numbers of the form m^2 + 4.
A308467 (program): The smallest positive n-digit 4th power.
A308469 (program): a(1) = 1, a(2)=2, a(n) = a(n-1) + gcd(a(n-2), n-2).
A308470 (program): a(n) = (gcd(phi(n), 4*n^2 - 1) - 1)/2, where phi is A000010, Euler’s totient function.
A308472 (program): Numbers that are divisible by the sum of the digits of the product of their digits.
A308473 (program): Sum of numbers < n which have common prime factors with n.
A308474 (program): a(n) = Sum_{k=1..n^2, gcd(n,k) = 1} k.
A308480 (program): a(n) = A000225(n) if n is prime, a(n) = A020639(n) otherwise.
A308481 (program): a(n) = Sum_{k=1..n, gcd(n,k) = 1} k^n.
A308485 (program): a(n) is the sum of the integer logs of all integers strictly between prime(n) and prime(n+1).
A308495 (program): a(n) is the position of the first occurrence of prime(n) in A027748.
A308498 (program): Triangle read by rows where T(n,k), n>=1, 1<=k<=n is the number of (0,1)-matrices of size n with the first row and column sum = k and remaining sums = 1.
A308501 (program): Partial products of odious numbers.
A308506 (program): Expansion of e.g.f.: -1/(1-LambertW(-2*x)).
A308520 (program): Expansion of e.g.f. exp(x)*(1 + x + x^2/2)*(sec(x) + tan(x)).
A308521 (program): Expansion of e.g.f. (sec(x) + tan(x))/(1 - 2*x).
A308523 (program): Number of essentially simple rooted toroidal triangulations with n vertices.
A308524 (program): Number of essentially 3-connected rooted toroidal maps with n edges.
A308528 (program): Number of length-n binary words having no nontrivial prefix that is a palindrome of odd length.
A308536 (program): Expansion of e.g.f. exp(1 - exp(2*x)).
A308538 (program): a(n) = exp(1) * Sum_{k>=0} (-1)^k*(k*(k + 1))^n/k!.
A308543 (program): Expansion of e.g.f. exp(2*(exp(2*x) - 1)).
A308546 (program): Number of double-closed subsets of {1..n}.
A308567 (program): Consider the second least-significant bits of the first n prime numbers: a(n) equals the number of zeros minus the number of ones.
A308570 (program): a(n) = sigma_{2*n}(n).
A308572 (program): a(n) = Fibonacci(2*prime(n)).
A308578 (program): Maximum number of non-overlapping circles of radius 1/n that can be placed inside a unit square.
A308579 (program): a(n) = (9*2^n - 6*n - 10)/2.
A308580 (program): a(n) = 3*2^n + n^2 - n.
A308585 (program): a(n) = 2^(n + 3) - 10*n - 6.
A308589 (program): Number of minimal edge covers in the (2n-1)-triangular snake graph.
A308592 (program): Number of total dominating sets in the (2n-1)-triangular snake (for n > 1).
A308593 (program): a(n) = Sum_{d|n} d^(n^2/d).
A308594 (program): a(n) = Sum_{d|n} d^(d+n).
A308596 (program): a(n) is the product of the prime(n) smallest primes other than prime(n).
A308598 (program): The smaller term of the pair (a(n), a(n+1)) is always prime and in each pair there is a composite number; a(1) = 2 and the sequence is always extended with the smallest integer not yet present and not leading to a contradiction.
A308599 (program): Number of (not necessarily maximum) cliques in the n-alternating group graph.
A308600 (program): Number of (not necessarily maximum) cliques in the n X n antelope graph.
A308602 (program): Number of (not necessarily maximum) cliques in the n-cycle graph.
A308603 (program): Number of (not necessarily maximal) cliques in the n-dipyramidal graph.
A308604 (program): Number of (not necessarily maximal) cliques in the n X n fiveleaper graph.
A308606 (program): Number of (not necessarily maximum) cliques in the n-transposition graph.
A308607 (program): Number of (not necessarily maximum) cliques in the wheel graph on n vertices.
A308616 (program): Number of well-formed formulas of length n in a formal propositional language with one unitary operator, one binary operator, and one propositional variable.
A308632 (program): Largest aggressor for the maximum number of peaceable coexisting queens as given in A250000.
A308645 (program): Expansion of e.g.f. exp(1 + x - exp(2*x)).
A308646 (program): a(n) = exp(1) * Sum_{k>=0} (-1)^k*k^(2*n)/k!.
A308647 (program): a(n) = exp(1) * Sum_{k>=0} (-1)^k*k^(2*n+1)/k!.
A308655 (program): Alternating partial sums of the prime gaps.
A308663 (program): Partial sums of A097805.
A308668 (program): a(n) = Sum_{d|n} d^(n/d+n).
A308677 (program): Kuba-Panholzer Table 2 pattern 312, 213 for Stirling permutation k = 2.
A308685 (program): The number of triangular lattice points whose Euclidean distance from the origin is less than or equal to n.
A308688 (program): a(n) = Sum_{d|n} d^(2*n/d - 1).
A308689 (program): a(n) = Sum_{d|n} d^(3*n/d - 2).
A308692 (program): a(n) = Sum_{d|n} d^(2*(n/d - 1)).
A308693 (program): a(n) = Sum_{d|n} d^(3*(n/d - 1)).
A308696 (program): a(n) = Sum_{d|n} d^(2*d).
A308697 (program): a(n) = Sum_{d|n} d^(3*d).
A308700 (program): a(n) = n * 2^(n - 2) * (2^(n - 1) - 1).
A308707 (program): a(n) = gcd(n, phi(n) + sigma(n)), where phi is A000010 and sigma is A000203.
A308709 (program): Start with 3, divide by 3, multiply by 2, multiply by 3, multiply by 2, repeat.
A308710 (program): Primitive practical numbers of the form 2^i * prime(k).
A308720 (program): The maximum value in the continued fraction of sqrt(n), or 0 if there is no fractional part.
A308722 (program): Number of edges in the smallest possible regular graceful graph of valence n.
A308723 (program): Total number of parts in all m-cyclic compositions of n (where each part of size m can be colored with one of m colors).
A308729 (program): a(n)/n! is the expected number of left-to-right maxima in the lexicographical or colexicographical ordering of all the 2-subsets of [n] under a random permutation of [n], when the 2-subsets hold the worst order of ranks.
A308733 (program): Sum of the smallest parts of the partitions of n into 4 parts.
A308737 (program): Triangle of scaled 1-tiered binomial coefficients, T(n,k) = 2^(n+1)*(n-k,k)_1 (n >= 0, 0 <= k <= n), where (N,M)_1 is the 1-tiered binomial coefficient.
A308739 (program): Decimal expansion of BesselI(1/3,2/3)/BesselI(-2/3,2/3).
A308740 (program): Decimal expansion of BesselI(2/3,2/3)/BesselI(-1/3,2/3).
A308741 (program): Decimal expansion of BesselI(1/4,1/2)/BesselI(-3/4,1/2).
A308742 (program): Decimal expansion of BesselI(3/4,1/2)/BesselI(-1/4,1/2).
A308743 (program): Decimal expansion of BesselI(1/5,2/5)/BesselI(-4/5,2/5).
A308747 (program): Number of achiral m-color cyclic compositions of n (that is, number of cyclic compositions of n with reflection symmetry where each part of size m can be colored with one of m colors).
A308753 (program): a(n) = Sum_{d|n} d^(2*(d-1)).
A308754 (program): a(0) = 0, a(n) = a(n-1) + 1 if 2*n + 3 is prime, otherwise a(n) = a(n-1).
A308755 (program): a(n) = Sum_{d|n} d^(d-2).
A308756 (program): a(n) = Sum_{d|n} d^(2*(d-2)).
A308757 (program): a(n) = Sum_{d|n} d^(3*(d-2)).
A308758 (program): Sum of the third largest parts of the partitions of n into 4 parts.
A308759 (program): Sum of the second largest parts of the partitions of n into 4 parts.
A308763 (program): a(n) = Sum_{d|n} d^(n-2).
A308775 (program): Sum of all the parts in the partitions of n into 4 parts.
A308806 (program): Expansion of 1 / Sum_{k>=0} (-x)^(k*(3*k - 1)/2).
A308807 (program): a(n) = 4*5^(n-1) + n.
A308808 (program): Limiting row sequence of Pascal-like triangle A141021 (with index of asymmetry s = 4).
A308812 (program): a(n) = Sum_{k=1..n} binomial(n,k) * floor(n/k).
A308814 (program): a(n) = Sum_{d|n} n^(d-1).
A308819 (program): Product of prime powers <= n.
A308820 (program): a(n) = Product_{k=1..n} ceiling(n/k)!.
A308822 (program): Sum of all the parts in the partitions of n into 5 parts.
A308823 (program): Sum of the smallest parts of the partitions of n into 5 parts.
A308828 (program): Number of sequences that include all residues modulo n starting with x_0 = 0 and then x_i given recursively by x_{i+1} = a * x_i + c (mod n) where a and c are integers in the interval [0..n-1].
A308833 (program): Numbers r such that the r-th tetrahedral number A000292(r) divides r!.
A308860 (program): a(n)/n! is the expected number of left-to-right maxima in the lexicographical or colexicographical ordering of all the 3-subsets of [n] under a random permutation of [n], when the 3-subsets hold the worst order of ranks.
A308861 (program): Expansion of e.g.f. 1/(1 - x*(1 + x)*exp(x)).
A308862 (program): Expansion of e.g.f. 1/(1 - x*(1 + 3*x + x^2)*exp(x)).
A308863 (program): Expansion of e.g.f. (1 + LambertW(-x))/(1 + 2*LambertW(-x)).
A308864 (program): a(n) = Sum_{k>=0} (n*k + 1)^n/2^(k+1).
A308865 (program): a(n) = Sum_{k>=0} k^(2*n+1)/2^(k+1).
A308867 (program): Sum of all the parts in the partitions of n into 6 parts.
A308868 (program): Sum of the smallest parts in the partitions of n into 6 parts.
A308874 (program): Composite numbers that are neither squares nor oblongs.
A308876 (program): Expansion of e.g.f. exp(x)*(1 - x)/(1 - 2*x).
A308877 (program): Expansion of e.g.f. (1 + log(1 - x))/(1 + 2*log(1 - x)).
A308878 (program): Expansion of e.g.f. (1 - log(1 + x))/(1 - 2*log(1 + x)).
A308898 (program): Fixed point of the morphism 0 -> 01, 1 -> 2, 2 -> 3, 3 -> 012.
A308900 (program): An explicit example of an infinite sequence with a(1)=1 and, for n >= 2, a(n) and S(n) = Sum_{i=1..n} a(i) have no digit in common.
A308901 (program): Lexicographically earliest overlap-free binary sequence.
A308914 (program): Number of unordered pairs of non-intersecting non-selfintersecting paths with nodes that cover all vertices of a convex n-gon, n > 3.
A308926 (program): Sum of all the parts in the partitions of n into 7 parts.
A308927 (program): Sum of the smallest parts in the partitions of n into 7 parts.
A308939 (program): Expansion of e.g.f. 1 / (1 - Sum_{k>=1} (2*k - 1)!!*x^k/k!).
A308942 (program): a(n) = Product_{k=1..n} Stirling2(n,k) * k!.
A308943 (program): a(n) = Product_{d|n} binomial(n,d).
A308944 (program): a(n) = Product_{k=1..n} lcm(n,k) / (k * gcd(n,k)).
A308946 (program): Expansion of e.g.f. 1/(1 - x*(1 + x/2)*exp(x)).
A308947 (program): a(n) = A000129(A214028(n)+1) mod n.
A308948 (program): a(n) = A006190(A322907(n)+1) mod n.
A308949 (program): a(n) is the greatest divisor of A000129(n) that is coprime to A000129(m) for all positive integers m < n.
A308985 (program): Expansion of Product_{k>=0} (1 + 2*x^(2^k))^2.
A308986 (program): Expansion of Product_{k>=0} 1/(1 + 2*x^(2^k)).
A308989 (program): Sum of all the parts in the partitions of n into 8 parts.
A308990 (program): Sum of the smallest parts in the partitions of n into 8 parts.
A309000 (program): Number of strings of length n from a 3-symbol alphabet (A,B,C, say) containing at least one “A” and at least two “B”s.
A309006 (program): Product minus sum of the two previous terms in the sequence, with a(1) = 2 and a(2) = 5.
A309010 (program): Square array A(n, k) = Sum_{j=0..n} binomial(n,j)^k, n >= 0, k >= 0, read by antidiagonals.
A309014 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * (Stirling2(n,k) mod 2).
A309025 (program): Expansion of x * Product_{k>=0} (1 + x^(2^k) + x^(2^(k+3))).
A309026 (program): Expansion of x * Product_{k>=0} (1 + x^(2^k) + x^(2^(k+4))).
A309027 (program): Prime powers of the form 12*c^2 + 4*c + 3, where c is an arbitrary integer.
A309036 (program): a(n) = gcd(A007504(n), A014285(n)).
A309037 (program): Exponential Demlo sequence, like 12345…54321, but for powers of 2 instead.
A309043 (program): Expansion of Product_{k>=0} (1 + x^(2^k) + x^(2^(k+1)))^2.
A309048 (program): Expansion of Product_{k>=0} (1 + x^(3^k) + x^(2*3^k) - x^(3^(k+1))).
A309057 (program): a(0) = 1; a(2*n) = 3*a(n), a(2*n+1) = a(n).
A309074 (program): a(0) = 1; a(2*n) = 4*a(n), a(2*n+1) = a(n).
A309075 (program): Total number of black cells after n iterations of Langton’s ant with two ants on the grid placed side-by-side on neighboring squares and initially looking in the same direction.
A309076 (program): The Zeckendorf representation of n read as a NegaFibonacci representation.
A309077 (program): Maximum sum of base lengths over all minimal factorizations of length-n binary strings.
A309081 (program): a(n) = n - floor(n/2^2) + floor(n/3^2) - floor(n/4^2) + …
A309082 (program): a(n) = n - floor(n/2^3) + floor(n/3^3) - floor(n/4^3) + …
A309083 (program): a(n) = n - floor(n/2^4) + floor(n/3^4) - floor(n/4^4) + …
A309084 (program): a(n) = exp(3) * Sum_{k>=0} (-3)^k*k^n/k!.
A309085 (program): a(n) = exp(4) * Sum_{k>=0} (-4)^k*k^n/k!.
A309091 (program): Decimal expansion of 4/(Pi-2).
A309093 (program): The analog of A309077(n), but allowing fractional powers.
A309097 (program): Number of partitions of n avoiding the partition (4,2,1).
A309099 (program): Number of partitions of n avoiding the partition (4,3,1).
A309118 (program): Number of tiles added at iteration n when successively, layer by layer, building a symmetric patch of a rhombille tiling around a central star of six rhombs.
A309119 (program): a(n) is the number of 1’s minus the number of 2’s among the ternary representations of the integers in the interval [0..n].
A309124 (program): a(n) = n - 3 * floor(n/3) + 5 * floor(n/5) - 7 * floor(n/7) + …
A309125 (program): a(n) = n + 2^2 * floor(n/2^2) + 3^2 * floor(n/3^2) + 4^2 * floor(n/4^2) + …
A309126 (program): a(n) = n + 2^3 * floor(n/2^3) + 3^3 * floor(n/3^3) + 4^3 * floor(n/4^3) + …
A309131 (program): Triangle read by rows: T(n, k) = (n - k)*prime(1 + k), with 0 <= k < n.
A309138 (program): Nonnegative integers of the form x^2 + 23*y^2.
A309152 (program): Numbers that can be written as the sum of two primes whose difference is also prime.
A309153 (program): a(n) = A000203(n)*A001227(n).
A309174 (program): E.g.f. A(x) satisfies: A(x) = (1/(1 - x)) * Product_{k>=2} A(x^k)^(1/k).
A309176 (program): a(n) = n^2 * (n + 1)/2 - Sum_{k=1..n} sigma_2(k).
A309192 (program): a(n) = Sum_{k=1..n} mu(k)^2 * k * floor(n/k).
A309198 (program): Fixed point of the morphism 1 -> 12, 2 -> 3, 3 -> 4, 4 -> 123.
A309212 (program): Nearest integer to (4/3)^n.
A309214 (program): a(0)=0; thereafter a(n) = a(n-1)+n if a(n-1) even, otherwise a(n) = a(n-1)-n.
A309215 (program): a(0)=0; thereafter a(n) = a(n-1)+n if a(n-1) odd, otherwise a(n) = a(n-1)-n.
A309220 (program): Square array A read by antidiagonals: the columns are given by A(n,1)=1, A(n,2)=n+1, A(n,3) = n^2+2n+3, A(n,4) = n^3+3*n^2+6*n+4, A(n,5) = n^4+4*n^3+10*n^2+12*n+7, …, whose coefficients are given by A104509 (see also A118981).
A309222 (program): a(0) = 6; thereafter a(n) = a(n-1) + prime(n) if prime(n) > a(n-1), otherwise a(n) = a(n-1) - prime(n).
A309231 (program): Column 3 of the array at A326662 see Comments.
A309243 (program): Completely multiplicative with a(p) = p * a(p-1) for any prime number p.
A309250 (program): a(n) is the index of the binary string of a Post’s Correspondence Problem Encoding with index n.
A309252 (program): a(n) is the least number not in the sequence so far and whose absolute difference from a(n-1) is not in the sequence so far, with a(1) = 1 and a(2) = 2.
A309255 (program): a(n) = n + 1 - Sum_{k=0..n} (Stirling1(n,k) mod 2).
A309256 (program): a(n) = n + 1 - Sum_{k=0..n} (Stirling2(n,k) mod 2).
A309265 (program): Numbers k such that s + t = k with 0 < s < t where s and t-s are both prime.
A309266 (program): Expansion of (1 + x) * Product_{k>=1} (1 + x^k)/(1 - x^k).
A309267 (program): Expansion of (1 + x) * Product_{k>=1} 1/(1 - x^k)^k.
A309269 (program): Numbers that are the sum of two successive prime powers.
A309288 (program): a(0) = 0, a(1) = 1, and for any n > 1, a(n) = Sum_{k > 1} (-1)^k * a(floor(n/k)).
A309294 (program): (1/2) times the sum of the elements of all subsets of [n] whose sum is divisible by two.
A309296 (program): (1/4) times the sum of the elements of all subsets of [n] whose sum is divisible by four.
A309303 (program): Expansion of g.f. (sqrt(x+1) - sqrt(1-3*x))/(2*(x+1)^(3/2)).
A309307 (program): Number of unitary divisors of n (excluding 1).
A309315 (program): Number of 5-colorings of an n-wheel graph.
A309322 (program): Expansion of Sum_{k>=1} phi(k) * x^k/(1 - x^k)^3, where phi = Euler totient function (A000010).
A309323 (program): Expansion of Sum_{k>=1} phi(k) * x^k/(1 - x^k)^4, where phi = Euler totient function (A000010).
A309324 (program): Expansion of Sum_{k>=1} psi(k) * x^k/(1 + x^k), where psi = Dedekind psi function (A001615).
A309325 (program): Numbers that are the sum of two successive palindromes.
A309327 (program): a(n) = Product_{k=1..n-1} (4^k + 1).
A309330 (program): Numbers k such that 10*k^2 + 40 is a square.
A309331 (program): Expansion of (x+x^3+x^5)/(1-x-3*x^3-x^5).
A309332 (program): Number of ways the n-th triangular number T(n) = A000217(n) can be written as the sum of two positive triangular numbers.
A309335 (program): a(n) = n^3 if n odd, 7*n^3/8 if n even.
A309336 (program): a(n) = n^4 if n odd, 15*n^4/16 if n even.
A309337 (program): a(n) = n^3 if n odd, 3*n^3/4 if n even.
A309338 (program): a(n) = n^4 if n odd, 7*n^4/8 if n even.
A309346 (program): Sums of two refactorable numbers.
A309355 (program): Even numbers k such that k! is divisible by k*(k+1)/2.
A309372 (program): a(n) = n^2 - n^3 + n^4.
A309379 (program): Number of unordered pairs of 4-colorings of an n-wheel that differ in the coloring of exactly one vertex.
A309380 (program): Number of unordered pairs of 5-colorings of an n-wheel that differ in the coloring of exactly one vertex.
A309383 (program): a(n) is the smallest b > 1 such that when c is equal to any of the first n composites the congruence b^(c-1) == 1 (mod c) is satisfied, i.e., smallest b larger than 1 such that any member of the set of smallest n composites is a base-b Fermat pseudoprime.
A309391 (program): a(n) = gcd(n, A064169(n-2)) for n > 2.
A309395 (program): Number of integer-sided triangles with sides a,b,c, max(a,b) < c, a + c = n that are right triangles.
A309397 (program): a(n) = gcd(n^2, A001008(n-1)) for n > 1.
A309398 (program): a(n) is the nearest integer to log(log(10^n)).
A309407 (program): a(n) = round(sqrt(3*n + 9/4)), with a(0) = 1.
A309416 (program): a(n) = Sum_{k > 0} d^k(n), where d^k corresponds to the k-th iterate of A296239.
A309419 (program): Decimal expansion of e/(e-2).
A309420 (program): Decimal expansion of 4/(3*Pi-8).
A309434 (program): a(n) = floor(n*Im(2*e^(i*Pi/5))/(Im(2*e^(i*Pi/5)) - 1)).
A309443 (program): Coefficients in 5-adic expansion of 4^(1/3).
A309444 (program): The successive approximations up to 5^n for 5-adic integer 4^(1/3).
A309445 (program): Coefficients in 7-adic expansion of 2^(1/5).
A309446 (program): Coefficients in 7-adic expansion of 3^(1/5).
A309448 (program): Coefficients in 7-adic expansion of 5^(1/5).
A309449 (program): Coefficients in 7-adic expansion of 6^(1/5).
A309450 (program): The successive approximations up to 7^n for 7-adic integer 2^(1/5).
A309451 (program): The successive approximations up to 7^n for 7-adic integer 3^(1/5).
A309452 (program): The successive approximations up to 7^n for 7-adic integer 4^(1/5).
A309453 (program): The successive approximations up to 7^n for 7-adic integer 5^(1/5).
A309454 (program): The successive approximations up to 7^n for 7-adic integer 6^(1/5).
A309462 (program): Limiting row sequence for Pascal-like triangle A140995 (Stepan’s triangle with index of asymmetry s = 3).
A309472 (program): a(n) = n^n - n * n!.
A309474 (program): Digits of one of the two 3-adic integers sqrt(-1/2).
A309475 (program): Digits of one of the two 3-adic integers sqrt(-1/2). Here the sequence with first digit 2.
A309476 (program): One of the two successive approximations up to 3^n for the 3-adic integer sqrt(-1/2).
A309477 (program): One of the two successive approximations up to 3^n for the 3-adic integer sqrt(-1/2).
A309490 (program): Total number of adjacent node merge operations to turn a circular list of size n to a node.
A309491 (program): Let gcd_2(b,c) be the second-largest common divisor of non-coprime integers b and c; then a(n) = Sum_{k=1..n} gcd_2(k,n). If b and c are coprime, then gcd_2(b,c) = 0.
A309492 (program): a(1) = a(2) = 1, a(3) = 3, a(4) = 5, a(5) = 2; a(n) = a(n-a(n-2)) + a(n-a(n-3)) for n > 5.
A309498 (program): Least number k > 0 such that 4*p^2*k^2 + 1 is prime, where p = prime(n) is the n-th prime.
A309507 (program): Number of ways the n-th triangular number T(n) = A000217(n) can be written as the difference of two positive triangular numbers.
A309511 (program): Number of odd parts in the partitions of n into 3 parts.
A309513 (program): Number of even parts in the partitions of n into 3 parts.
A309525 (program): a(n) is the greatest divisor of A006190(n) that is coprime to A006190(m) for all positive integers m < n.
A309526 (program): a(n) is the greatest divisor of A001353(n) that is coprime to A001353(m) for all positive integers m < n.
A309535 (program): Total number of square parts in all compositions of n.
A309536 (program): Total number of triangular numbers in all compositions of n.
A309537 (program): Total number of Fibonacci parts in all compositions of n.
A309538 (program): Total number of factorial parts in all compositions of n.
A309555 (program): Triangle read by rows: T(n,k) = 3 + k*(n-k) for n >= 0, 0 <= k <= n.
A309557 (program): Number triangle with T(n,k) = 2 + 3*n - 2*k + 2*k*(n-k) for n >= 0, 0 <= k <= n.
A309559 (program): Triangle read by rows: T(n,k) = 1 + n + k^2/2 - k/2 + k*(n-k), n >= 0, 0 <= k <= n.
A309561 (program): Total sum of prime parts in all compositions of n.
A309574 (program): n-th prime minus its ternary (base 3) reversal.
A309575 (program): Expansion of Product_{k>=1} (1 - (x*(1 + x))^k).
A309579 (program): Maximum principal ratio of a strongly connected digraph on n nodes.
A309580 (program): Primes p with 1 zero in a fundamental period of A000129 mod p.
A309581 (program): Primes p with 2 zeros in a fundamental period of A000129 mod p.
A309583 (program): Numbers k with 1 zero in a fundamental period of A000129 mod k.
A309585 (program): Numbers k with 4 zeros in a fundamental period of A000129 mod k.
A309591 (program): Numbers k with 1 zero in a fundamental period of A006190 mod k.
A309593 (program): Numbers k with 4 zeros in a fundamental period of A006190 mod k.
A309616 (program): a(n) is the number of ways to represent 2*n in the decibinary system.
A309618 (program): a(n) = Sum_{k=0..floor(n/2)} k! * 2^k * (n - 2*k)!.
A309619 (program): a(n) = Sum_{k=0..floor(n/2)} k! * (n - 2*k)!.
A309649 (program): Sieved recursive primeth recurrence (see Comments for precise definition).
A309665 (program): a(1)=1; for n > 1, a(n) = a(n-1)/gcd(a(n-1),n) + n + 1.
A309674 (program): a(1) = 1, a(n) = hamming_weight(Sum_{k=1..n-1} a(k) ) for n>=2.
A309675 (program): a(n) = 4^n^2 + n!.
A309676 (program): Number of compositions (ordered partitions) of n into odd primes (including 1).
A309677 (program): G.f. A(x) satisfies: A(x) = A(x^3) / (1 - x)^2.
A309678 (program): G.f. A(x) satisfies: A(x) = A(x^4) / (1 - x)^2.
A309679 (program): G.f. A(x) satisfies: A(x) = A(x^5) / (1 - x)^2.
A309683 (program): Number of odd parts appearing among the smallest parts of the partitions of n into 3 parts.
A309684 (program): Sum of the odd parts appearing among the smallest parts of the partitions of n into 3 parts.
A309685 (program): Number of even parts appearing among the smallest parts of the partitions of n into 3 parts.
A309686 (program): Sum of the even parts appearing among the smallest parts of the partitions of n into 3 parts.
A309687 (program): Number of odd parts appearing among the second largest parts of the partitions of n into 3 parts.
A309688 (program): Sum of the odd parts appearing among the second largest parts of the partitions of n into 3 parts.
A309689 (program): Number of even parts appearing among the second largest parts of the partitions of n into 3 parts.
A309690 (program): Sum of the even parts appearing among the second largest parts of the partitions of n into 3 parts.
A309697 (program): a(n) is the digit that precedes the last nonzero digit of n^n.
A309698 (program): Digits of the 4-adic integer 3^(1/3).
A309700 (program): Digits of the 8-adic integer 7^(1/7).
A309702 (program): G.f. A(x) satisfies: A(x) = A(x^2) / (1 - x - x^2 - x^3).
A309705 (program): a(n) = lcm(a(n-1), n) - gcd(a(n-1), n) where a(1) = 1.
A309709 (program): Number of binary digits that change when n is multiplied by 4.
A309714 (program): The smallest possible nonnegative difference between the sum of the first n positive integers (A000217) and the sum of any number of the directly following and consecutive integers.
A309715 (program): Number of even parts appearing among the third largest parts of the partitions of n into 4 parts.
A309722 (program): Digits of the 4-adic integer (1/3)^(1/3).
A309724 (program): Digits of the 8-adic integer (1/7)^(1/7).
A309725 (program): Number of set partitions of {1,2,…,3n} with sizes in {[n, n, n], [2n, n], [3n]}.
A309726 (program): Numbers n such that n^2 - 12 is prime.
A309728 (program): G.f. A(x) satisfies: A(x) = A(x^2) / (1 - 2*x).
A309729 (program): Expansion of Sum_{k>=1} x^k/(1 - x^k - 2*x^(2*k)).
A309730 (program): Expansion of Sum_{k>=1} x^k * (1 - x^(3*k))/(1 - x^k)^4.
A309731 (program): Expansion of Sum_{k>=1} k * x^k/(1 - x^k)^3.
A309732 (program): Expansion of Sum_{k>=1} k^2 * x^k/(1 - x^k)^3.
A309750 (program): Number of letters in the English names of the months when the names are arranged in alphabetical order.
A309758 (program): Numbers that are sums of consecutive powers of 3.
A309759 (program): Numbers that are sums of consecutive powers of 4.
A309760 (program): Even numbers k such that k-p is composite where p is the largest prime <= k.
A309761 (program): Numbers that are sums of consecutive powers of 10.
A309772 (program): Least common multiple of prime(n+1)+1 and prime(n)+1.
A309773 (program): n directly precedes a(n) in Sharkovskii ordering.
A309775 (program): Expansion of e.g.f. exp(2 * (1 - exp(x)) + x).
A309779 (program): Squares that can be expressed as the sum of two positive squares but not as the sum of three positive squares.
A309786 (program): a(n) is the length of the cycle of the trajectory of 1/n under the map f(x) = min(2*x, 2-2*x).
A309788 (program): Product of digits of (n written in base 9).
A309790 (program): G.f. A(x) satisfies: A(x) = 2*x*(1 - x)*A(x^2) + x/(1 - x).
A309792 (program): Expansion of (2 + 6*x + 3*x^2 +4*x^3 - 10*x^4)/(1 - x - 4*x^4 + 4*x^5).
A309801 (program): If 2*n = Sum (2^e_k) then a(n) = Sum (e_k^n).
A309805 (program): Maximum number of nonattacking kings placeable on a hexagonal board with edge-length n in Glinski’s hexagonal chess.
A309808 (program): Primes formed by concatenating k and 2k+1.
A309809 (program): a(n) is the concatenation of n and 2n+1.
A309812 (program): Odd integers k such that k^2 is arithmetic mean of two other perfect squares.
A309816 (program): a(n) is the 2-adic valuation of A014664(n).
A309827 (program): a(n) is the square of the number consisting of one 1 and n 6’s: (166…6)^2.
A309831 (program): Number of even parts appearing among the smallest parts of the partitions of n into 5 parts.
A309840 (program): If n = Sum (2^e_k) then a(n) = Product (Fibonacci(e_k + 3)).
A309841 (program): If n = Sum (2^e_k) then a(n) = Product ((e_k + 2)!).
A309842 (program): a(n) is the total surface area of a hollow cubic block (defined as a block with a shell thickness of 1 cube) where n is the edge length of the removed volume.
A309845 (program): Expansion of e.g.f.: sec(x) + 2*tan(x).
A309867 (program): Expansion of Product_{k>0} (1+sqrt(1-4*x^k))/2.
A309873 (program): Period-doubling turn sequence, +1 when the 2-adic valuation of n is even or -1 when odd.
A309874 (program): a(n) = 2*n*Fibonacci(n-2) + (-1)^n + 1.
A309878 (program): The real part of b(n) where b(n) = (n + b(n-1)) * (1 + i) with b(-1)=0; i = sqrt(-1).
A309891 (program): a(n) is the total number of trailing zeros in the representations of n over all bases b >= 2.
A309892 (program): a(0) = 0, a(1) = 1, and for any n > 1, a(n) is the number of iterations of the map x -> x - gpf(x) (where gpf(x) denotes the greatest prime factor of x) required to reach 0 starting from n.
A309907 (program): a(n) is the square of the number consisting of one 1 and n 3’s: (133…3)^2.
A309914 (program): Distance from n to closest triangular number that is different from n.
A309945 (program): a(n) = floor(n - sqrt(2*n-1)).
A309948 (program): Decimal expansion of the real part of the square root of 1 + i.
A309949 (program): Decimal expansion of the imaginary part of the square root of 1 + i.
A309952 (program): XOR contraction of binary representation of n.
A309953 (program): Product of digits of (n written in base 3).
A309954 (program): Product of digits of (n written in base 4).
A309956 (program): Product of digits of (n written in base 5).
A309957 (program): Product of digits of (n written in base 6).
A309958 (program): Product of digits of (n written in base 7).
A309959 (program): Product of digits of (n written in base 8).
A309970 (program): Period 12: repeat [1, 1, 0, 0, -1, -1, -1, -1, 0, 0, 1, 1].
A309976 (program): Vacation Dyck paths. Discrete analog for vacation M/M/1 queue embedded chain.
A309978 (program): a(n) is the number of positive integers k such that there exists a nonnegative integer m with k + k^m = n.
A309983 (program): Numbers n resulting from adding the exponents of 2 associated with the “1” terms of their binary representation and subtracting the exponents of 2 associated with the “0” terms of their binary representation.
A309989 (program): Digits of one of the two 17-adic integers sqrt(-1).
A309990 (program): Digits of one of the two 17-adic integers sqrt(-1).
A309991 (program): Balanced quinary (base 5) enumeration (or balanced quinary representation) of integers, write n in quinary, and then replace 3’s with (-2)’s and 4’s with (-1)’s.
A309995 (program): Balanced septenary enumeration (or balanced septenary representation) of integers; write n in septenary and then replace 4’s with (-3),s, 5’s with (-2)’s, and 6’s with (-1)’s.
A310185 (program): Coordination sequence Gal.4.15.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310215 (program): Coordination sequence Gal.3.2.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310238 (program): Coordination sequence Gal.4.7.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310341 (program): Coordination sequence Gal.6.527.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310342 (program): Coordination sequence Gal.5.253.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310367 (program): Coordination sequence Gal.6.129.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310368 (program): Coordination sequence Gal.6.230.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310369 (program): Coordination sequence Gal.5.64.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310370 (program): Coordination sequence Gal.5.109.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310371 (program): Coordination sequence Gal.6.258.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310372 (program): Coordination sequence Gal.4.52.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310373 (program): Coordination sequence Gal.6.150.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310374 (program): Coordination sequence Gal.6.245.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310375 (program): Coordination sequence Gal.5.82.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310378 (program): Coordination sequence Gal.6.320.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310379 (program): Coordination sequence Gal.6.321.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310380 (program): Coordination sequence Gal.6.322.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310393 (program): Coordination sequence Gal.6.193.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310396 (program): Coordination sequence Gal.6.320.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310397 (program): Coordination sequence Gal.4.76.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310398 (program): Coordination sequence Gal.5.136.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310400 (program): Coordination sequence Gal.6.337.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310404 (program): Coordination sequence Gal.6.338.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310405 (program): Coordination sequence Gal.6.339.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310408 (program): Coordination sequence Gal.6.196.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310409 (program): Coordination sequence Gal.3.19.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310410 (program): Coordination sequence Gal.6.344.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310411 (program): Coordination sequence Gal.4.72.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310412 (program): Coordination sequence Gal.5.129.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310413 (program): Coordination sequence Gal.6.323.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310416 (program): Coordination sequence Gal.6.367.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310419 (program): Coordination sequence Gal.5.130.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310420 (program): Coordination sequence Gal.6.324.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310421 (program): Coordination sequence Gal.5.131.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310422 (program): Coordination sequence Gal.6.325.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310423 (program): Coordination sequence Gal.6.326.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310438 (program): Coordination sequence Gal.6.194.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310439 (program): Coordination sequence Gal.6.321.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310440 (program): Coordination sequence Gal.6.202.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310441 (program): Coordination sequence Gal.4.77.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310442 (program): Coordination sequence Gal.6.327.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310444 (program): Coordination sequence Gal.6.340.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310446 (program): Coordination sequence Gal.5.137.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310452 (program): Coordination sequence Gal.6.195.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310454 (program): Coordination sequence Gal.5.140.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310455 (program): Coordination sequence Gal.6.348.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310456 (program): Coordination sequence Gal.6.322.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310457 (program): Coordination sequence Gal.6.345.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310458 (program): Coordination sequence Gal.4.78.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310459 (program): Coordination sequence Gal.6.341.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310461 (program): Coordination sequence Gal.6.350.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310462 (program): Coordination sequence Gal.5.138.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310464 (program): Coordination sequence Gal.5.139.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310465 (program): Coordination sequence Gal.6.342.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310466 (program): Coordination sequence Gal.6.343.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310469 (program): Coordination sequence Gal.5.141.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310470 (program): Coordination sequence Gal.6.349.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310471 (program): Coordination sequence Gal.6.346.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310472 (program): Coordination sequence Gal.6.347.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310491 (program): Coordination sequence Gal.6.154.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310492 (program): Coordination sequence Gal.6.249.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310493 (program): Coordination sequence Gal.5.86.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310496 (program): Coordination sequence Gal.6.327.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310498 (program): Coordination sequence Gal.3.20.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310499 (program): Coordination sequence Gal.6.351.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310501 (program): Coordination sequence Gal.6.328.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310502 (program): Coordination sequence Gal.5.132.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310503 (program): Coordination sequence Gal.4.73.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310504 (program): Coordination sequence Gal.6.329.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310505 (program): Coordination sequence Gal.6.330.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310509 (program): Coordination sequence Gal.5.142.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310511 (program): Coordination sequence Gal.6.354.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310512 (program): Coordination sequence Gal.6.352.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310513 (program): Coordination sequence Gal.6.353.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310517 (program): Coordination sequence Gal.6.206.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310518 (program): Coordination sequence Gal.3.21.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310520 (program): Coordination sequence Gal.6.331.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310521 (program): Coordination sequence Gal.5.133.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310523 (program): Coordination sequence Gal.6.355.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310524 (program): Coordination sequence Gal.6.356.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310525 (program): Coordination sequence Gal.4.74.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310526 (program): Coordination sequence Gal.6.332.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310529 (program): Coordination sequence Gal.4.75.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310530 (program): Coordination sequence Gal.5.134.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310531 (program): Coordination sequence Gal.5.135.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310532 (program): Coordination sequence Gal.6.333.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310533 (program): Coordination sequence Gal.6.334.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310538 (program): Coordination sequence Gal.6.215.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310564 (program): Coordination sequence Gal.3.23.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310565 (program): Coordination sequence Gal.4.82.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310704 (program): Coordination sequence Gal.3.2.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A310725 (program): Coordination sequence Gal.5.19.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311101 (program): Coordination sequence Gal.3.47.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311196 (program): Coordination sequence Gal.6.115.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311225 (program): Coordination sequence Gal.6.216.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311257 (program): Coordination sequence Gal.6.115.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311262 (program): Coordination sequence Gal.6.216.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311285 (program): Coordination sequence Gal.4.70.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311287 (program): Coordination sequence Gal.4.50.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311289 (program): Coordination sequence Gal.5.107.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311290 (program): Coordination sequence Gal.5.62.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311312 (program): Coordination sequence Gal.6.118.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311331 (program): Coordination sequence Gal.6.119.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311332 (program): Coordination sequence Gal.6.120.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311344 (program): Coordination sequence Gal.5.95.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311356 (program): Coordination sequence Gal.6.219.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311366 (program): Coordination sequence Gal.6.288.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311384 (program): Coordination sequence Gal.6.220.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311385 (program): Coordination sequence Gal.6.221.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311426 (program): Coordination sequence Gal.6.115.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311433 (program): Coordination sequence Gal.5.97.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311434 (program): Coordination sequence Gal.6.216.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311440 (program): Coordination sequence Gal.5.50.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311458 (program): Coordination sequence Gal.5.95.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311475 (program): Coordination sequence Gal.6.118.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311481 (program): Coordination sequence Gal.6.219.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311501 (program): Coordination sequence Gal.4.38.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311512 (program): Coordination sequence Gal.6.130.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311523 (program): Coordination sequence Gal.6.119.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311535 (program): Coordination sequence Gal.5.53.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311536 (program): Coordination sequence Gal.6.120.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311541 (program): Coordination sequence Gal.6.221.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311548 (program): Coordination sequence Gal.5.54.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311549 (program): Coordination sequence Gal.6.132.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311552 (program): Coordination sequence Gal.5.55.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311553 (program): Coordination sequence Gal.6.133.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311554 (program): Coordination sequence Gal.6.134.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311586 (program): Coordination sequence Gal.4.58.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311593 (program): Coordination sequence Gal.6.192.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311601 (program): Coordination sequence Gal.6.230.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311612 (program): Coordination sequence Gal.5.98.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311613 (program): Coordination sequence Gal.6.231.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311625 (program): Coordination sequence Gal.5.99.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311626 (program): Coordination sequence Gal.6.232.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311633 (program): Coordination sequence Gal.5.100.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311634 (program): Coordination sequence Gal.6.233.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311635 (program): Coordination sequence Gal.6.234.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311683 (program): Coordination sequence Gal.6.419.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311687 (program): Coordination sequence Gal.6.125.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311705 (program): Coordination sequence Gal.4.89.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311709 (program): Coordination sequence Gal.4.121.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311710 (program): Coordination sequence Gal.4.68.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311801 (program): Coordination sequence Gal.6.115.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311804 (program): Coordination sequence Gal.6.216.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311806 (program): Coordination sequence Gal.4.60.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311807 (program): Coordination sequence Gal.3.12.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311816 (program): Coordination sequence Gal.5.95.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311843 (program): Coordination sequence Gal.4.38.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311861 (program): Coordination sequence Gal.6.130.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311889 (program): Coordination sequence Gal.6.129.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311914 (program): Coordination sequence Gal.4.58.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311924 (program): Coordination sequence Gal.6.118.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311931 (program): Coordination sequence Gal.3.17.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311932 (program): Coordination sequence Gal.6.192.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311943 (program): Coordination sequence Gal.4.80.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311958 (program): Coordination sequence Gal.5.53.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311964 (program): Coordination sequence Gal.6.131.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311993 (program): Coordination sequence Gal.5.98.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A311994 (program): Coordination sequence Gal.6.231.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312065 (program): Coordination sequence Gal.3.10.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312068 (program): Coordination sequence Gal.6.119.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312077 (program): Coordination sequence Gal.5.65.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312100 (program): Coordination sequence Gal.5.54.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312101 (program): Coordination sequence Gal.6.150.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312113 (program): Coordination sequence Gal.6.132.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312123 (program): Coordination sequence Gal.6.120.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312125 (program): Coordination sequence Gal.6.221.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312140 (program): Coordination sequence Gal.4.41.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312143 (program): Coordination sequence Gal.5.55.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312144 (program): Coordination sequence Gal.6.151.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312151 (program): Coordination sequence Gal.6.133.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312152 (program): Coordination sequence Gal.6.134.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312160 (program): Coordination sequence Gal.5.100.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312162 (program): Coordination sequence Gal.6.233.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312163 (program): Coordination sequence Gal.6.234.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312183 (program): Coordination sequence Gal.4.42.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312184 (program): Coordination sequence Gal.6.155.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312185 (program): Coordination sequence Gal.6.154.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312194 (program): Coordination sequence Gal.6.156.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312195 (program): Coordination sequence Gal.5.67.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312205 (program): Coordination sequence Gal.4.43.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312206 (program): Coordination sequence Gal.6.157.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312207 (program): Coordination sequence Gal.5.68.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312208 (program): Coordination sequence Gal.5.69.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312209 (program): Coordination sequence Gal.6.158.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312210 (program): Coordination sequence Gal.6.159.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312245 (program): Coordination sequence Gal.3.31.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312289 (program): Coordination sequence Gal.6.527.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312472 (program): Coordination sequence Gal.6.149.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312475 (program): Coordination sequence Gal.3.16.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312484 (program): Coordination sequence Gal.5.81.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312506 (program): Coordination sequence Gal.5.109.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312507 (program): Coordination sequence Gal.6.245.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312526 (program): Coordination sequence Gal.6.254.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312549 (program): Coordination sequence Gal.4.61.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312555 (program): Coordination sequence Gal.5.110.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312556 (program): Coordination sequence Gal.6.246.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312561 (program): Coordination sequence Gal.6.247.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312562 (program): Coordination sequence Gal.6.248.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312606 (program): Coordination sequence Gal.6.255.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312620 (program): Coordination sequence Gal.6.256.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312655 (program): Coordination sequence Gal.4.62.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312656 (program): Coordination sequence Gal.6.201.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312658 (program): Coordination sequence Gal.6.249.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312668 (program): Coordination sequence Gal.6.250.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312669 (program): Coordination sequence Gal.5.111.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312680 (program): Coordination sequence Gal.4.63.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312681 (program): Coordination sequence Gal.6.251.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312682 (program): Coordination sequence Gal.5.112.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312683 (program): Coordination sequence Gal.5.113.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312684 (program): Coordination sequence Gal.6.252.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312685 (program): Coordination sequence Gal.6.253.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312839 (program): Coordination sequence Gal.4.12.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312890 (program): Coordination sequence Gal.6.115.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312891 (program): Coordination sequence Gal.6.216.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312892 (program): Coordination sequence Gal.5.50.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312893 (program): Coordination sequence Gal.5.95.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312894 (program): Coordination sequence Gal.4.38.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312895 (program): Coordination sequence Gal.4.58.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312896 (program): Coordination sequence Gal.6.130.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312897 (program): Coordination sequence Gal.6.192.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312901 (program): Coordination sequence Gal.3.10.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312902 (program): Coordination sequence Gal.6.129.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312903 (program): Coordination sequence Gal.5.65.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312908 (program): Coordination sequence Gal.5.64.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312909 (program): Coordination sequence Gal.6.150.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312926 (program): Coordination sequence Gal.6.118.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312927 (program): Coordination sequence Gal.6.149.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312928 (program): Coordination sequence Gal.3.16.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312932 (program): Coordination sequence Gal.5.81.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312933 (program): Coordination sequence Gal.6.131.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312935 (program): Coordination sequence Gal.4.105.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312938 (program): Coordination sequence Gal.5.127.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312941 (program): Coordination sequence Gal.5.14.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312943 (program): Coordination sequence Gal.4.41.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312944 (program): Coordination sequence Gal.6.245.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312948 (program): Coordination sequence Gal.5.66.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312950 (program): Coordination sequence Gal.6.151.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312960 (program): Coordination sequence Gal.4.106.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312961 (program): Coordination sequence Gal.6.152.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312963 (program): Coordination sequence Gal.6.153.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312969 (program): Coordination sequence Gal.6.254.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312974 (program): Coordination sequence Gal.4.61.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312975 (program): Coordination sequence Gal.5.110.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312976 (program): Coordination sequence Gal.6.246.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312979 (program): Coordination sequence Gal.6.247.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312980 (program): Coordination sequence Gal.6.248.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312981 (program): Coordination sequence Gal.5.146.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312983 (program): Coordination sequence Gal.3.25.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A312998 (program): Coordination sequence Gal.4.85.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313023 (program): Coordination sequence Gal.6.130.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313024 (program): Coordination sequence Gal.6.119.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313025 (program): Coordination sequence Gal.5.65.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313026 (program): Coordination sequence Gal.5.54.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313031 (program): Coordination sequence Gal.6.258.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313045 (program): Coordination sequence Gal.6.258.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313046 (program): Coordination sequence Gal.6.454.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313051 (program): Coordination sequence Gal.3.33.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313053 (program): Coordination sequence Gal.5.114.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313054 (program): Coordination sequence Gal.6.318.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313057 (program): Coordination sequence Gal.6.132.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313062 (program): Coordination sequence Gal.6.154.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313064 (program): Coordination sequence Gal.6.195.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313076 (program): Coordination sequence Gal.6.156.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313078 (program): Coordination sequence Gal.5.67.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313088 (program): Coordination sequence Gal.6.120.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313089 (program): Coordination sequence Gal.6.221.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313090 (program): Coordination sequence Gal.5.114.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313099 (program): Coordination sequence Gal.6.259.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313100 (program): Coordination sequence Gal.5.100.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313103 (program): Coordination sequence Gal.6.260.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313110 (program): Coordination sequence Gal.3.13.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313113 (program): Coordination sequence Gal.6.133.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313115 (program): Coordination sequence Gal.4.43.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313116 (program): Coordination sequence Gal.5.116.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313117 (program): Coordination sequence Gal.6.134.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313118 (program): Coordination sequence Gal.6.234.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313119 (program): Coordination sequence Gal.6.157.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313124 (program): Coordination sequence Gal.6.250.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313125 (program): Coordination sequence Gal.5.111.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313126 (program): Coordination sequence Gal.6.198.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313127 (program): Coordination sequence Gal.5.69.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313128 (program): Coordination sequence Gal.6.158.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313129 (program): Coordination sequence Gal.6.159.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313136 (program): Coordination sequence Gal.6.256.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313137 (program): Coordination sequence Gal.6.263.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313144 (program): Coordination sequence Gal.5.219.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313145 (program): Coordination sequence Gal.6.264.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313147 (program): Coordination sequence Gal.4.63.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313148 (program): Coordination sequence Gal.6.251.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313152 (program): Coordination sequence Gal.5.112.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313154 (program): Coordination sequence Gal.6.252.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313155 (program): Coordination sequence Gal.6.253.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313174 (program): Coordination sequence Gal.6.478.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313193 (program): Coordination sequence Gal.4.106.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313201 (program): Coordination sequence Gal.5.115.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313212 (program): Coordination sequence Gal.6.263.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313213 (program): Coordination sequence Gal.6.260.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313228 (program): Coordination sequence Gal.6.155.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313229 (program): Coordination sequence Gal.6.201.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313232 (program): Coordination sequence Gal.3.14.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313237 (program): Coordination sequence Gal.6.202.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313241 (program): Coordination sequence Gal.5.86.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313246 (program): Coordination sequence Gal.6.264.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313247 (program): Coordination sequence Gal.6.261.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313251 (program): Coordination sequence Gal.6.203.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313255 (program): Coordination sequence Gal.5.87.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313258 (program): Coordination sequence Gal.4.54.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313259 (program): Coordination sequence Gal.6.204.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313262 (program): Coordination sequence Gal.6.205.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313276 (program): Coordination sequence Gal.6.265.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313280 (program): Coordination sequence Gal.3.15.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313281 (program): Coordination sequence Gal.6.206.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313283 (program): Coordination sequence Gal.6.207.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313284 (program): Coordination sequence Gal.5.88.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313289 (program): Coordination sequence Gal.4.55.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313290 (program): Coordination sequence Gal.6.208.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313292 (program): Coordination sequence Gal.4.56.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313293 (program): Coordination sequence Gal.5.89.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313295 (program): Coordination sequence Gal.5.90.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313296 (program): Coordination sequence Gal.6.209.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313297 (program): Coordination sequence Gal.6.210.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313416 (program): Coordination sequence Gal.4.106.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313474 (program): Coordination sequence Gal.6.118.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313475 (program): Coordination sequence Gal.6.119.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313476 (program): Coordination sequence Gal.5.53.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313477 (program): Coordination sequence Gal.5.54.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313480 (program): Coordination sequence Gal.4.41.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313485 (program): Coordination sequence Gal.6.254.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313487 (program): Coordination sequence Gal.4.42.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313494 (program): Coordination sequence Gal.6.155.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313498 (program): Coordination sequence Gal.6.255.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313506 (program): Coordination sequence Gal.5.114.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313510 (program): Coordination sequence Gal.3.13.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313514 (program): Coordination sequence Gal.6.154.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313515 (program): Coordination sequence Gal.6.264.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313519 (program): Coordination sequence Gal.6.196.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313525 (program): Coordination sequence Gal.6.249.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313533 (program): Coordination sequence Gal.6.131.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313534 (program): Coordination sequence Gal.6.231.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313537 (program): Coordination sequence Gal.5.66.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313538 (program): Coordination sequence Gal.5.110.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313540 (program): Coordination sequence Gal.6.151.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313543 (program): Coordination sequence Gal.6.196.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313546 (program): Coordination sequence Gal.6.156.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313556 (program): Coordination sequence Gal.6.132.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313560 (program): Coordination sequence Gal.6.201.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313561 (program): Coordination sequence Gal.4.53.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313565 (program): Coordination sequence Gal.5.219.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313568 (program): Coordination sequence Gal.3.14.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313569 (program): Coordination sequence Gal.6.197.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313572 (program): Coordination sequence Gal.6.250.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313575 (program): Coordination sequence Gal.6.202.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313580 (program): Coordination sequence Gal.5.111.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313581 (program): Coordination sequence Gal.4.57.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313583 (program): Coordination sequence Gal.6.345.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313589 (program): Coordination sequence Gal.5.141.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313591 (program): Coordination sequence Gal.6.346.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313592 (program): Coordination sequence Gal.6.347.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313610 (program): Coordination sequence Gal.5.136.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313611 (program): Coordination sequence Gal.6.337.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313613 (program): Coordination sequence Gal.4.72.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313614 (program): Coordination sequence Gal.5.129.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313615 (program): Coordination sequence Gal.6.323.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313616 (program): Coordination sequence Gal.4.57.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313619 (program): Coordination sequence Gal.6.260.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313620 (program): Coordination sequence Gal.6.348.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313622 (program): Coordination sequence Gal.6.203.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313623 (program): Coordination sequence Gal.5.87.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313635 (program): Coordination sequence Gal.4.54.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313639 (program): Coordination sequence Gal.6.204.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313646 (program): Coordination sequence Gal.6.205.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313680 (program): Coordination sequence Gal.6.120.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313681 (program): Coordination sequence Gal.6.221.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313682 (program): Coordination sequence Gal.5.55.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313683 (program): Coordination sequence Gal.5.100.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313684 (program): Coordination sequence Gal.6.259.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313685 (program): Coordination sequence Gal.4.43.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313687 (program): Coordination sequence Gal.6.202.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313688 (program): Coordination sequence Gal.6.151.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313689 (program): Coordination sequence Gal.6.152.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313692 (program): Coordination sequence Gal.5.136.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313693 (program): Coordination sequence Gal.6.197.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313694 (program): Coordination sequence Gal.4.63.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313696 (program): Coordination sequence Gal.6.327.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313698 (program): Coordination sequence Gal.6.157.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313702 (program): Coordination sequence Gal.6.337.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313703 (program): Coordination sequence Gal.5.129.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313704 (program): Coordination sequence Gal.6.323.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313707 (program): Coordination sequence Gal.6.198.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313711 (program): Coordination sequence Gal.6.251.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313717 (program): Coordination sequence Gal.6.151.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313718 (program): Coordination sequence Gal.6.133.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313719 (program): Coordination sequence Gal.5.116.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313720 (program): Coordination sequence Gal.6.153.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313721 (program): Coordination sequence Gal.5.129.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313722 (program): Coordination sequence Gal.6.248.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313726 (program): Coordination sequence Gal.6.340.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313729 (program): Coordination sequence Gal.6.134.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313730 (program): Coordination sequence Gal.6.234.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313735 (program): Coordination sequence Gal.6.646.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313737 (program): Coordination sequence Gal.6.363.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313738 (program): Coordination sequence Gal.6.158.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313739 (program): Coordination sequence Gal.6.159.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313740 (program): Coordination sequence Gal.5.309.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313744 (program): Coordination sequence Gal.6.345.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313745 (program): Coordination sequence Gal.6.199.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313746 (program): Coordination sequence Gal.5.113.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313747 (program): Coordination sequence Gal.6.200.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313752 (program): Coordination sequence Gal.5.300.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313753 (program): Coordination sequence Gal.6.253.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313754 (program): Coordination sequence Gal.4.142.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313768 (program): Coordination sequence Gal.6.261.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313769 (program): Coordination sequence Gal.6.339.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313772 (program): Coordination sequence Gal.6.328.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313773 (program): Coordination sequence Gal.5.131.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313774 (program): Coordination sequence Gal.6.622.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313778 (program): Coordination sequence Gal.6.203.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313779 (program): Coordination sequence Gal.6.328.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313780 (program): Coordination sequence Gal.3.23.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313781 (program): Coordination sequence Gal.6.617.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313782 (program): Coordination sequence Gal.5.289.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313786 (program): Coordination sequence Gal.4.128.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313788 (program): Coordination sequence Gal.6.326.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313789 (program): Coordination sequence Gal.6.208.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313791 (program): Coordination sequence Gal.6.354.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313793 (program): Coordination sequence Gal.4.134.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313794 (program): Coordination sequence Gal.6.619.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313795 (program): Coordination sequence Gal.6.647.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313799 (program): Coordination sequence Gal.3.53.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313801 (program): Coordination sequence Gal.5.291.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313802 (program): Coordination sequence Gal.6.209.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313803 (program): Coordination sequence Gal.6.210.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313811 (program): Coordination sequence Gal.6.649.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313813 (program): Coordination sequence Gal.5.309.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313814 (program): Coordination sequence Gal.5.314.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313824 (program): Coordination sequence Gal.6.195.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313825 (program): Coordination sequence Gal.6.322.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313826 (program): Coordination sequence Gal.4.78.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313827 (program): Coordination sequence Gal.5.141.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313829 (program): Coordination sequence Gal.6.203.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313831 (program): Coordination sequence Gal.6.328.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313833 (program): Coordination sequence Gal.6.341.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313834 (program): Coordination sequence Gal.6.616.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313835 (program): Coordination sequence Gal.5.299.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313836 (program): Coordination sequence Gal.3.23.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313837 (program): Coordination sequence Gal.6.618.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313838 (program): Coordination sequence Gal.6.649.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313842 (program): Coordination sequence Gal.5.289.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313846 (program): Coordination sequence Gal.5.308.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313849 (program): Coordination sequence Gal.5.309.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313853 (program): Coordination sequence Gal.6.156.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313854 (program): Coordination sequence Gal.6.250.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313855 (program): Coordination sequence Gal.5.87.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313859 (program): Coordination sequence Gal.6.340.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313860 (program): Coordination sequence Gal.5.132.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313862 (program): Coordination sequence Gal.6.354.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313869 (program): Coordination sequence Gal.6.206.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313872 (program): Coordination sequence Gal.6.617.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313873 (program): Coordination sequence Gal.3.21.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313875 (program): Coordination sequence Gal.4.134.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313876 (program): Coordination sequence Gal.6.342.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313877 (program): Coordination sequence Gal.6.646.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313878 (program): Coordination sequence Gal.6.647.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313879 (program): Coordination sequence Gal.6.343.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313884 (program): Coordination sequence Gal.6.347.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313886 (program): Coordination sequence Gal.4.143.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313887 (program): Coordination sequence Gal.6.331.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313888 (program): Coordination sequence Gal.5.311.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313889 (program): Coordination sequence Gal.6.652.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313890 (program): Coordination sequence Gal.6.648.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313891 (program): Coordination sequence Gal.4.142.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313892 (program): Coordination sequence Gal.5.309.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313893 (program): Coordination sequence Gal.5.310.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313894 (program): Coordination sequence Gal.5.133.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313898 (program): Coordination sequence Gal.5.291.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313899 (program): Coordination sequence Gal.6.620.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313900 (program): Coordination sequence Gal.6.621.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313905 (program): Coordination sequence Gal.6.352.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313906 (program): Coordination sequence Gal.5.308.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313907 (program): Coordination sequence Gal.5.315.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313908 (program): Coordination sequence Gal.6.639.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313909 (program): Coordination sequence Gal.6.648.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313912 (program): Coordination sequence Gal.6.207.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313913 (program): Coordination sequence Gal.6.331.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313915 (program): Coordination sequence Gal.6.647.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313916 (program): Coordination sequence Gal.5.293.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313918 (program): Coordination sequence Gal.6.332.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313922 (program): Coordination sequence Gal.6.356.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313923 (program): Coordination sequence Gal.4.139.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313924 (program): Coordination sequence Gal.6.626.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313926 (program): Coordination sequence Gal.4.140.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313927 (program): Coordination sequence Gal.5.135.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313928 (program): Coordination sequence Gal.5.302.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313929 (program): Coordination sequence Gal.6.334.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313930 (program): Coordination sequence Gal.6.638.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313937 (program): Coordination sequence Gal.6.650.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313938 (program): Coordination sequence Gal.6.662.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313952 (program): Coordination sequence Gal.4.143.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313954 (program): Coordination sequence Gal.3.55.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313955 (program): Coordination sequence Gal.4.144.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313959 (program): Coordination sequence Gal.5.311.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313962 (program): Coordination sequence Gal.3.53.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313967 (program): Coordination sequence Gal.5.315.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313975 (program): Coordination sequence Gal.4.145.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313978 (program): Coordination sequence Gal.6.653.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313979 (program): Coordination sequence Gal.6.654.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A313982 (program): Coordination sequence Gal.3.57.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314015 (program): Coordination sequence Gal.4.100.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314019 (program): Coordination sequence Gal.6.152.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314020 (program): Coordination sequence Gal.6.247.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314021 (program): Coordination sequence Gal.5.84.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314022 (program): Coordination sequence Gal.6.203.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314024 (program): Coordination sequence Gal.6.156.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314025 (program): Coordination sequence Gal.6.250.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314026 (program): Coordination sequence Gal.5.130.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314027 (program): Coordination sequence Gal.5.87.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314028 (program): Coordination sequence Gal.6.198.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314029 (program): Coordination sequence Gal.6.328.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314031 (program): Coordination sequence Gal.6.340.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314032 (program): Coordination sequence Gal.6.324.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314034 (program): Coordination sequence Gal.5.132.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314038 (program): Coordination sequence Gal.6.616.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314039 (program): Coordination sequence Gal.5.299.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314040 (program): Coordination sequence Gal.4.133.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314043 (program): Coordination sequence Gal.6.618.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314044 (program): Coordination sequence Gal.6.649.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314048 (program): Coordination sequence Gal.6.618.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314049 (program): Coordination sequence Gal.3.51.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314051 (program): Coordination sequence Gal.5.308.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314052 (program): Coordination sequence Gal.6.639.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314053 (program): Coordination sequence Gal.5.311.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314054 (program): Coordination sequence Gal.4.142.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314056 (program): Coordination sequence Gal.4.135.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314057 (program): Coordination sequence Gal.6.635.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314059 (program): Coordination sequence Gal.6.652.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314060 (program): Coordination sequence Gal.6.636.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314061 (program): Coordination sequence Gal.6.647.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314065 (program): Coordination sequence Gal.4.143.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314066 (program): Coordination sequence Gal.4.144.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314067 (program): Coordination sequence Gal.3.53.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314068 (program): Coordination sequence Gal.3.55.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314069 (program): Coordination sequence Gal.6.652.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314071 (program): Coordination sequence Gal.5.311.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314075 (program): Coordination sequence Gal.5.315.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314085 (program): Coordination sequence Gal.6.132.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314086 (program): Coordination sequence Gal.6.232.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314087 (program): Coordination sequence Gal.5.67.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314088 (program): Coordination sequence Gal.5.111.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314089 (program): Coordination sequence Gal.6.260.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314090 (program): Coordination sequence Gal.4.54.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314091 (program): Coordination sequence Gal.6.153.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314092 (program): Coordination sequence Gal.6.248.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314093 (program): Coordination sequence Gal.5.137.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314094 (program): Coordination sequence Gal.6.345.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314095 (program): Coordination sequence Gal.6.204.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314096 (program): Coordination sequence Gal.4.73.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314097 (program): Coordination sequence Gal.6.354.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314098 (program): Coordination sequence Gal.6.339.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314099 (program): Coordination sequence Gal.5.131.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314100 (program): Coordination sequence Gal.6.329.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314106 (program): Coordination sequence Gal.6.199.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314107 (program): Coordination sequence Gal.6.205.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314108 (program): Coordination sequence Gal.6.198.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314109 (program): Coordination sequence Gal.6.204.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314110 (program): Coordination sequence Gal.6.200.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314111 (program): Coordination sequence Gal.5.289.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314112 (program): Coordination sequence Gal.4.134.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314117 (program): Coordination sequence Gal.6.330.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314118 (program): Coordination sequence Gal.6.652.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314120 (program): Coordination sequence Gal.3.55.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314121 (program): Coordination sequence Gal.6.657.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314122 (program): Coordination sequence Gal.5.311.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314124 (program): Coordination sequence Gal.6.619.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314126 (program): Coordination sequence Gal.5.315.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314127 (program): Coordination sequence Gal.6.326.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314128 (program): Coordination sequence Gal.5.315.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314129 (program): Coordination sequence Gal.5.312.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314133 (program): Coordination sequence Gal.6.623.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314134 (program): Coordination sequence Gal.6.624.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314135 (program): Coordination sequence Gal.6.489.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314140 (program): Coordination sequence Gal.6.633.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314141 (program): Coordination sequence Gal.5.290.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314142 (program): Coordination sequence Gal.6.636.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314144 (program): Coordination sequence Gal.6.634.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314145 (program): Coordination sequence Gal.4.145.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314148 (program): Coordination sequence Gal.4.139.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314149 (program): Coordination sequence Gal.6.620.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314151 (program): Coordination sequence Gal.6.621.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314156 (program): Coordination sequence Gal.6.651.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314157 (program): Coordination sequence Gal.6.623.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314159 (program): Coordination sequence Gal.6.624.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314160 (program): Coordination sequence Gal.6.650.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314161 (program): Coordination sequence Gal.4.140.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314163 (program): Coordination sequence Gal.5.301.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314164 (program): Coordination sequence Gal.5.302.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314165 (program): Coordination sequence Gal.5.307.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314167 (program): Coordination sequence Gal.6.638.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314185 (program): Coordination sequence Gal.6.205.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314186 (program): Coordination sequence Gal.6.330.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314188 (program): Coordination sequence Gal.4.145.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314189 (program): Coordination sequence Gal.6.636.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314191 (program): Coordination sequence Gal.5.292.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314192 (program): Coordination sequence Gal.6.651.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314193 (program): Coordination sequence Gal.4.141.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314194 (program): Coordination sequence Gal.6.625.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314201 (program): Coordination sequence Gal.6.157.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314202 (program): Coordination sequence Gal.6.251.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314203 (program): Coordination sequence Gal.5.88.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314204 (program): Coordination sequence Gal.6.341.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314205 (program): Coordination sequence Gal.5.133.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314208 (program): Coordination sequence Gal.6.619.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314209 (program): Coordination sequence Gal.5.293.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314210 (program): Coordination sequence Gal.6.623.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314211 (program): Coordination sequence Gal.6.650.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314216 (program): Coordination sequence Gal.6.624.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314218 (program): Coordination sequence Gal.5.304.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314220 (program): Coordination sequence Gal.5.306.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314221 (program): Coordination sequence Gal.6.641.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314222 (program): Coordination sequence Gal.6.643.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314225 (program): Coordination sequence Gal.5.316.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314231 (program): Coordination sequence Gal.5.305.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314233 (program): Coordination sequence Gal.6.208.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314234 (program): Coordination sequence Gal.6.332.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314236 (program): Coordination sequence Gal.6.626.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314239 (program): Coordination sequence Gal.6.642.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314240 (program): Coordination sequence Gal.6.643.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314244 (program): Coordination sequence Gal.6.644.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314247 (program): Coordination sequence Gal.3.50.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314249 (program): Coordination sequence Gal.4.136.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314250 (program): Coordination sequence Gal.4.137.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314251 (program): Coordination sequence Gal.5.294.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314252 (program): Coordination sequence Gal.5.295.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314253 (program): Coordination sequence Gal.6.627.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314254 (program): Coordination sequence Gal.6.628.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314263 (program): Coordination sequence Gal.6.662.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314264 (program): Coordination sequence Gal.5.316.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314283 (program): Coordination sequence Gal.5.318.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314347 (program): Coordination sequence Gal.4.85.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314364 (program): Coordination sequence Gal.5.91.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314458 (program): Coordination sequence Gal.3.40.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314548 (program): Coordination sequence Gal.4.99.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314668 (program): Coordination sequence Gal.6.115.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314669 (program): Coordination sequence Gal.6.216.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314670 (program): Coordination sequence Gal.5.50.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314671 (program): Coordination sequence Gal.5.95.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314672 (program): Coordination sequence Gal.4.38.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314674 (program): Coordination sequence Gal.4.58.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314677 (program): Coordination sequence Gal.3.10.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314680 (program): Coordination sequence Gal.6.149.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314683 (program): Coordination sequence Gal.6.130.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314684 (program): Coordination sequence Gal.6.149.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314685 (program): Coordination sequence Gal.3.16.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314688 (program): Coordination sequence Gal.6.254.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314689 (program): Coordination sequence Gal.6.255.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314691 (program): Coordination sequence Gal.6.256.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314692 (program): Coordination sequence Gal.5.81.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314706 (program): Coordination sequence Gal.6.130.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314707 (program): Coordination sequence Gal.6.129.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314708 (program): Coordination sequence Gal.5.65.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314710 (program): Coordination sequence Gal.5.64.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314712 (program): Coordination sequence Gal.6.150.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314720 (program): Coordination sequence Gal.6.245.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314725 (program): Coordination sequence Gal.5.114.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314726 (program): Coordination sequence Gal.6.259.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314736 (program): Coordination sequence Gal.5.115.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314737 (program): Coordination sequence Gal.6.260.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314740 (program): Coordination sequence Gal.5.116.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314741 (program): Coordination sequence Gal.6.261.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314742 (program): Coordination sequence Gal.6.262.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314752 (program): Coordination sequence Gal.6.258.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314753 (program): Coordination sequence Gal.4.52.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314754 (program): Coordination sequence Gal.5.82.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314758 (program): Coordination sequence Gal.6.193.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314765 (program): Coordination sequence Gal.6.194.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314770 (program): Coordination sequence Gal.6.195.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314776 (program): Coordination sequence Gal.6.478.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314825 (program): Coordination sequence Gal.6.118.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314826 (program): Coordination sequence Gal.6.129.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314827 (program): Coordination sequence Gal.5.53.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314828 (program): Coordination sequence Gal.5.64.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314829 (program): Coordination sequence Gal.4.41.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314830 (program): Coordination sequence Gal.6.150.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314832 (program): Coordination sequence Gal.6.245.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314836 (program): Coordination sequence Gal.6.131.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314837 (program): Coordination sequence Gal.6.231.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314838 (program): Coordination sequence Gal.4.52.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314840 (program): Coordination sequence Gal.5.66.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314841 (program): Coordination sequence Gal.6.151.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314847 (program): Coordination sequence Gal.6.193.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314848 (program): Coordination sequence Gal.5.110.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314849 (program): Coordination sequence Gal.6.246.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314874 (program): Coordination sequence Gal.3.33.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314884 (program): Coordination sequence Gal.6.150.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314885 (program): Coordination sequence Gal.6.245.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314886 (program): Coordination sequence Gal.5.114.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314887 (program): Coordination sequence Gal.6.318.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314890 (program): Coordination sequence Gal.6.152.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314893 (program): Coordination sequence Gal.6.259.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314894 (program): Coordination sequence Gal.6.194.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314896 (program): Coordination sequence Gal.4.53.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314898 (program): Coordination sequence Gal.5.136.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314899 (program): Coordination sequence Gal.6.153.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314902 (program): Coordination sequence Gal.6.322.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314903 (program): Coordination sequence Gal.6.339.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314912 (program): Coordination sequence Gal.6.195.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314915 (program): Coordination sequence Gal.6.248.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314922 (program): Coordination sequence Gal.6.474.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314941 (program): Coordination sequence Gal.3.41.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314943 (program): Coordination sequence Gal.6.321.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314945 (program): Coordination sequence Gal.5.84.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314947 (program): Coordination sequence Gal.6.198.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314953 (program): Coordination sequence Gal.6.202.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314954 (program): Coordination sequence Gal.4.77.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314955 (program): Coordination sequence Gal.6.322.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314959 (program): Coordination sequence Gal.6.340.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314961 (program): Coordination sequence Gal.5.137.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314963 (program): Coordination sequence Gal.6.199.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314964 (program): Coordination sequence Gal.6.200.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314969 (program): Coordination sequence Gal.4.78.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314970 (program): Coordination sequence Gal.6.341.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314971 (program): Coordination sequence Gal.5.138.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314972 (program): Coordination sequence Gal.5.139.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314973 (program): Coordination sequence Gal.6.342.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A314974 (program): Coordination sequence Gal.6.343.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315018 (program): Coordination sequence Gal.6.193.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315019 (program): Coordination sequence Gal.6.320.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315020 (program): Coordination sequence Gal.4.76.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315024 (program): Coordination sequence Gal.6.196.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315026 (program): Coordination sequence Gal.6.337.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315030 (program): Coordination sequence Gal.6.344.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315032 (program): Coordination sequence Gal.4.72.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315033 (program): Coordination sequence Gal.5.129.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315034 (program): Coordination sequence Gal.6.323.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315036 (program): Coordination sequence Gal.4.122.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315050 (program): Coordination sequence Gal.5.140.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315052 (program): Coordination sequence Gal.6.338.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315053 (program): Coordination sequence Gal.6.345.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315056 (program): Coordination sequence Gal.6.348.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315057 (program): Coordination sequence Gal.4.57.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315058 (program): Coordination sequence Gal.6.339.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315060 (program): Coordination sequence Gal.5.141.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315061 (program): Coordination sequence Gal.5.130.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315062 (program): Coordination sequence Gal.6.324.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315064 (program): Coordination sequence Gal.6.347.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315067 (program): Coordination sequence Gal.6.349.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315068 (program): Coordination sequence Gal.5.131.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315069 (program): Coordination sequence Gal.6.325.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315070 (program): Coordination sequence Gal.6.326.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315075 (program): Coordination sequence Gal.6.350.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315170 (program): Coordination sequence Gal.6.119.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315171 (program): Coordination sequence Gal.6.220.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315172 (program): Coordination sequence Gal.5.54.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315173 (program): Coordination sequence Gal.5.99.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315175 (program): Coordination sequence Gal.4.42.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315177 (program): Coordination sequence Gal.6.255.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315178 (program): Coordination sequence Gal.4.62.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315182 (program): Coordination sequence Gal.6.155.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315183 (program): Coordination sequence Gal.6.201.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315185 (program): Coordination sequence Gal.5.115.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315186 (program): Coordination sequence Gal.6.263.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315187 (program): Coordination sequence Gal.3.14.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315188 (program): Coordination sequence Gal.6.265.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315191 (program): Coordination sequence Gal.5.186.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315194 (program): Coordination sequence Gal.6.154.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315195 (program): Coordination sequence Gal.6.249.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315196 (program): Coordination sequence Gal.6.202.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315198 (program): Coordination sequence Gal.5.86.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315202 (program): Coordination sequence Gal.6.194.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315203 (program): Coordination sequence Gal.6.321.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315204 (program): Coordination sequence Gal.4.77.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315207 (program): Coordination sequence Gal.5.140.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315208 (program): Coordination sequence Gal.6.348.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315210 (program): Coordination sequence Gal.6.327.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315211 (program): Coordination sequence Gal.3.20.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315212 (program): Coordination sequence Gal.6.351.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315214 (program): Coordination sequence Gal.5.142.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315215 (program): Coordination sequence Gal.6.352.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315216 (program): Coordination sequence Gal.6.353.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315237 (program): Coordination sequence Gal.4.128.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315244 (program): Coordination sequence Gal.6.156.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315245 (program): Coordination sequence Gal.6.250.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315246 (program): Coordination sequence Gal.6.203.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315247 (program): Coordination sequence Gal.5.87.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315253 (program): Coordination sequence Gal.6.132.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315254 (program): Coordination sequence Gal.6.232.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315255 (program): Coordination sequence Gal.5.67.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315256 (program): Coordination sequence Gal.5.111.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315257 (program): Coordination sequence Gal.4.100.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315258 (program): Coordination sequence Gal.6.260.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315259 (program): Coordination sequence Gal.4.54.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315260 (program): Coordination sequence Gal.6.340.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315261 (program): Coordination sequence Gal.6.204.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315264 (program): Coordination sequence Gal.6.328.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315265 (program): Coordination sequence Gal.5.132.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315266 (program): Coordination sequence Gal.6.205.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315267 (program): Coordination sequence Gal.6.215.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315270 (program): Coordination sequence Gal.5.137.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315271 (program): Coordination sequence Gal.6.345.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315272 (program): Coordination sequence Gal.6.351.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315273 (program): Coordination sequence Gal.4.73.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315274 (program): Coordination sequence Gal.6.354.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315275 (program): Coordination sequence Gal.6.329.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315277 (program): Coordination sequence Gal.6.330.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315302 (program): Coordination sequence Gal.6.152.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315303 (program): Coordination sequence Gal.6.247.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315304 (program): Coordination sequence Gal.5.84.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315305 (program): Coordination sequence Gal.6.338.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315306 (program): Coordination sequence Gal.5.130.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315307 (program): Coordination sequence Gal.6.616.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315308 (program): Coordination sequence Gal.5.299.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315309 (program): Coordination sequence Gal.4.133.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315310 (program): Coordination sequence Gal.6.618.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315311 (program): Coordination sequence Gal.3.51.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315312 (program): Coordination sequence Gal.6.639.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315315 (program): Coordination sequence Gal.6.198.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315316 (program): Coordination sequence Gal.6.324.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315318 (program): Coordination sequence Gal.6.622.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315319 (program): Coordination sequence Gal.5.289.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315320 (program): Coordination sequence Gal.4.135.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315321 (program): Coordination sequence Gal.6.635.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315322 (program): Coordination sequence Gal.6.636.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315326 (program): Coordination sequence Gal.6.204.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315327 (program): Coordination sequence Gal.6.329.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315329 (program): Coordination sequence Gal.6.635.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315333 (program): Coordination sequence Gal.5.292.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315334 (program): Coordination sequence Gal.6.623.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315335 (program): Coordination sequence Gal.6.624.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315337 (program): Coordination sequence Gal.4.145.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315339 (program): Coordination sequence Gal.4.141.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315340 (program): Coordination sequence Gal.6.625.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315342 (program): Coordination sequence Gal.5.303.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315343 (program): Coordination sequence Gal.5.304.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315344 (program): Coordination sequence Gal.6.640.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315345 (program): Coordination sequence Gal.6.641.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315351 (program): Coordination sequence Gal.6.650.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315361 (program): Coordination sequence Gal.5.328.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315395 (program): Coordination sequence Gal.6.120.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315396 (program): Coordination sequence Gal.6.221.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315397 (program): Coordination sequence Gal.5.55.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315398 (program): Coordination sequence Gal.5.100.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315399 (program): Coordination sequence Gal.4.43.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315400 (program): Coordination sequence Gal.6.256.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315401 (program): Coordination sequence Gal.4.63.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315402 (program): Coordination sequence Gal.5.116.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315403 (program): Coordination sequence Gal.6.264.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315404 (program): Coordination sequence Gal.6.265.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315405 (program): Coordination sequence Gal.3.15.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315406 (program): Coordination sequence Gal.6.206.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315409 (program): Coordination sequence Gal.6.195.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315410 (program): Coordination sequence Gal.6.322.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315411 (program): Coordination sequence Gal.4.78.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315412 (program): Coordination sequence Gal.5.141.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315413 (program): Coordination sequence Gal.6.157.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315414 (program): Coordination sequence Gal.6.206.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315415 (program): Coordination sequence Gal.6.207.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315416 (program): Coordination sequence Gal.5.142.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315417 (program): Coordination sequence Gal.6.354.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315418 (program): Coordination sequence Gal.3.21.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315420 (program): Coordination sequence Gal.6.355.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315421 (program): Coordination sequence Gal.6.356.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315423 (program): Coordination sequence Gal.5.208.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315425 (program): Coordination sequence Gal.6.341.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315426 (program): Coordination sequence Gal.6.331.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315427 (program): Coordination sequence Gal.5.133.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315432 (program): Coordination sequence Gal.6.650.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315444 (program): Coordination sequence Gal.6.133.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315445 (program): Coordination sequence Gal.6.233.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315447 (program): Coordination sequence Gal.5.112.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315450 (program): Coordination sequence Gal.6.261.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315452 (program): Coordination sequence Gal.4.55.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315453 (program): Coordination sequence Gal.6.207.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315454 (program): Coordination sequence Gal.6.331.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315455 (program): Coordination sequence Gal.6.208.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315459 (program): Coordination sequence Gal.6.134.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315460 (program): Coordination sequence Gal.6.234.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315461 (program): Coordination sequence Gal.5.69.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315462 (program): Coordination sequence Gal.6.339.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315463 (program): Coordination sequence Gal.5.113.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315464 (program): Coordination sequence Gal.6.346.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315465 (program): Coordination sequence Gal.6.157.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315466 (program): Coordination sequence Gal.6.158.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315467 (program): Coordination sequence Gal.6.159.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315468 (program): Coordination sequence Gal.5.300.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315469 (program): Coordination sequence Gal.4.134.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315470 (program): Coordination sequence Gal.6.253.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315471 (program): Coordination sequence Gal.3.52.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315474 (program): Coordination sequence Gal.6.341.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315475 (program): Coordination sequence Gal.5.133.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315476 (program): Coordination sequence Gal.6.619.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315477 (program): Coordination sequence Gal.5.293.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315478 (program): Coordination sequence Gal.6.209.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315479 (program): Coordination sequence Gal.6.210.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315481 (program): Coordination sequence Gal.5.139.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315482 (program): Coordination sequence Gal.6.347.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315485 (program): Coordination sequence Gal.6.205.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315486 (program): Coordination sequence Gal.6.330.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315488 (program): Coordination sequence Gal.6.343.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315489 (program): Coordination sequence Gal.5.292.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315490 (program): Coordination sequence Gal.4.141.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315491 (program): Coordination sequence Gal.6.625.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315492 (program): Coordination sequence Gal.6.625.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315495 (program): Coordination sequence Gal.5.135.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315496 (program): Coordination sequence Gal.5.306.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315498 (program): Coordination sequence Gal.6.334.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315499 (program): Coordination sequence Gal.6.643.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315505 (program): Coordination sequence Gal.3.59.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315507 (program): Coordination sequence Gal.6.199.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315508 (program): Coordination sequence Gal.6.325.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315509 (program): Coordination sequence Gal.6.633.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315510 (program): Coordination sequence Gal.5.290.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315511 (program): Coordination sequence Gal.4.139.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315512 (program): Coordination sequence Gal.6.626.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315515 (program): Coordination sequence Gal.6.200.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315516 (program): Coordination sequence Gal.6.326.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315517 (program): Coordination sequence Gal.6.208.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315518 (program): Coordination sequence Gal.5.291.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315519 (program): Coordination sequence Gal.6.332.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315520 (program): Coordination sequence Gal.4.140.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315521 (program): Coordination sequence Gal.6.620.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315522 (program): Coordination sequence Gal.6.621.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315523 (program): Coordination sequence Gal.5.301.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315525 (program): Coordination sequence Gal.3.49.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315526 (program): Coordination sequence Gal.6.637.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315527 (program): Coordination sequence Gal.6.638.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315530 (program): Coordination sequence Gal.4.148.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315534 (program): Coordination sequence Gal.6.624.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315535 (program): Coordination sequence Gal.5.304.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315536 (program): Coordination sequence Gal.5.306.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315537 (program): Coordination sequence Gal.6.641.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315538 (program): Coordination sequence Gal.3.50.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315539 (program): Coordination sequence Gal.6.642.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315540 (program): Coordination sequence Gal.6.643.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315541 (program): Coordination sequence Gal.4.136.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315543 (program): Coordination sequence Gal.4.137.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315546 (program): Coordination sequence Gal.5.294.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315547 (program): Coordination sequence Gal.5.295.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315548 (program): Coordination sequence Gal.6.627.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315549 (program): Coordination sequence Gal.6.628.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315563 (program): Coordination sequence Gal.5.320.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315610 (program): Coordination sequence Gal.5.256.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315614 (program): Coordination sequence Gal.5.318.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315629 (program): Coordination sequence Gal.6.133.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315630 (program): Coordination sequence Gal.6.233.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315631 (program): Coordination sequence Gal.5.68.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315632 (program): Coordination sequence Gal.5.112.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315633 (program): Coordination sequence Gal.6.261.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315634 (program): Coordination sequence Gal.4.55.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315635 (program): Coordination sequence Gal.5.138.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315636 (program): Coordination sequence Gal.6.346.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315637 (program): Coordination sequence Gal.6.352.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315638 (program): Coordination sequence Gal.6.355.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315639 (program): Coordination sequence Gal.4.74.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315641 (program): Coordination sequence Gal.6.208.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315642 (program): Coordination sequence Gal.6.332.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315643 (program): Coordination sequence Gal.6.199.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315644 (program): Coordination sequence Gal.6.325.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315645 (program): Coordination sequence Gal.6.633.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315646 (program): Coordination sequence Gal.5.290.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315647 (program): Coordination sequence Gal.4.139.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315649 (program): Coordination sequence Gal.6.626.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315650 (program): Coordination sequence Gal.6.623.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315651 (program): Coordination sequence Gal.5.303.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315653 (program): Coordination sequence Gal.5.305.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315654 (program): Coordination sequence Gal.3.49.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315655 (program): Coordination sequence Gal.6.644.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315666 (program): Coordination sequence Gal.6.134.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315667 (program): Coordination sequence Gal.6.234.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315668 (program): Coordination sequence Gal.5.69.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315669 (program): Coordination sequence Gal.5.113.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315670 (program): Coordination sequence Gal.6.262.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315671 (program): Coordination sequence Gal.4.56.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315672 (program): Coordination sequence Gal.5.139.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315673 (program): Coordination sequence Gal.6.347.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315674 (program): Coordination sequence Gal.6.353.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315675 (program): Coordination sequence Gal.6.356.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315676 (program): Coordination sequence Gal.4.75.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315678 (program): Coordination sequence Gal.6.158.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315679 (program): Coordination sequence Gal.6.252.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315680 (program): Coordination sequence Gal.5.89.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315681 (program): Coordination sequence Gal.6.159.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315682 (program): Coordination sequence Gal.6.253.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315683 (program): Coordination sequence Gal.6.634.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315684 (program): Coordination sequence Gal.5.291.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315685 (program): Coordination sequence Gal.4.140.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315686 (program): Coordination sequence Gal.6.209.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315687 (program): Coordination sequence Gal.6.210.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315688 (program): Coordination sequence Gal.6.343.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315689 (program): Coordination sequence Gal.6.624.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315690 (program): Coordination sequence Gal.5.135.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315691 (program): Coordination sequence Gal.5.306.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315692 (program): Coordination sequence Gal.6.334.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315693 (program): Coordination sequence Gal.3.50.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315695 (program): Coordination sequence Gal.6.620.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315696 (program): Coordination sequence Gal.5.301.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315697 (program): Coordination sequence Gal.6.621.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315698 (program): Coordination sequence Gal.5.302.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315699 (program): Coordination sequence Gal.6.637.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315700 (program): Coordination sequence Gal.6.638.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315701 (program): Coordination sequence Gal.4.136.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315702 (program): Coordination sequence Gal.6.641.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315703 (program): Coordination sequence Gal.6.643.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315704 (program): Coordination sequence Gal.4.137.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315706 (program): Coordination sequence Gal.5.294.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315707 (program): Coordination sequence Gal.5.295.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315709 (program): Coordination sequence Gal.6.627.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315710 (program): Coordination sequence Gal.6.628.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315725 (program): Coordination sequence Gal.6.158.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315726 (program): Coordination sequence Gal.6.252.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315727 (program): Coordination sequence Gal.5.89.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315728 (program): Coordination sequence Gal.6.342.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315729 (program): Coordination sequence Gal.5.134.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315730 (program): Coordination sequence Gal.6.620.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315731 (program): Coordination sequence Gal.5.301.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315732 (program): Coordination sequence Gal.6.640.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315733 (program): Coordination sequence Gal.6.642.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315734 (program): Coordination sequence Gal.4.136.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315735 (program): Coordination sequence Gal.6.159.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315736 (program): Coordination sequence Gal.6.253.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315737 (program): Coordination sequence Gal.5.90.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315738 (program): Coordination sequence Gal.6.343.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315739 (program): Coordination sequence Gal.5.135.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315740 (program): Coordination sequence Gal.6.209.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315741 (program): Coordination sequence Gal.6.210.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315742 (program): Coordination sequence Gal.5.302.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315743 (program): Coordination sequence Gal.6.334.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315744 (program): Coordination sequence Gal.6.643.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315745 (program): Coordination sequence Gal.4.137.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315746 (program): Coordination sequence Gal.6.637.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315747 (program): Coordination sequence Gal.6.638.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315748 (program): Coordination sequence Gal.5.294.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315749 (program): Coordination sequence Gal.5.295.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315750 (program): Coordination sequence Gal.6.627.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315751 (program): Coordination sequence Gal.6.628.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315753 (program): Coordination sequence Gal.5.316.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315754 (program): Coordination sequence Gal.6.209.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315755 (program): Coordination sequence Gal.6.333.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315756 (program): Coordination sequence Gal.6.637.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315757 (program): Coordination sequence Gal.5.294.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315758 (program): Coordination sequence Gal.6.210.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315759 (program): Coordination sequence Gal.6.334.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315760 (program): Coordination sequence Gal.6.638.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315761 (program): Coordination sequence Gal.5.295.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315762 (program): Coordination sequence Gal.6.627.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315763 (program): Coordination sequence Gal.6.628.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315767 (program): Coordination sequence Gal.6.627.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315768 (program): Coordination sequence Gal.6.628.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315769 (program): Coordination sequence Gal.6.370.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315847 (program): Coordination sequence Gal.5.232.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315886 (program): Coordination sequence Gal.6.527.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315889 (program): Coordination sequence Gal.5.253.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315907 (program): Coordination sequence Gal.3.40.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315943 (program): Coordination sequence Gal.5.229.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A315972 (program): Coordination sequence Gal.3.41.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A316026 (program): Coordination sequence Gal.3.36.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A316047 (program): Coordination sequence Gal.6.374.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
A316087 (program): Expansion of 1/(1 + Sum_{k>=1} k^2 * x^k).
A316088 (program): Expansion of 1/(1 + Sum_{k>=1} k^3 * x^k).
A316091 (program): Heinz numbers of integer partitions of prime numbers.
A316100 (program): Numbers k such that k is deficient but k+1 is abundant, that is, a deficient number followed by an abundant number.
A316131 (program): Decimal expansion of the least x such that 1/x + 1/(x+1) + 1/(x+3) = 1, negated.
A316132 (program): Decimal expansion of the middle x such that 1/x + 1/(x+1) + 1/(x+3) = 1, negated.
A316133 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+1) + 1/(x+3) = 1.
A316134 (program): Decimal expansion of the least x such that 1/x + 1/(x+2) + 1/(x+3) = 1 (negated).
A316135 (program): Decimal expansion of the middle x such that 1/x + 1/(x+2) + 1/(x+3) = 1 (negated).
A316136 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+2) + 1/(x+3) = 1.
A316137 (program): Decimal expansion of the least x such that 1/x + 1/(x+2) + 1/(x+4) = 1.
A316138 (program): Decimal expansion of the middle x such that 1/x + 1/(x+2) + 1/(x+4) = 1.
A316139 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+2) + 1/(x+4) = 1.
A316140 (program): Denominator of the autosequence 2/((n+2)*(n+3)) difference table written by antidiagonals.
A316148 (program): Number of non-congruent solutions of x^2+y^2 == z^2+w^2 (mod n).
A316160 (program): Number of pairs of compositions of n corresponding to a seaweed algebra of index n-3.
A316161 (program): Decimal expansion of the least x such that 1/x + 1/(x+1) + 1/(x+2) = 2.
A316162 (program): Decimal expansion of the middle x such that 1/x + 1/(x+1) + 1/(x+2) = 2.
A316163 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+1) + 1/(x+2) = 2.
A316164 (program): Decimal expansion of the least x such that 1/x + 1/(x+1) + 1/(x+3) = 2.
A316165 (program): Decimal expansion of the middle x such that 1/x + 1/(x+1) + 1/(x+3) = 2.
A316166 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+1) + 1/(x+3) = 2.
A316167 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+2) + 1/(x+4) = 2.
A316168 (program): Decimal expansion of the middle x such that 1/x + 1/(x+2) + 1/(x+4) = 2, negated.
A316169 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+2) + 1/(x+4) = 2, negated.
A316193 (program): Number of symmetric self-avoiding polygons on honeycomb net with perimeter 2*n, not counting rotations and reflections as distinct.
A316224 (program): a(n) = n*(2*n + 1)*(4*n + 1).
A316246 (program): Decimal expansion of the least x such that 1/x + 1/(x+1) + 1/(x+2) = 3.
A316247 (program): Decimal expansion of the middle x such that 1/x + 1/(x+1) + 1/(x+2) = 3.
A316248 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+1) + 1/(x+2) = 3.
A316249 (program): Decimal expansion of the least x such that 1/x + 1/(x+1) + 1/(x+3) = 3.
A316250 (program): Decimal expansion of the middle x such that 1/x + 1/(x+1) + 1/(x+3) = 3.
A316251 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+1) + 1/(x+3) = 3.
A316252 (program): Decimal expansion of the least x such that 1/x + 1/(x+2) + 1/(x+3) = 3.
A316253 (program): Decimal expansion of the middle x such that 1/x + 1/(x+2) + 1/(x+3) = 3.
A316254 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+2) + 1/(x+3) = 3.
A316255 (program): Decimal expansion of the least x such that 1/x + 1/(x+2) + 1/(x+4) = 3.
A316256 (program): Decimal expansion of the middle x such that 1/x + 1/(x+2) + 1/(x+4) = 3.
A316257 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+2) + 1/(x+4) = 3.
A316258 (program): Decimal expansion of the least x such that 1/x + 1/(x+3) + 1/(x+4) = 3 (negated).
A316259 (program): Decimal expansion of the middle x such that 1/x + 1/(x+3) + 1/(x+4) = 3 (negated).
A316260 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+3) + 1/(x+4) = 3.
A316261 (program): The number of ways to induce a single pinch on a compact 2-manifold with n handles. (Note: The manifold is embedded in Euclidean 2-space, and each pinch partitions it into at most two submanifolds.)
A316262 (program): Numbers k such that gcd(k, floor(phi*k)) > 1, where phi is the golden ratio.
A316269 (program): Array T(n,k) = n*T(n,k-1) - T(n,k-2) read by upward antidiagonals, with T(n,0) = 0, T(n,1) = 1, n >= 2.
A316270 (program): Number of tricolorable prime knots with n minimal crossings.
A316275 (program): Lucas analog to A101361.
A316296 (program): a(n) = Sum_{k=1..n} f(k, n), where f(i, j) is the number of multiples of i greater than j and less than 2*j.
A316297 (program): a(n) = n! times the denominator of the n-th harmonic number H(n).
A316316 (program): Coordination sequence for tetravalent node in chamfered version of square grid.
A316317 (program): Coordination sequence for trivalent node in chamfered version of square grid.
A316319 (program): Coordination sequence for a trivalent node in a chamfered version of the 3^6 triangular tiling of the plane.
A316320 (program): Coordination sequence for a hexavalent node in a chamfered version of the 3^6 triangular tiling of the plane.
A316322 (program): Sum of piles of first n primes: a(n) = Sum(prime(i)*(2*i-1): 1<=i<=n).
A316324 (program): Indices of 1’s in A305389.
A316325 (program): Indices of 2’s in A305389.
A316326 (program): Indices of 3’s in A305389.
A316327 (program): First differences of indices of 1’s in A305389.
A316330 (program): a(n) = A000085(4*n)/2^n.
A316331 (program): a(n) = A000085(4*n+1)/2^n.
A316332 (program): a(n) = A000085(4*n+2)/2^(n+1).
A316333 (program): a(n) = A000085(4*n+3)/2^(n+2).
A316340 (program): Image of 1 under repeated application of the morphism 1 -> 12312, 2 -> 341, 3 -> 34134, 4 -> 123,
A316341 (program): Characteristic function of the factorials 1!, 2!, 3!, …
A316342 (program): Fibonacci word A003849 with first two terms replaced by 2’s.
A316344 (program): An example of a word that is uniform morphic, but neither pure morphic, primitive morphic, nor recurrent.
A316345 (program): An example of a word that is uniform morphic and recurrent, but neither pure morphic nor primitive morphic.
A316346 (program): a(n) = A316297(n+1)/A316297(n).
A316347 (program): a(n) = n^2 mod(10^m), where m is the number of digits in n (written in base 10).
A316351 (program): Numbers k such that k^2 + 1 has exactly four distinct prime factors.
A316352 (program): Decimal expansion of (BesselI(0,1/2)-BesselI(1,1/2))/(BesselI(0,1/2)-3*BesselI(1,1/2)).
A316355 (program): 2k-1 appears 2k times after 2k-2 appears once.
A316357 (program): Partial sums of A316316.
A316358 (program): Partial sums of A316317.
A316359 (program): a(n) is the number of solutions to the Diophantine equation i^3 + j^3 + k^3 = n^3, where 0 < i <= j <= k.
A316363 (program): O.g.f. A(x) satisfies: Sum_{n>=1} (x + (-1)^n*A(x))^n / n = 0.
A316371 (program): G.f.: A(x) = Sum_{n>=0} binomial(3*(n+1), n)/(n+1) * x^n / (1+x)^(2*(n+1)).
A316384 (program): Number of ways to stack n triangles symmetrically in a valley (pointing upwards or downwards depending on row parity).
A316385 (program): Lexicographically earliest sequence of distinct positive terms such that for any n > 0, a(n) AND a(2*n) = a(n) (where AND denotes the binary AND operator).
A316386 (program): Binomial transform of [0, 1, 2, -3, -4, 5, 6, -7, -8, …].
A316457 (program): Expansion of x*(31 + 326*x + 336*x^2 + 26*x^3 + x^4) / (1 - x)^6.
A316458 (program): Expansion of 60*x*(1 + 4*x + x^2) / (1 - x)^5.
A316459 (program): Expansion of 30*x*(1 + x) / (1 - x)^4.
A316461 (program): Expansion of Product_{k>=1} 1/(1-x^k)^(9*k).
A316462 (program): Expansion of Product_{k>=1} 1/(1-x^k)^(10*k).
A316463 (program): Expansion of Product_{k>0} (1 - x^k)^(4*k).
A316464 (program): Expansion of Product_{k>0} (1 - x^k)^(5*k).
A316466 (program): a(n) = 2*n*(7*n - 3).
A316505 (program): a(n) is the smallest number k > 1 such that k^n - 1 is divisible by 3^n.
A316523 (program): Number of odd multiplicities minus number of even multiplicities in the canonical prime factorization of n.
A316524 (program): Signed sum over the prime indices of n.
A316528 (program): a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3) for n > 2, a(0)=1, a(1)=4, a(2)=10.
A316529 (program): Heinz numbers of totally strong integer partitions.
A316533 (program): a(n) is the Sprague-Grundy value of the Node-Kayles game played on the generalized Petersen graph P(n,2).
A316553 (program): Number of elements of order 2 in the group SL(2, Z(n)).
A316562 (program): Koechel number for the works of W. A. Mozart rounded from age 11.
A316568 (program): Largest k such that 1^2 + n, 2^2 + n, …, k^2 + n are composite.
A316569 (program): a(n) = Jacobi (or Kronecker) symbol (n, 15).
A316570 (program): Multiplicative digital root of sigma(n).
A316571 (program): a(1) = 1; for n > 1: a(n) = smallest number such that (Sum_{k=1..n} a(k)) is divisible by n - 1
A316592 (program): a(n) equals the coefficient of x^n in Sum_{m>=0} (x^m + 2 + 1/x^m)^m for n >= 1.
A316626 (program): a(1)=a(2)=a(3)=1; a(n) = a(n-2*a(n-1))+a(n-1-2*a(n-2)) for n > 3.
A316627 (program): a(1)=2, a(2)=3; a(n) = a(n+1-a(n-1))+a(n-a(n-2)) for n > 2.
A316628 (program): a(1)=1, a(2)=2, a(3)=2, a(4)=3; a(n) = a(n-a(n-1))+a(n-1-a(n-2)-a(n-2-a(n-2))) for n > 4.
A316631 (program): Expansion of A(x) = x*(1+3*x^2+x^3+3*x^4+x^6)/(1-x^4)^2.
A316649 (program): Triangle read by rows in which T(n,k) is the number of length k chains from (0,0) to (n,n) of the poset [n] X [n] ordered by the product order, 0 <= k <= 2n, n>=0.
A316660 (program): Number of n-bit binary necklaces (unmarked cyclic n-bit binary strings) containing no runs of length > 2.
A316661 (program): a(n) = ceiling(sqrt((2*n)^n)).
A316662 (program): Expansion of f(x, x^2) * psi(x^3)^3 in powers of x where psi() is a Ramanujan theta function and f(, ) is Ramanujan’s general theta function.
A316663 (program): Floor(sqrt((2*n)^(n+1)))
A316666 (program): Number of simple relaxed compacted binary trees of right height at most one with no sequences on level 1 and no final sequences on level 0.
A316669 (program): Squares visited by queen moves on a diagonally numbered board and moving to the lowest available unvisited square at each step.
A316670 (program): Squares visited by bishop moves on a diagonally numbered board and moving to the lowest available unvisited square at each step.
A316671 (program): Squares visited by moving diagonally one square on a diagonally numbered board and moving to the lowest available unvisited square at each step.
A316672 (program): Numbers k for which 120*k + 169 is a square.
A316673 (program): Number of paths from (0,0,0) to (n,n,n) that always move closer to (n,n,n).
A316688 (program): Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
A316708 (program): Bisection of the odd-indexed Pell numbers A001653: part 1.
A316709 (program): Bisection of the odd-indexed Pell numbers A001853: part 2.
A316711 (program): Decimal expansion of s:= t/(t - 1), with the tribonacci constant t = A058265.
A316714 (program): a(n) is the number of digits of A316713(n). This is the number of A, B and C sequences used in the tribonacci ABC-representation of n >= 0.
A316715 (program): a(n) is the number of 1s in A316713(n). That is, a(n) is the number of B-sequences (A278039) used in the tribonacci ABC-representation of n >= 0.
A316716 (program): a(n) is the number of 2s in A316713(n). That is, a(n) is the number of A-sequences (A278040) used in the tribonacci ABC-representation of n >= 0.
A316717 (program): a(n) is the number of 3s in A316713(n). That is, a(n) is the number of C-sequences (A278041) used in the tribonacci ABC-representation of n >= 0.
A316724 (program): Generalized 26-gonal (or icosihexagonal) numbers: m*(12*m - 11) with m = 0, +1, -1, +2, -2, +3, -3, …
A316725 (program): Generalized 27-gonal (or icosiheptagonal) numbers: m*(25*m - 23)/2 with m = 0, +1, -1, +2, -2, +3, -3, …
A316726 (program): The number of ways to tile (with squares and rectangles) a 2 X (n+2) strip with the upper left and upper right squares removed.
A316729 (program): Generalized 30-gonal (or triacontagonal) numbers: m*(14*m - 13) with m = 0, +1, -1, +2, -2, +3, -3, …
A316742 (program): Stepping through the Mersenne sequence (A000225) one step back, two steps forward.
A316776 (program): a(n) is the number of integers 0 < k < n such that n^2 - k^2 is a semiprime.
A316777 (program): a(n) = Sum_{k=1..n} (k!)^5.
A316779 (program): Expansion of 1 + (1/(1-x) + 1/(1-3*x))*x/2 + (1/(1-x) - 8/(1-2*x) + 9/(1-3*x))*x^5/2.
A316793 (program): Numbers whose prime multiplicities are distinct and relatively prime.
A316823 (program): Balanced nonary enumeration (or balanced nonary representation) of integers; write n in nonary (base 9) and then replace 5’s with (-4)’s, 6’s with (-3)’s, 7’s with (-2)’s, and 8’s with (-1)’s.
A316824 (program): A second example of a word that is uniform morphic and recurrent, but neither pure morphic nor primitive morphic.
A316825 (program): Fibonacci word A003849 with its initial term changed to 2.
A316826 (program): Image of 3 under repeated application of the morphism 3 -> 3,2, 2 -> 1,0,2,0,1,2, 1 -> 1,0,1,2, 0 -> 0,2.
A316828 (program): Image of the Thue-Morse sequence A010060 under the morphism {1 -> 1,2; 0 -> 0,2}.
A316829 (program): Image of 0 under repeated application of the morphism 0 -> 0,1,0, 1 -> 1,1,1.
A316831 (program): Trajectory of 0 under repeated application of the morphism 0 -> 01, 1 -> 21, 2 -> 13, 3 -> 33.
A316832 (program): In A316831, replace 2’s and 3’s with 0’s.
A316843 (program): Column 1 of table A316841.
A316846 (program): Column 1 of table A316842.
A316862 (program): Expansion of 1/(Sum_{k>=0} (k!)^3 x^k).
A316863 (program): Number of times 2 appears in the decimal expansion of n.
A316864 (program): Number of times 3 appears in decimal expansion of n.
A316865 (program): Number of times 4 appears in decimal expansion of n.
A316866 (program): Number of times 5 appears in decimal expansion of n.
A316867 (program): Number of times 6 appears in decimal expansion of n.
A316868 (program): Number of times 7 appears in decimal expansion of n.
A316869 (program): Number of times 8 appears in decimal expansion of n.
A316886 (program): Where records occur in A299773.
A316936 (program): a(n) is the maximum state complexity of the language C(w) of conjugates of w, over all length-n binary strings w.
A316937 (program): a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3) for n > 2, a(0)=3, a(1)=10, a(2)=26.
A316964 (program): Same as A316669, except numbering of the squares starts at 0 rather than 1..
A316965 (program): Same as A316670, except numbering of the squares starts at 0 rather than 1.
A316966 (program): Same as A316671, except numbering of the squares starts at 0 rather than 1.
A316987 (program): G.f.: A(x) = Sum_{n>=0} binomial(2*(n+1), n)/(n+1) * x^n / (1+x)^(3*(n+1)).
A317014 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = 7 * T(n-1,k) + T(n-2,k-1) for k = 0..floor(n/2). T(n,k)=0 for n or k < 0.
A317016 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = T(n-1,k) + 7 * T(n-2,k-1) for k = 0..floor(n/2). T(n,k)=0 for n or k < 0.
A317023 (program): Square array A(n,k), n >= 0, k >= 0, read by ascending antidiagonals, where the sequence of row n is the expansion of (1-x^(n+1))/((1-x)^(n+1)).
A317026 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = T(n-1,k) + 8 * T(n-2,k-1) for k = 0..floor(n/2); T(n,k)=0 for n or k < 0.
A317028 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = 8 * T(n-1,k) + T(n-2,k-1) for k = 0..floor(n/2); T(n,k)=0 for n or k < 0.
A317044 (program): Numbers k such that A(k+1) = A(k) + 1, where A() = A005100() are the deficient numbers.
A317045 (program): Numbers k such that A(k+1) = A(k) + 2, where A() = A005100() are the deficient numbers.
A317047 (program): Numbers k such that both k and k + 1 are deficient.
A317048 (program): Numbers k such that both k and k + 2 are consecutive deficient numbers.
A317050 (program): a(0) = 0 and for any n >= 0, a(n+1) is obtained by changing the rightmost possible digit in the negabinary representation of a(n) so as to get a value not yet in the sequence.
A317051 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = T(n-1,k) + 9 * T(n-2,k-1) for k = 0..floor(n/2); T(n,k)=0 for n or k < 0.
A317052 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = 9 T(n-1,k) + T(n-2,k-1) for k = 0..floor(n/2); T(n,k)=0 for n or k < 0.
A317054 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = T(n-1,k) + 10 * T(n-2,k-1) for k = 0..floor(n/2); T(n,k)=0 for n or k < 0.
A317055 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = 10 T(n-1,k) + T(n-2,k-1) for k = 0..floor(n/2); T(n,k)=0 for n or k < 0.
A317057 (program): a(n) is the number of time-dependent assembly trees satisfying the connected gluing rule for a cycle on n vertices.
A317090 (program): Positive integers whose prime multiplicities span an initial interval of positive integers.
A317094 (program): a(n) = (n + 1)^2 + n!*L_n(-1), where L_n(x) is the Laguerre polynomial.
A317095 (program): a(n) = 40*n.
A317096 (program): Expansion of e.g.f. ((1 - x)/(1 - 2*x))*exp(x/(x - 1)).
A317100 (program): Number of series-reduced planted achiral trees with n leaves spanning an initial interval of positive integers.
A317101 (program): Numbers whose prime multiplicities are pairwise indivisible.
A317108 (program): Numbers missing from A317106.
A317111 (program): Number of permutations of [n] in which the length of every increasing run is 0 or 1 (mod 4).
A317133 (program): G.f.: Sum_{n>=0} binomial(4*(n+1), n)/(n+1) * x^n / (1+x)^(n+1).
A317134 (program): G.f.: Sum_{n>=0} binomial(4*(n+1), n)/(n+1) * x^n / (1+x)^(2*(n+1)).
A317137 (program): a(n) is the number of nonzero triangular numbers <= n-th prime.
A317138 (program): Numbers k such that (2k)^3 - 1 is a semiprime.
A317140 (program): Number of permutations of [2n+1] with exactly n increasing runs of length two.
A317163 (program): a(n) = 48277590120607451 + (n-1)*8440735245322380.
A317164 (program): a(n) = 55837783597462913 + (n-1)*13858932213216090.
A317173 (program): a(n) is the least k > 0 such that k * n contains a digit 1 in its decimal representation.
A317180 (program): a(n) is the least positive multiple of n that contains at least one digit 1 in its decimal representation.
A317185 (program): Number of edges in a minimum gossip graph on n nodes.
A317186 (program): One of many square spiral sequences: a(n) = n^2 + n - floor((n-1)/2).
A317187 (program): Arrange primes along the square spiral; sequence lists primes on the X-axis.
A317188 (program): a(n) = 1 + 2 * (a(n-1) + a(n-4) + a(n-6)) + a(n-7) for n>3, with initial values 0 if n<0, and 1,3,8,18 for n=0..3.
A317189 (program): A morphic sequence related to the ternary Thue-Morse sequence.
A317192 (program): A140100(n) - A140102(n).
A317193 (program): First differences of A317192.
A317198 (program): Yet another version of the ternary tribonacci word: fixed point of the morphism 1 -> 1,0; 0 -> 1,-1; -1 -> 1; starting from a(0) = 1.
A317200 (program): G.f.: -x*(2*x^3+2*x^2+x-2)/(x^4-2*x+1).
A317202 (program): Decimal expansion of 3 + (t^2+t^4)/2, where t = 0.543689… (A192918) is the real root of x^3+x^2+x=1.
A317203 (program): Fixed under the morphism 1 -> 132, 2 -> 1, 3 -> 3, starting with 31.
A317207 (program): Length of alternative tribonacci representation of n defined in A317206.
A317243 (program): a(n) is the number of open intervals (m, m+1) containing at least one fraction n/k, where m and k are integers between 1 and n.
A317255 (program): a(n) = 149836681069944461 + (n-1)*1723457117682300.
A317259 (program): a(n) = 136926916457315893 + (n - 1)*9843204333812850.
A317276 (program): a(n) = Sum_{k=0..n} binomial(n-1,k-1)*binomial(2*k,k)*n!/(k + 1)!.
A317277 (program): a(n) = Sum_{k=0..n} binomial(n-1,k-1)*k^n*n!/k!; a(0) = 1.
A317278 (program): a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n-1,k-1)*k^n*n!/k!.
A317279 (program): a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n-1,k-1)*n^k*n!/k!.
A317280 (program): Expansion of e.g.f. 1/(1 - log(1 + x))^2.
A317294 (program): Numbers with a noncomposite number of 1’s in their binary expansion.
A317295 (program): Numbers with a composite number of 1’s in their binary expansion.
A317297 (program): a(n) = (n - 1)*(4*n^2 - 8*n + 5).
A317298 (program): a(n) = (1/2)*(1 + (-1)^n + 2*n + 4*n^2).
A317300 (program): Sequence obtained by taking the general formula for generalized k-gonal numbers: m*((k - 2)*m - k + 4)/2, where m = 0, +1, -1, +2, -2, +3, -3, … and k >= 5. Here k = 0.
A317301 (program): Sequence obtained by taking the general formula for generalized k-gonal numbers: m*((k - 2)*m - k + 4)/2, where m = 0, +1, -1, +2, -2, +3, -3, … and k >= 5. Here k = 1.
A317302 (program): Square array T(n,k) = (n - 2)*(k - 1)*k/2 + k, with n >= 0, k >= 0, read by antidiagonals upwards.
A317303 (program): Numbers k such that both Dyck paths of the symmetric representation of sigma(k) have a central peak.
A317304 (program): Numbers k with the property that both Dyck paths of the symmetric representation of sigma(k) have a central valley.
A317308 (program): Primes p such that the largest Dyck path of the symmetric representation of sigma(p) has a central peak.
A317309 (program): Primes p such that the largest Dyck path of the symmetric representation of sigma(p) has a central valley.
A317311 (program): Multiples of 11 and odd numbers interleaved.
A317312 (program): Multiples of 12 and odd numbers interleaved.
A317313 (program): Multiples of 13 and odd numbers interleaved.
A317314 (program): Multiples of 14 and odd numbers interleaved.
A317315 (program): Multiples of 15 and odd numbers interleaved.
A317316 (program): Multiples of 16 and odd numbers interleaved.
A317317 (program): Multiples of 17 and odd numbers interleaved.
A317318 (program): Multiples of 18 and odd numbers interleaved.
A317319 (program): Multiples of 19 and odd numbers interleaved.
A317320 (program): Multiples of 20 and odd numbers interleaved.
A317321 (program): Multiples of 21 and odd numbers interleaved.
A317322 (program): Multiples of 22 and odd numbers interleaved.
A317323 (program): Multiples of 23 and odd numbers interleaved.
A317324 (program): Multiples of 24 and odd numbers interleaved.
A317325 (program): Multiples of 25 and odd numbers interleaved.
A317326 (program): Multiples of 26 and odd numbers interleaved.
A317331 (program): Indices m for which A058304(m) = 1.
A317332 (program): Indices m for which A058304(m) = 8.
A317333 (program): Indices m for which A058304(m) = 9.
A317334 (program): Maximum number of runs in binary strings of length n.
A317335 (program): a(n) = A317332(n) - 8*n.
A317336 (program): a(n) = A317333(n) - 8*n.
A317362 (program): Expansion of e.g.f. exp(exp(x/(1 + x)) - 1).
A317364 (program): Expansion of e.g.f. exp(2*x/(1 + x)).
A317365 (program): Expansion of e.g.f. x*exp(x/(1 + x))/(1 + x).
A317366 (program): Expansion of e.g.f. exp(exp(x/(1 - x)) - 1)/(1 - x).
A317404 (program): a(n) = 3*n*(2^n - 1).
A317405 (program): a(n) = n * A001353(n).
A317406 (program): Expansion of e.g.f. sin(x/(1 - x)).
A317407 (program): The “OOPS” numbers – numbers with ones in all odd-numbered positions of the binary representation of n.
A317408 (program): a(n) = n * Fibonacci(2n).
A317409 (program): Expansion of e.g.f. cos(x/(1 - x)).
A317421 (program): a(n) = Sum_{k=1..n} binomial(n-1,k-1)*prime(k)*n!/k!.
A317451 (program): a(n) = (n*A003500(n) - A231896(n))/2.
A317483 (program): Circuit rank of the n-Bruhat graph.
A317487 (program): Number of 4-cycles in the n-Bruhat graph.
A317494 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = T(n-1,k) + 2 * T(n-3,k-1) for k = 0..floor(n/3); T(n,k)=0 for n or k < 0.
A317495 (program): Triangle read by rows: T(0,0) = 1; T(n,k) =2 * T(n-1,k) + T(n-3,k-1) for k = 0..floor(n/3); T(n,k)=0 for n or k < 0.
A317496 (program): Triangle T(n,k) = T(n-1,k) + 3*T(n-3,k-1) for k = 0..floor(n/3) with T(0,0) = 1, T(n,k) = 0 for n or k < 0, read by rows.
A317497 (program): Triangle T(n,k) = 3*T(n-1,k) + T(n-3,k-1) for k = 0..floor(n/3) with T(0,0) = 1 and T(n,k) = 0 for n or k < 0, read by rows.
A317498 (program): Triangle read by rows of coefficients in expansions of (-2 + 3x)^n, where n is nonnegative integer.
A317499 (program): Coefficients in expansion of 1/(1 + 2*x - 3*x^3).
A317500 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = T(n-1,k) + 2 * T(n-4,k-1) for k = 0..floor(n/4); T(n,k)=0 for n or k < 0.
A317501 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = 2 T(n-1,k) + T(n-4,k-1) for k = 0..floor(n/4); T(n,k)=0 for n or k < 0.
A317509 (program): Coefficients in Expansion of 1/(1 + x - 2*x^5).
A317510 (program): Numbers (4p+1)/3 where p is a Sophie Germain prime p > 3.
A317512 (program): Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
A317513 (program): Number of nX4 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
A317527 (program): Number of edges in the n-alternating group graph.
A317528 (program): Expansion of Sum_{k>=1} mu(k)^2*x^k/(1 + x^k), where mu() is the Moebius function (A008683).
A317529 (program): Expansion of Sum_{k>=1} x^(k^2)/(1 + x^(k^2)).
A317531 (program): Expansion of Sum_{p prime, k>=1} x^(p^k)/(1 + x^(p^k)).
A317534 (program): Numbers k such that the poset of factorizations of k, ordered by refinement, is not a lattice.
A317535 (program): Expansion of 1/(1 + 1/(1 - x) - Product_{k>=1} 1/(1 - x^k)).
A317538 (program): Indices m for which A317413(m) = 1.
A317542 (program): Formal inverse of the period-doubling sequence A096268.
A317543 (program): Positions of 1’s in A317542, the formal inverse of the period-doubling sequence A096268.
A317544 (program): Positions of 0’s in A317542, the formal inverse of the period-doubling sequence A096268.
A317551 (program): Fertility numbers.
A317553 (program): Sum of coefficients in the expansion of Sum_{y a composition of n} p(y) in terms of Schur functions, where p is power-sum symmetric functions.
A317581 (program): a(1) = 1; a(n > 1) = 1 + Sum_{d|n, d<n} mu(n/d) a(d).
A317591 (program): Lexicographically earliest sequence of distinct terms such that erasing the last digit of a(n+1) and adding the resulting integer to a(n) gives back a(n+1).
A317592 (program): Lexicographically first sequence of different terms such that erasing the last two digits of a(n+1) and adding this new reshaped integer to a(n) gives back a(n+1).
A317594 (program): Lexicographically first sequence of different terms such that erasing the last three digits of a(n+1) and adding this new reshaped integer to a(n) gives back a(n+1).
A317613 (program): Permutation of the nonnegative integers: lodumo_4 of A047247.
A317614 (program): a(n) = (1/2)*(n^3 + n*(n mod 2)).
A317618 (program): Expansion of e.g.f. sqrt((1 - x)/(1 - 3*x)).
A317625 (program): a(n) = Sum_{k=1..n} phi(floor(n/k)) where phi is the Euler totient function.
A317626 (program): Intersections with the x-axis of a bouncing ball on a Sophie Germain billiard table.
A317633 (program): Numbers congruent to {1, 7, 9} mod 10.
A317637 (program): a(n) = n*(n+1)*(n+3).
A317639 (program): Number of equivalence classes of Dyck paths of semilength n for the consecutive pattern UDUDD, where U=(1,1) and D=(1,-1).
A317640 (program): The 7x+-1 function: a(n) = 7n+1 if n == +1 (mod 4), a(n) = 7n-1 if n == -1 (mod 4), otherwise a(n) = n/2.
A317645 (program): Expansion of (1 + theta_3(q))^3*(1 + theta_3(q^2))/16, where theta_3() is the Jacobi theta function.
A317646 (program): Expansion of (1 + theta_3(q))^2*(1 + theta_3(q^2))^2/16, where theta_3() is the Jacobi theta function.
A317657 (program): Numbers congruent to {15, 75, 95} mod 100.
A317665 (program): Expansion of 1/Sum_{k>=0} x^(k^2).
A317669 (program): Number of equivalence classes of binary words of length n for the subword 10110.
A317673 (program): Moebius transform of A129502.
A317713 (program): Number of distinct terminal subtrees of the rooted tree with Matula-Goebel number n.
A317714 (program): Chessboard rectangles sequence (see Comments), also A037270 interleaved with A163102.
A317729 (program): Number of nX4 0..1 arrays with every element unequal to 1, 2, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
A317735 (program): Number of nX2 0..1 arrays with every element unequal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A317753 (program): Number of steps to reach 1 in 7x+-1 problem, or -1 if 1 is never reached.
A317759 (program): Number of nX2 0..1 arrays with every element unequal to 0, 1 or 2 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A317760 (program): Number of nX4 0..1 arrays with every element unequal to 0, 1 or 2 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A317767 (program): Number of nX2 0..1 arrays with every element unequal to 0, 1 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A317774 (program): a(n) = A322667(n) + 1.
A317783 (program): Number of equivalence classes of binary words of length n for the set of subwords {010, 101}.
A317790 (program): a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*(n-5) + a(n-6) for n>5, a(0)=a(1)=1, a(2)=a(3)=7, a(4)=13, a(5)=19.
A317793 (program): a(n) = (4^n + (-3)^n + 2^n + (-1)^n)/2.
A317809 (program): Number of nX2 0..1 arrays with every element unequal to 0, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A317817 (program): Number of nX2 0..1 arrays with every element unequal to 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A317837 (program): a(n) = Sum_{d|n, d<n} A002487(d).
A317838 (program): a(n) = Sum_{d|n} A002487(d).
A317848 (program): Multiplicative with a(p^e) = binomial(2*e, e).
A317849 (program): Number of states of the Finite State Automaton Gn accepting the language of maximal (or minimal) lexicographic representatives of elements in the positive braid monoid An.
A317890 (program): Number of nX2 0..1 arrays with every element unequal to 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A317910 (program): Expansion of -1/(1 - x)^2 + (1/(1 - x))*Product_{k>=1} (1 + x^k).
A317912 (program): Expansion of Product_{k>=2} 1/(1 - k*x^k).
A317914 (program): a(n) = 142099325379199423 + (n-1)*3691994023167450.
A317934 (program): Multiplicative with a(p^n) = 2^A011371(n); denominators for certain “Dirichlet Square Roots” sequences.
A317943 (program): Filter sequence constructed from the coefficients of the Stern polynomials B(d,t) collected for each proper divisor d of n; Restricted growth sequence transform of A317942.
A317946 (program): Additive with a(p^n) = A011371(n); the 2-adic valuation of A317934(n).
A317948 (program): An example of a morphic word: the sorted (by length, then alphabetically) sequence of words of the form a*b* under the action of a finite automaton defined as follows: start state is 0; a and b map states [0, 1, 2, 3] to states [1, 2, 3, 0] and [0, 3, 1, 2], respectively.
A317950 (program): First differences of ternary tribonacci word A080843.
A317951 (program): An S-automatic sequence for the system S = (a*b*, {a,b}, a<b).
A317952 (program): Trajectory of 1 under repeated application of the morphism 1->121, 2->232, 3->343, 4->414.
A317960 (program): Trajectory of 12 under the morphism f: X -> XYX, where Y=1 if X contains an odd number of 1’s, otherwise Y = 2.
A317961 (program): Trajectory of 10 under the morphism f: X -> XYX, where Y=1 if X contains an odd number of 1’s, otherwise Y = 0.
A317973 (program): a(n) = 2*(a(n-1)+a(n-2)+a(n-3))-a(n-4) for n >= 4, with initial terms -1, 2, 3, 6.
A317974 (program): a(n) = 2*(a(n-1)+a(n-2)+a(n-3))-a(n-4) for n >= 4, with initial terms 0,0,1,1.
A317975 (program): a(n) = 2*(a(n-1)+a(n-2)+a(n-3))-a(n-4) for n >= 4, with initial terms 0, 1, 1, 0.
A317976 (program): a(n) = 2*(a(n-1)+a(n-2)+a(n-3))-a(n-4) for n >= 4, with initial terms 0,0,1,0.
A317980 (program): a(n) = Product_{i=1..n} floor(5*i/2).
A317982 (program): Expansion of 14*x*(29 + 784*x + 1974*x^2 + 784*x^3 + 29*x^4) / (1 - x)^7.
A317983 (program): Expansion of 420*x*(1 + x)*(1 + 10*x + x^2) / (1 - x)^6.
A317984 (program): Expansion of 140*x*(1 + 4*x + x^2) / (1 - x)^5.
A317990 (program): Number of genera of real quadratic field Q(sqrt(k)), k squarefree > 1.
A317992 (program): 2-rank of the narrow class group of real quadratic field Q(sqrt(k)), k squarefree > 1.
A317996 (program): Expansion of e.g.f. exp((1 - exp(-3*x))/3).
A318010 (program): Number of nX2 0..1 arrays with every element unequal to 0, 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A318018 (program): Number of nX2 0..1 arrays with every element unequal to 0, 1, 2 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A318025 (program): Expansion of Sum_{k>=1} (-1 + Product_{j>=1} 1/(1 - j*x^(k*j))).
A318026 (program): Expansion of Product_{k>=1} 1/((1 - x^k)*(1 - x^(3*k))).
A318027 (program): Expansion of Product_{k>=1} 1/((1 - x^k)*(1 - x^(4*k))).
A318029 (program): Expansion of Sum_{k>=2} x^(k*(k+3)/2) / Product_{j=1..k} (1 - x^j).
A318031 (program): Number of nX2 0..1 arrays with every element unequal to 0, 1, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A318039 (program): Number of nX2 0..1 arrays with every element unequal to 0, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A318047 (program): a(n) = sum of values taken by all parking functions of length n.
A318054 (program): a(n) = n*(n + 1)*(n^2 + n + 22)/24.
A318059 (program): a(n) is the numerator of sigma(sigma(n))/n.
A318060 (program): a(n) is the denominator of sigma(sigma(n))/n.
A318062 (program): Number of nX2 0..1 arrays with every element unequal to 1, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A318111 (program): Number of maximal 1-intersecting families of 2-sets of [n] = {1,2,…,n}.
A318113 (program): Number of compositions of n into exactly n nonnegative parts <= five.
A318114 (program): Number of compositions of n into exactly n nonnegative parts <= six.
A318115 (program): Number of compositions of n into exactly n nonnegative parts <= seven.
A318116 (program): Number of compositions of n into exactly n nonnegative parts <= eight.
A318117 (program): Number of compositions of n into exactly n nonnegative parts <= ten.
A318151 (program): e-numbers of unlabeled rooted trees with empty leaves o[] allowed. A number n is in the sequence iff n = 2^(prime(y_1) * … * prime(y_k)) for some k >= 0 and y_1, …, y_k already in the sequence.
A318155 (program): Expansion of (1/(1 - x)) * Sum_{k>=0} x^(k*(2*k+1)) / Product_{j=1..2*k} (1 - x^j).
A318156 (program): Expansion of (1/(1 - x)) * Sum_{k>=1} x^(k*(2*k-1)) / Product_{j=1..2*k-1} (1 - x^j).
A318158 (program): Prime numbers of the form p1^4 + p2^3 + p3^2 + p4, where p1, p2, p3 and p4 are distinct primes.
A318159 (program): Figurate numbers based on the small stellated dodecahedron: a(n) = n*(21*n^2 - 33*n + 14)/2.
A318161 (program): Number of compositions of 2n into exactly 2n nonnegative parts with largest part n.
A318162 (program): Number of compositions of 2n-1 into exactly 2n-1 nonnegative parts with largest part n.
A318179 (program): Expansion of e.g.f. exp((1 - exp(-4*x))/4).
A318180 (program): Expansion of e.g.f. exp((1 - exp(-5*x))/5).
A318181 (program): Expansion of e.g.f. exp((1 - exp(-6*x))/6).
A318192 (program): a(n) = U_{n}(n)/(n+1) where U_{n}(x) is a Chebyshev polynomial of the second kind.
A318197 (program): a(n) = 2^((n - 1)*(n + 2)/2)*3^(n*(n - 1))*n^n.
A318206 (program): Numbers having no divisor d > 1 that is a binary palindrome (i.e., an element of A006995).
A318215 (program): Expansion of e.g.f. exp(x/(1 + x)^2).
A318223 (program): Expansion of e.g.f. exp(x/(1 + 2*x)).
A318224 (program): a(n) = n! * [x^n] exp(x/(1 + n*x)).
A318236 (program): a(n) = (3*2^(4*n+3) + 1)/5.
A318241 (program): Column 3 of array in A318240.
A318249 (program): a(n) = (n - 1)! * d(n), where d(n) = number of divisors of n (A000005).
A318250 (program): a(n) = (n - 1)! * sigma_2(n), where sigma_2(n) = sum of squares of divisors of n (A001157).
A318274 (program): Triangle read by rows: T(n,k) = n for 0 < k < n and T(n,0) = T(n,n) = 1.
A318283 (program): Sum of elements of the multiset spanning an initial interval of positive integers with multiplicities equal to the prime indices of n in weakly decreasing order.
A318290 (program): Expansion of Sum_{k>=1} (-1 + Product_{j>=1} (1 + j*x^(k*j))).
A318296 (program): Number of conjugacy classes of the Sylow 2-subgroup of the alternating group on n letters.
A318297 (program): a(n) = ((2n - 1)! + (4n - 2)!/(2n - 1)!)/(4n - 1).
A318303 (program): a(0) = 0, a(n) = n + a(n-1) if n is odd, a(n) = -3*a(n/2) if n is even.
A318304 (program): a(n) = A083254(n)/A003557(n) = (2*A173557(n) - A007947(n)).
A318305 (program): a(n) = product_{p} - product_{p-1}, where p are distinct primes dividing n; a(n) = A007947(n) - A173557(n).
A318314 (program): Denominators of the sequence whose Dirichlet convolution with itself yields A068068, number of odd unitary divisors of n.
A318315 (program): The 2-adic valuation of A318314.
A318320 (program): a(n) = (psi(n) - phi(n))/2.
A318321 (program): Numerators of rational valued sequence whose Dirichlet convolution with itself yields A003961.
A318325 (program): a(n) = Sum_{d|n} [moebius(n/d) > 0]*(sigma(d)-d).
A318326 (program): a(n) = Sum_{d|n} [moebius(n/d) < 0]*(sigma(d)-d).
A318327 (program): The 10-adic integer a_0 = …34474674850 satisfying a_0^5 + 1 = a_1, a_1^5 + 1 = a_2, …, a_8^5 + 1 = a_9 and a_9^5 + 1 = a_0.
A318328 (program): The 10-adic integer a_1 = …67812500001 satisfying a_1^5 + 1 = a_2, a_2^5 + 1 = a_3, … , a_9^5 + 1 = a_0 and a_0^5 + 1 = a_1.
A318329 (program): The 10-adic integer a_2 = …39062500002 satisfying a_2^5 + 1 = a_3, a_3^5 + 1 = a_4, … , a_0^5+ 1 = a_1 and a_1^5 + 1 = a_2.
A318330 (program): The 10-adic integer a_3 = …25000000033 satisfying a_3^5 + 1 = a_4, a_4^5 + 1 = a_5, … , a_1^5+ 1 = a_2 and a_2^5 + 1 = a_3.
A318331 (program): The 10-adic integer a_4 = …25039135394 satisfying a_4^5 + 1 = a_5, a_5^5 + 1 = a_6, … , a_2^5+ 1 = a_3 and a_3^5 + 1 = a_4.
A318332 (program): The 10-adic integer a_5 = …85011784225 satisfying a_5^5 + 1 = a_6, a_6^5 + 1 = a_7, … , a_3^5 + 1 = a_4 and a_4^5 + 1 = a_5.
A318333 (program): The 10-adic integer a_6 = …17275390626 satisfying a_6^5 + 1 = a_7, a_7^5 + 1 = a_8, … , a_4^5 + 1 = a_5 and a_5^5 + 1 = a_6.
A318334 (program): The 10-adic integer a_7 = …89599609377 satisfying a_7^5 + 1 = a_8, a_8^5 + 1 = a_9, … , a_5^5 + 1 = a_6 and a_6^5 + 1 = a_7.
A318335 (program): The 10-adic integer a_8 = …74462890658 satisfying a_8^5 + 1 = a_9, a_9^5 + 1 = a_0, … , a_6^5 + 1 = a_7 and a_7^5 + 1 = a_8.
A318336 (program): The 10-adic integer a_9 = …75576244769 satisfying a_9^5 + 1 = a_0, a_0^5 + 1 = a_1, … , a_7^5 + 1 = a_8 and a_8^5 + 1 = a_9.
A318338 (program): Number of nX3 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A318368 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*d*2^(d-1).
A318369 (program): Number of non-isomorphic set multipartitions (multisets of sets) of the multiset of prime indices of n.
A318370 (program): Number of non-isomorphic strict set multipartitions (sets of sets) of the multiset of prime indices of n.
A318372 (program): a(1) = 1; a(n+1) = Sum_{d|n} d*a(d).
A318376 (program): a(n) = F(n+1)^3 - 3*F(n-1)*F(n)^2, where F(n) = A000045(n), the n-th Fibonacci number.
A318379 (program): The 10-adic integer a_0 = …7644773889965429250 satisfying a_0^9 + 1 = a_1, a_1^9 + 1 = a_2, … , a_8^9 + 1 = a_9 and a_9^9 + 1 = a_0.
A318380 (program): The 10-adic integer a_1 = …7705078125000000001 satisfying a_1^9 + 1 = a_2, a_2^9 + 1 = a_3, … , a_9^9 + 1 = a_0 and a_0^9 + 1 = a_1.
A318381 (program): The 10-adic integer a_2 = …9345703125000000002 satisfying a_2^9 + 1 = a_3, a_3^9 + 1 = a_4, … , a_0^9 + 1 = a_1 and a_1^9 + 1 = a_2.
A318382 (program): The 10-adic integer a_3 = …2500000000000000513 satisfying a_3^9 + 1 = a_4, a_4^9 + 1 = a_5, … , a_1^9 + 1 = a_2 and a_2^9 + 1 = a_3.
A318383 (program): The 10-adic integer a_4 = …8996619787545743874 satisfying a_4^9 + 1 = a_5, a_5^9 + 1 = a_6, … , a_2^9 + 1 = a_3 and a_3^9 + 1 = a_4.
A318384 (program): The 10-adic integer a_5 = …3747888971752538625 satisfying a_5^9 + 1 = a_6, a_6^9 + 1 = a_7, … , a_3^9 + 1 = a_4 and a_4^9 + 1 = a_5.
A318385 (program): The 10-adic integer a_6 = …1601963043212890626 satisfying a_6^9 + 1 = a_7, a_7^9 + 1 = a_8, … , a_4^9 + 1 = a_5 and a_5^9 + 1 = a_6.
A318386 (program): The 10-adic integer a_7 = …5448818206787109377 satisfying a_7^9 + 1 = a_8, a_8^9 + 1 = a_9, … , a_5^9 + 1 = a_6 and a_6^9 + 1 = a_7.
A318397 (program): Triangle read by rows: T(n,k) = binomial(n,k)^2 * binomial(2*(n-k), n-k).
A318400 (program): Numbers whose prime indices are all powers of 2 (including 1).
A318403 (program): Number of strict connected antichains of sets whose multiset union is an integer partition of n.
A318406 (program): For n > 4, a(n) = a(n-1) + a(n-2) if n is even and a(n) = 3*a(n-2) + a(n-4) - a(n-5) if n is odd; a(0) = 0, a(1) = 1, a(2) = 1, a(3) = 2, and a(4) = 3.
A318409 (program): The 10-adic integer a_8 = …6396884918212891138 satisfying a_8^9 + 1 = a_9, a_9^9 + 1 = a_0, … , a_6^9 + 1 = a_7 and a_7^9 + 1 = a_8.
A318410 (program): The 10-adic integer a_9 = …5099734869332853249 satisfying a_9^9 + 1 = a_0, a_0^9 + 1 = a_1, … , a_7^9 + 1 = a_8 and a_8^9 + 1 = a_9.
A318411 (program): Least k (>1) such that m^k == m mod A005117(n) for 0 <= m <= A005117(n) - 1.
A318417 (program): Scaled g.f. T(u) = Sum_{n>=0} a(n)*(3*u/48)^n satisfies 3*(2*u-1)*T + d/du(4*u*(2*u-1)*(u-1)*T’) = 0, and a(0)=1; sequence gives a(n).
A318435 (program): Decimal expansion of the nominal Jovian mass parameter in m^3 s^-2.
A318436 (program): Decimal expansion of the nominal solar mass parameter in m^3 s^-2.
A318438 (program): For any n >= 0 with binary expansion Sum_{k=0..w} b_k * 2^k, let h(n) = Sum_{k=0..w} b_k * (i-1)^k (where i denotes the imaginary unit); a(n) is the real part of h(n).
A318439 (program): For any n >= 0 with binary expansion Sum_{k=0..w} b_k * 2^k, let h(n) = Sum_{k=0..w} b_k * (i-1)^k (where i denotes the imaginary unit); a(n) is the imaginary part of h(n).
A318440 (program): a(n) = A046645(n) - A007814(n); the 2-adic valuation of A299150.
A318445 (program): a(n) = Sum_{d|n, d<n} A005187(d).
A318446 (program): Inverse Möbius transform of A005187: a(n) = Sum_{d|n} A005187(d).
A318447 (program): a(n) = Sum_{d|n, d<n} A294898(d), where A294898(d) = A005187(d) - sigma(d).
A318448 (program): a(n) = Sum_{d|n} A294898(d), where A294898(d) = A005187(d) - sigma(d).
A318449 (program): Numerators of the sequence whose Dirichlet convolution with itself yields A001511, the 2-adic valuation of 2n.
A318450 (program): Denominators of the sequence whose Dirichlet convolution with itself yields A001511, the 2-adic valuation of 2n.
A318451 (program): The 2-adic valuation of A318450.
A318453 (program): Numerators of the sequence whose Dirichlet convolution with itself yields A001227, number of odd divisors of n.
A318454 (program): Denominators of the sequence whose Dirichlet convolution with itself yields A001227, number of odd divisors of n.
A318455 (program): The 2-adic valuation of A318454(n).
A318456 (program): a(n) = n OR A001065(n), where OR is bitwise-or (A003986) and A001065 = sum of proper divisors.
A318457 (program): a(n) = n XOR A001065(n), where XOR is bitwise-xor (A003987) and A001065 = sum of proper divisors.
A318458 (program): a(n) = n AND A001065(n), where AND is bitwise-and (A004198) & A001065 = sum of proper divisors.
A318459 (program): a(n) = gcd(n, tau(n), phi(n)), where tau = A000005 and phi = A000010.
A318466 (program): a(n) = 2*n OR A000203(n), where OR is bitwise-or (A003986) and A000203 = sum of divisors.
A318467 (program): a(n) = 2*n XOR A000203(n), where XOR is bitwise-xor (A003987) and A000203 = sum of divisors.
A318468 (program): a(n) = 2*n AND A000203(n), where AND is bitwise-and (A004198) and A000203 = sum of divisors.
A318471 (program): Additive with a(p^e) = A000045(e).
A318472 (program): Multiplicative with a(p^e) = 2^A000045(e).
A318473 (program): Additive with a(p^e) = A000045(e+1).
A318474 (program): Multiplicative with a(p^e) = 2^A000045(e+1).
A318491 (program): a(n) is the numerator of Sum_{d|n} Sum_{j|d} 1/j.
A318492 (program): a(n) is the denominator of Sum_{d|n} Sum_{j|d} 1/j.
A318493 (program): Expansion of 1/(1 - Sum_{i>=1, j>=1} i*j*x^(i*j)).
A318505 (program): Sum of divisors of n, up to, but not including the second largest of them A032742(n); a(1) = 0 by convention.
A318512 (program): Denominators (in their lowest terms) of the sequence whose Dirichlet convolution with itself yields squares (A000290), or equally A064549.
A318513 (program): The 2-adic valuation of A318512.
A318514 (program): a(n) = n OR (greatest proper divisor of n).
A318515 (program): a(n) = n AND A032742(n), where AND is bitwise-and (A004198) and A032742 = the largest proper divisor of n.
A318516 (program): a(n) = A032742(n) OR n-A032742(n), where OR is bitwise-or (A003986) and A032742 = the largest proper divisor of n.
A318517 (program): a(n) = A032742(n) XOR n-A032742(n), where XOR is bitwise-xor (A003987) and A032742 = the largest proper divisor of n.
A318518 (program): a(n) = A032742(n) AND n-A032742(n), where AND is bitwise-and (A004198) and A032742 = the largest proper divisor of n.
A318519 (program): a(n) = A000005(n) * A003557(n).
A318522 (program): Decimal expansion of sqrt(28^(1/3)-27^(1/3)).
A318525 (program): Decimal expansion of ((3+2*5^(1/4))/(3-2*5^(1/4)))^(1/4).
A318556 (program): a(n) is the number of lesser tetrahedral numbers that divide the n-th tetrahedral number.
A318570 (program): Expansion of Product_{k>=1} ((1 - x)^k + x^k)/((1 - x)^k - x^k).
A318583 (program): a(1) = a(2) = 1; for n > 2, a(n+2) = Sum_{d|n} mu(n/d)*a(d).
A318591 (program): Number of n-member subsets of [3*n] whose elements sum to a multiple of three.
A318605 (program): Decimal expansion of geometric progression constant for Coxeter’s Loxodromic Sequence of Tangent Circles.
A318608 (program): Moebius function mu(n) defined for the Gaussian integers.
A318609 (program): a(1) = 2, a(2) = 4, a(3) = 6; for n > 3, a(n) = 3*a(n-1) - 3*a(n-2) + 9*a(n-3).
A318610 (program): a(1) = 0, a(2) = 4, a(3) = 12; for n > 3, a(n) = 3*a(n-1) - 3*a(n-2) + 9*a(n-3).
A318614 (program): Scaled g.f. S(u) = Sum_{n>0} a(n)*16*(u/16)^n satisfies T(u) = d/du S(u), with T(u) as defined by A318417; sequence gives a(n).
A318618 (program): a(n) is the number of rooted forests on n nodes that avoid the patterns 321, 2143, and 3142.
A318623 (program): a(n) = 2^phi(n) mod n.
A318624 (program): Number of 3-member subsets of [3*n] whose elements sum to a multiple of n.
A318636 (program): G.f.: Sum_{n>=1} ( (1 + x^n)^n - 1 ).
A318637 (program): G.f.: Sum_{n>=1} ( (2 + x^n)^n - 2^n ).
A318651 (program): a(n) = A046644(n)/A318512(n).
A318652 (program): The 2-adic valuation of A046644(n)/A318512(n) (A318651).
A318654 (program): Positions of even terms in A318649.
A318655 (program): The 2-adic valuation of A318649, the numerators of “Dirichlet Square Root” of squares.
A318656 (program): The 2-adic valuation of ratio A318649(n)/A318512(n); a(n) = 2*A007814(n) - A046645(n).
A318658 (program): Denominators of the sequence whose Dirichlet convolution with itself yields A087003, a(2n) = 0 and a(2n+1) = moebius(2n+1).
A318659 (program): The 2-adic valuation of A318658.
A318660 (program): Remainder when A064988(n) is divided by n.
A318666 (program): a(n) = 2^{the 3-adic valuation of n}.
A318668 (program): a(n) = gcd(n, A064988(n)).
A318674 (program): Sum of squarefree divisors of n that have an even number of prime factors.
A318675 (program): Sum of squarefree divisors of n that have an odd number of prime factors.
A318676 (program): Sum of divisors of n that have an even number of prime factors (counted with multiplicity).
A318677 (program): Sum of divisors of n that have an odd number of prime factors (counted with multiplicity).
A318681 (program): a(n) = n * A299149(n).
A318682 (program): a(n) is the number of odd values minus the number of even values of the integer log of all positive integers up to and including n.
A318695 (program): Expansion of e.g.f. Product_{i>=1, j>=1} 1/(1 - x^(i*j))^(1/(i*j)).
A318696 (program): Expansion of e.g.f. Product_{i>=1, j>=1} (1 + x^(i*j))^(1/(i*j)).
A318700 (program): Positive numbers that contain odd and even digits.
A318702 (program): For any n >= 0 with binary expansion Sum_{k=0..w} b_k * 2^k, let f(n) = Sum_{k=0..w} b_k * i^k * 2^floor(k/2) (where i denotes the imaginary unit); a(n) is the real part of f(n).
A318703 (program): For any n >= 0 with binary expansion Sum_{k=0..w} b_k * 2^k, let f(n) = Sum_{k=0..w} b_k * i^k * 2^floor(k/2) (where i denotes the imaginary unit); a(n) is the imaginary part of f(n).
A318704 (program): For any n >= 0 with binary expansion Sum_{k=0..w} b_k * 2^k, let f(n) = Sum_{k=0..w} b_k * i^k * 2^floor(k/2) (where i denotes the imaginary unit); a(n) is the square of the modulus of f(n).
A318720 (program): Numbers k such that there exists a strict relatively prime factorization of k in which no pair of factors is relatively prime.
A318733 (program): Decimal expansion of the nontrivial real solution to x^6 + x^5 - x^3 - x^2 - x + 1 = 0.
A318734 (program): a(n) = Sum_{k=1..n} (-1)^(k + 1) * d(2*k - 1), where d(k) is the number of divisors of k (A000005).
A318739 (program): Decimal expansion of Pi^2 / 24 - (1/12) * log(2 + sqrt(5))^2.
A318742 (program): a(n) = Sum_{k=1..n} floor(n/k)^3.
A318743 (program): a(n) = Sum_{k=1..n} floor(n/k)^4.
A318744 (program): a(n) = Sum_{k=1..n} floor(n/k)^5.
A318750 (program): a(n) = Sum_{k=1..n} k * tau_3(k), where tau_3 is A007425.
A318755 (program): a(n) = Sum_{k=1..n} tau(k)^3, where tau is A000005.
A318762 (program): Number of permutations of a multiset whose multiplicities are the prime indices of n.
A318765 (program): a(n) = (n + 2)*(n^2 + n - 1).
A318766 (program): a(0) = 1; for n > 0, a(n) = (prime(n)^2 - 1) * a(n-1).
A318768 (program): a(n) = Sum_{d|n} (-1)^(n/d+1) * Sum_{j|d} tau(j), where tau = number of divisors (A000005).
A318769 (program): Expansion of e.g.f. Product_{k>=1} (1 + x^k)^(sigma(k)/k), where sigma(k) is the sum of the divisors of k.
A318772 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = T(n-1,k) + 3 * T(n-4,k-1) for k = 0..floor(n/4); T(n,k)=0 for n or k < 0.
A318773 (program): Triangle T(n,k) = 3*T(n-1,k) + T(n-4,k-1) for k = 0..floor(n/4), with T(0,0) = 1 and T(n,k) = 0 for n or k < 0, read by rows.
A318774 (program): Coefficients in expansion of 1/(1 - x - 3*x^4).
A318775 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = T(n-1,k) + 2 * T(n-5,k-1) for k = 0..floor(n/5); T(n,k)=0 for n or k < 0.
A318776 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = 2 T(n-1,k) + T(n-5,k-1) for k = 0..floor(n/5); T(n,k)=0 for n or k < 0.
A318777 (program): Coefficients in expansion of 1/(1 - x - 2*x^5).
A318778 (program): Number of different positions that an elementary sphinx can occupy in a sphinx of order n.
A318784 (program): Expansion of Product_{k>=1} 1/(1 - x^k)^(sigma_1(k)-k), where sigma_1(k) = sum of divisors of k (A000203).
A318785 (program): Numbers which are prime if each digit is replaced by its 9’s complement.
A318791 (program): Prime generating polynomial: a(n) = 9*n^2 - 249*n + 1763.
A318809 (program): Number of necklace permutations of the multiset of prime indices of n > 1.
A318811 (program): Expansion of e.g.f. exp(Sum_{k>=1} phi(k)*x^k), where phi is the Euler totient function A000010.
A318814 (program): Expansion of e.g.f. Product_{k>=1} ((1 + x^k)/(1 - x^k))^(sigma(k)/k).
A318827 (program): a(n) = n - gcd(n - 1, phi(n)).
A318828 (program): a(n) = n - A063994(n) = n - Product_{primes p dividing n} gcd(p-1, n-1).
A318830 (program): a(n) = phi(n) - gcd(phi(n), n-1).
A318833 (program): a(n) = n + A023900(n).
A318834 (program): a(n) = Product_{d|n, d<n} A019565(phi(d)), where phi is the Euler totient function A000010.
A318840 (program): a(n) = phi(n) - Product_{primes p dividing n} gcd(p-1, n-1).
A318841 (program): a(n) = n - A173557(n).
A318845 (program): a(n) = Sum_{d|n} (-1)^(n/d+1) * Sum_{j|d} sigma(j), where sigma(j) = sum of divisors of j (A000203).
A318868 (program): a(n) = 1^2 + 3^4 + 5^6 + 7^8 + 9^10 + 11^12 + 13^14 + … + (up to n).
A318874 (program): Number of divisors d of n for which 2*phi(d) > d.
A318875 (program): Number of divisors d of n for which 2*phi(d) < d.
A318876 (program): Sum of divisors d of n for which 2*phi(d) > d.
A318877 (program): Sum of divisors d of n for which 2*phi(d) < d.
A318878 (program): Sum of A083254(d) for all such divisors d of n for which A083254(d) > 0.
A318879 (program): a(n) = Sum_{d|n} [d-(2*phi(d)) > 0]*(d-(2*phi(d))).
A318885 (program): If n = p^a * q^b * … * r^c, with p < q < r primes, with nonzero exponents a, b, c, then a(n) = prime(1+p-p)^a * prime(1+q-p)^b * … * prime(1+r-p)^c; a(1) = 1.
A318889 (program): a(n) = A001065(n) - A001065(A252463(n)).
A318912 (program): Expansion of e.g.f. Product_{k>=1} 1/(1 - x^k)^(mu(k)^2/k), where mu = Möbius function (A008683).
A318913 (program): Expansion of e.g.f. Product_{k>=1} 1/(1 - x^prime(k))^(1/prime(k)).
A318914 (program): Expansion of e.g.f. Product_{p prime, k>=1} 1/(1 - x^(p^k))^(1/(p^k)).
A318917 (program): Expansion of e.g.f. exp(Sum_{k>=1} phi(k)*x^k/k), where phi is the Euler totient function A000010.
A318919 (program): Define b(0)=0, b(1)[1]=1, b(1)[2]=1; and for n>=2, b(n)[1] = total number of digits in b(n-1), and b(n)[2] = total number of digits in b(0),…,b(n-1); a(n) = b(n)[2].
A318921 (program): In binary expansion of n, delete one symbol from each run. Set a(n)=0 if the result is the empty string.
A318922 (program): Apply Lenormand’s transformation k -> A318921(k) to the Fibonacci numbers.
A318923 (program): Apply Lenormand’s transformation k -> A318921(k) to the primes.
A318926 (program): Take the binary expansion of n, starting with the least significant bit, and concatenate the lengths of the runs.
A318927 (program): Take the binary expansion of n, starting with the most significant bit, and concatenate the lengths of the runs.
A318930 (program): RUNS transform of A279620.
A318934 (program): Numbers whose binary expansion begins with exactly two 1’s.
A318935 (program): a(n) = Sum_{2^m divides n} 2^(3*m).
A318937 (program): a(n) = 16 times the sum of the cubes of the divisors of 2*n+1.
A318938 (program): If n=0 then 1 otherwise 16*(1+22*A318935(n))*(sum of cubes of odd divisors of n).
A318939 (program): If n=0 then 1 otherwise 48*(1+12*A318935(n))*(sum of cubes of odd divisors of n).
A318941 (program): Number of Dyck paths with n nodes and altitude 2.
A318946 (program): Column 1 of triangle A318945.
A318947 (program): Column 2 of triangle A318945.
A318960 (program): One of the two successive approximations up to 2^n for 2-adic integer sqrt(-7). This is the 1 (mod 4) case.
A318961 (program): One of the two successive approximations up to 2^n for 2-adic integer sqrt(-7). This is the 3 (mod 4) case.
A318962 (program): Digits of one of the two 2-adic integers sqrt(-7) that ends in 01.
A318963 (program): Digits of one of the two 2-adic integers sqrt(-7) that ends in 11.
A318966 (program): Expansion of e.g.f. Product_{i>=1, j>=1, k>=1} 1/(1 - x^(i*j*k))^(1/(i*j*k)).
A318967 (program): Expansion of e.g.f. Product_{i>=1, j>=1, k>=1} (1 + x^(i*j*k))^(1/(i*j*k)).
A318968 (program): Expansion of exp(Sum_{k>=1} ( Sum_{d|k, d odd} d^k ) * x^k/k).
A318969 (program): Expansion of exp(Sum_{k>=1} ( Sum_{p|k, p prime} p^k ) * x^k/k).
A318972 (program): The 7x+-1 function (“shortcut” definition): a(n) = (7n+1)/4 if n == +1 (mod 4), a(n) = (7n-1)/4 if n == -1 (mod 4), otherwise a(n) = n/2.
A318976 (program): Expansion of e.g.f. Product_{k>=1} ((1 + x^k)/(1 - x^k))^(phi(k)/k), where phi is the Euler totient function A000010.
A318978 (program): Heinz numbers of integer partitions with a common divisor > 1.
A318979 (program): Number of divisors of n with relatively prime prime indices, meaning they belong to A289509.
A318981 (program): Numbers whose prime indices plus 1 are relatively prime.
A318994 (program): Totally additive with a(prime(n)) = n + 1.
A318995 (program): Totally additive with a(prime(n)) = n - 1.
A319006 (program): Sum of the next n positive integers repeated (A008619).
A319007 (program): Sum of the next n nonnegative integers repeated (A004526).
A319010 (program): a(0) = 0, a(1) = 1; for n >= 1, a(2*n) = a(2*n-1), a(2*n+1) = 2*(n - a(n)).
A319013 (program): a(n) is the sum over each permutation of S_n of the least element of the descent set.
A319014 (program): a(n) = 1*2*3 + 4*5*6 + 7*8*9 + 10*11*12 + 13*14*15 + 16*17*18 + … + (up to n).
A319028 (program): Number of permutations pi of [n] such that s(pi) avoids the patterns 132 and 321, where s is West’s stack-sorting map.
A319034 (program): Decimal expansion of the height that minimizes the total surface area of the four triangular faces of a square pyramid of unit volume.
A319054 (program): Maximum product of an aperiodic integer partition of n.
A319058 (program): Number of relatively prime aperiodic factorizations of n into factors > 1.
A319073 (program): Square array read by antidiagonals upwards: T(n,k) = k*sigma(n), n >= 1, k >= 1.
A319074 (program): a(n) is the sum of the first n nonnegative powers of the n-th prime.
A319075 (program): Square array T(n,k) read by antidiagonal upwards in which row n lists the n-th powers of primes, hence column k lists the powers of the k-th prime, n >= 0, k >= 1.
A319076 (program): Square array T(n,k) read by antidiagonal upwards in which column k lists the partial sums of the powers of the k-th prime, n >= 0, k >= 1.
A319078 (program): Expansion of phi(-q) * phi(q)^2 in powers of q where phi() is a Ramanujan theta function.
A319084 (program): Numbers k such that the denominator of the Bernoulli polynomial B_k(x) is the squarefree kernel of k+1.
A319085 (program): a(n) = Sum_{k=1..n} k^2*tau(k), where tau is A000005.
A319086 (program): a(n) = Sum_{k=1..n} k^2*sigma(k), where sigma is A000203.
A319087 (program): a(n) = Sum_{k=1..n} k^2*phi(k), where phi is the Euler totient function A000010.
A319088 (program): a(n) = Sum_{k=1..n} k^2*tau_3(k), where tau_3 is A007425.
A319089 (program): a(n) = tau(n)^3, where tau is A000005.
A319097 (program): One of the three successive approximations up to 7^n for 7-adic integer 6^(1/3). This is the 3 (mod 7) case (except for n = 0).
A319098 (program): One of the three successive approximations up to 7^n for 7-adic integer 6^(1/3). This is the 5 (mod 7) case (except for n = 0).
A319100 (program): Number of solutions to x^6 == 1 (mod n).
A319102 (program): Triangle read by rows: The k-th column has alternating blocks of k 1’s followed by k 0’s (see example).
A319104 (program): Expansion of e.g.f. Product_{k>=1} 1/(1 - x^(k^2))^(1/k^2).
A319105 (program): Expansion of e.g.f. Product_{k>=0} 1/(1 - x^(2^k))^(1/2^k).
A319108 (program): Expansion of Product_{k>=1} (1 - x^k)^(k-1).
A319116 (program): Signs of the Maclaurin coefficients of 1/(exp(x) + Pi/2).
A319117 (program): Sign of the n-th Maclaurin coefficient of 1/(exp(x) + exp(1)/2).
A319120 (program): T(n, k) = binomial(n - k - 1, k)*binomial(2*n - 2*k, n)/(n + 1), for n >= 1 and 0 <= k <= floor((n - 1)/2), triangle read by rows.
A319127 (program): Crossing number of the complete bipartite graph K_{6,n}.
A319128 (program): Interleave n*(3*n - 2), 3*n^2 + n - 1, n=0,0,1,1, … .
A319129 (program): Decimal expansion of (1 + sqrt(3) + sqrt(2*sqrt(3)))/2.
A319130 (program): Expansion of Product_{k>=1} 1/(1 - x^k)^(2^omega(k)), where omega(k) = number of distinct primes dividing k (A001221).
A319131 (program): a(n) = Sum_{d|n} Sum_{p|d, p prime} p.
A319132 (program): a(n) = Sum_{d|n} Sum_{j|d} mu(j)^2*j, where mu = Möbius function (A008683).
A319158 (program): Given an equilateral triangular grid with side n, containing n(n+1)/2 points, a(n) is the minimal number of points to be selected, such that any equilateral triangle of points will include at least one of the selection, if the triangle has the same orientation as the grid.
A319159 (program): Given an equilateral triangular grid with side n, containing n(n+1)/2 points, a(n) is the minimal number of points to be selected, such that any equilateral triangle of points will include at least one of the selection.
A319161 (program): Numbers whose prime multiplicities appear with relatively prime multiplicities.
A319170 (program): Triangular numbers of the form 2..21..1; n_times 2 followed with n_times 1; n >= 1.
A319172 (program): a(n) = 2*(a(n-1) + a(n-3)) - a(n-4), with a(0) = 1, a(1) = 2, a(2) = 5 and a(3) = 12.
A319187 (program): Number of pairwise coprime subsets of {1,…,n} of maximum cardinality (A036234).
A319194 (program): a(n) = Sum_{k=1..n} sigma(n,k).
A319196 (program): a(n) = 2^(n-1)*Fibonacci(n-3), n >= 0.
A319198 (program): Partial sums of the infinite self-similar tribonacci word, written in the form A080843.
A319199 (program): One of the three successive approximations up to 7^n for 7-adic integer 6^(1/3). This is the 6 (mod 7) case (except for n = 0).
A319200 (program): a(n) = -(A(n) - A(n-1)) where A(n) = A057597(n+1), for n >= 0.
A319201 (program): Expansion of f(t) = F^{[-1]}(t)/t, where F(x) = x/(1 - x^2 - x^3).
A319202 (program): a(n) is the A-sequence for the Riordan matrix R = (1/(1- x^2 - x^3), x/(1 - x^2 - x^3)) from A104578.
A319204 (program): Sequence used for the Boas-Buck type recurrence for Riordan triangle A319203.
A319210 (program): a(n) = phi(n^2 - 1)/2 where phi is A000010.
A319213 (program): a(n) = phi(n^3 - 1)/3 where phi is A000010.
A319234 (program): T(n, k) is the coefficient of x^k of the polynomial p(n) which is defined as the scalar part of P(n) = Q(x, 1, 1, 1) * P(n-1) for n > 0 and P(0) = Q(1, 0, 0, 0) where Q(a, b, c, d) is a quaternion, triangle read by rows.
A319237 (program): Positions of nonzero terms in A114592, the list of coefficients in the expansion of Product_{n > 1} (1 - 1/n^s).
A319238 (program): Positions of zeros in A114592, the list of coefficients in the expansion of Product_{n > 1} (1 - 1/n^s).
A319246 (program): Sum of prime indices of the n-th squarefree number.
A319258 (program): a(n) = 1 + 2*3 + 4 + 5*6 + 7 + 8*9 + 10 + 11*12 + … + (up to n).
A319273 (program): Signed sum over the prime multiplicities of n.
A319279 (program): Numbers that are congruent to {0, 3, 7, 10} mod 12.
A319280 (program): Numbers that are congruent to {0, 4, 7, 11} mod 12.
A319288 (program): a(n) is the smallest k such that A319284(n, k) >= A319284(n, j) for all 0 <= j <= n.
A319289 (program): The x coordinates of the shell enumeration of N X N where N = {0, 1, 2, …} (A319514).
A319290 (program): The y coordinates of the shell enumeration of N X N where N = {0, 1, 2, …}(A319514).
A319296 (program): a(n) = (Sum_{d|n} (sigma(d))) mod sigma(n).
A319297 (program): Digits of one of the three 7-adic integers 6^(1/3) that is related to A319097.
A319301 (program): Sum of GCDs of strict integer partitions of n.
A319305 (program): Digits of one of the three 7-adic integers 6^(1/3) that is related to A319098.
A319307 (program): Expansion of theta_4(q)^16 in powers of q = exp(Pi i t).
A319308 (program): Expansion of theta_4(q)^20 in powers of q = exp(Pi i t).
A319309 (program): Expansion of theta_4(q)^24 in powers of q = exp(Pi i t).
A319310 (program): Expansion of theta_4(q)^28 in powers of q = exp(Pi i t).
A319316 (program): Numbers k such that A090616(k) < A054861(k).
A319317 (program): Numbers k such that A090616(k) > A054861(k).
A319340 (program): Sum of Euler totient function and its Dirichlet inverse: a(n) = A000010(n) + A023900(n).
A319341 (program): a(n) = A000010(n) - A173557(n).
A319359 (program): Expansion of Product_{i>=1, j>=1, k>=1} (1 - x^(i*j*k)).
A319364 (program): Expansion of e.g.f. exp(x^3/3)/(1 - x).
A319365 (program): Expansion of e.g.f. exp(x^4/4)/(1 - x).
A319371 (program): Numbers k such that the characteristic polynomial of a wheel graph of k nodes has exactly one monomial with vanishing coefficient.
A319373 (program): a(n) = 1*2 - 3*4 + 5*6 - 7*8 + 9*10 - 11*12 + 13*14 - … + (up to n).
A319384 (program): a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5), a(0)=1, a(1)=5, a(2)=9, a(3)=21, a(4)=29.
A319388 (program): Non-palindromic squares.
A319389 (program): Non-palindromic cubes.
A319390 (program): a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5), a(0)=1, a(1)=2, a(2)=3, a(3)=6, a(4)=8.
A319392 (program): a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*k!*n^k.
A319395 (program): Number of partitions of n into exactly two positive Fibonacci numbers.
A319404 (program): a(n) is the period of the periodic k-sequence q_k=lcm(k+1,k+2,…,k+n)/(n*binomial(k+n,n)).
A319406 (program): Write n-th prime in binary, then increase each run of 0’s by one 0, and increase each run of 1’s by one 1. a(n) is the decimal equivalent of the result.
A319407 (program): a(n) = A175046(n)-n.
A319408 (program): a(n) = A319407(n)/2.
A319409 (program): a(n) = n - A318921(n).
A319410 (program): Twice A032741.
A319412 (program): Maximal runs-resistance of a binary vector of length n.
A319413 (program): Number of trailing zero entries in row n of triangle A319411.
A319423 (program): Indices of records in A175046.
A319430 (program): First differences of the tribonacci representation numbers (A003726 or A278038).
A319432 (program): The first differences (A129761) of the tribonacci representation numbers (A003714 or A014417) consists of runs of 1’s separated by the terms of the present sequence.
A319433 (program): Take Zeckendorf representation of n (A014417(n)), drop least significant bit, take inverse Zeckendorf representation.
A319434 (program): Take Golomb’s sequence A001462 and shorten all the runs by 1.
A319438 (program): a(n) = 1^2 - 3^4 + 5^6 - 7^8 + 9^10 - 11^12 + 13^14 - … + (up to n).
A319440 (program): Squares of non-palindromic number.
A319441 (program): Cubes of non-palindromic numbers.
A319443 (program): Number of distinct Eisenstein primes in the factorization of n.
A319444 (program): Total number of factors in a factorization of n into Eisenstein primes.
A319445 (program): Number of Eisenstein integers in a reduced system modulo n.
A319448 (program): Moebius function mu(n) defined for the Eisenstein integers.
A319451 (program): Numbers that are congruent to {0, 3, 6} mod 12; a(n) = 3*floor(4*n/3).
A319452 (program): Numbers that are congruent to {0, 3, 6, 10} mod 12.
A319455 (program): Expansion of Product_{k>=1} 1/((1 - x^k)*(1 - x^(2*k)))^2.
A319468 (program): Number of partitions of n into exactly two nonzero decimal palindromes.
A319497 (program): a(0)=0, a(3*n)=9*a(n), a(3*n+1)=9*a(n)+1, a(3*n+2)=9*a(n)+3.
A319512 (program): a(n) = 7*a(n-1) - 14*a(n-2) + 7*a(n-3), a(0) = 1, a(1) = 3, a(2) = 11.
A319516 (program): Number of integers x such that 1 <= x <= n and gcd(x,n) = gcd(x+2,n) = gcd(x+6,n) = gcd(x+8,n) = 1.
A319522 (program): Completely multiplicative with a(prime(2*k)) = prime(k) and a(prime(2*k-1)) = 1 for any k > 0 (where prime(k) denotes the k-th prime number).
A319525 (program): Completely multiplicative with a(prime(k)) = prime(2*k - 1) (where prime(k) denotes the k-th prime).
A319526 (program): Square array read by antidiagonals upwards: T(n,k) = sigma(n*k), n >= 1, k >= 1.
A319527 (program): a(n) = 7 * sigma(n).
A319528 (program): a(n) = 8 * sigma(n).
A319529 (program): Odd numbers that have middle divisors.
A319534 (program): Number of integers x such that 1 <= x <= n and gcd(x,n) = gcd(x+2,n) = gcd(x+6,n) = 1.
A319536 (program): Number of signed permutations of length n where numbers occur in consecutive order.
A319552 (program): Expansion of 1/theta_4(q)^3 in powers of q = exp(Pi i t).
A319553 (program): Expansion of 1/theta_4(q)^8 in powers of q = exp(Pi i t).
A319554 (program): Expansion of 1/theta_4(q)^12 in powers of q = exp(Pi i t).
A319555 (program): Digits of one of the three 7-adic integers 6^(1/3) that is related to A319199.
A319556 (program): a(n) gives the alternating sum of length n, starting at n: n - (n+1) + (n+2) - … + (-1)^(n+1) * (2n-1).
A319571 (program): The stripe enumeration of N X N where N = {0, 1, 2, …}, also called boustrophedonic Cantor enumeration. Terms are interleaved x and y coordinates.
A319572 (program): The x coordinates of the stripe enumeration of N X N where N = {0, 1, 2, …}.
A319573 (program): The y coordinates of the stripe enumeration of N X N where N = {0, 1, 2, …}.
A319575 (program): a(n) = (2/3)*n*(n^3 - 6*n^2 + 11*n - 3).
A319576 (program): a(n) = (4/15)*n*(n - 1)*(n^3 - 9*n^2 + 26*n - 9).
A319577 (program): a(n) = (4/45)*n*(n - 2)*(n - 1)*(n^3 - 12*n^2 + 47*n - 15).
A319578 (program): a(n) = (1/3)*(n+2)^2*(3*n+3)!/(n+2)!^3.
A319588 (program): First of three consecutive triangular numbers that add up to a perfect square.
A319597 (program): Number of conjugacy classes for a non-abelian group of order p^3, where p is prime: a(n) = p^2 + p - 1 where p = prime(n).
A319603 (program): a(n) = n^3 + reversal of digits of n^3.
A319610 (program): a(n) is the minimal number of successive OFF cells that appears in n-th generation of rule-30 1D cellular automaton started from a single ON cell.
A319611 (program): a(n) is the number of gaps in the n-th generation of the rule-30 1D cellular automaton started from a single ON.
A319613 (program): a(n) = prime(n) * prime(2n).
A319617 (program): Number of Integer solutions to w^2 + x^2 + y^2 + z^2 < n^2; number of lattice points inside a 4-sphere of radius n.
A319618 (program): Number of non-isomorphic weight-n antichains of multisets whose dual is a chain of multisets.
A319622 (program): Number of non-isomorphic connected weight-n antichains of distinct sets whose dual is also an antichain of (not necessarily distinct) sets.
A319625 (program): Number of non-isomorphic connected weight-n antichains of distinct sets whose dual is also an antichain of distinct sets.
A319626 (program): Primorial deflation of n (numerator): Let f be the completely multiplicative function over the positive rational numbers defined by f(p) = A034386(p) for any prime number p; f constitutes a permutation of the positive rational numbers; let g be the inverse of f; for any n > 0, a(n) is the numerator of g(n).
A319627 (program): Primorial deflation of n (denominator): Let f be the completely multiplicative function over the positive rational numbers defined by f(p) = A034386(p) for any prime number p; f constitutes a permutation of the positive rational numbers; let g be the inverse of f; for any n > 0, a(n) is the denominator of g(n).
A319630 (program): Positive numbers that are not divisible by two consecutive prime numbers.
A319635 (program): Number of non-isomorphic weight-n antichains of distinct multisets whose dual is also an antichain of (not necessarily distinct) multisets.
A319636 (program): a(n) = Sum_{k=1..n} binomial(2*n - 3*k + 1, n - k)*k/(n - k + 1).
A319638 (program): Number of non-isomorphic weight-n antichains of distinct sets whose dual is also an antichain of distinct sets.
A319642 (program): Number of non-isomorphic weight-n antichains of distinct multisets whose dual is a chain of (not necessarily distinct) multisets.
A319645 (program): Number of non-isomorphic weight-n antichains of distinct multisets whose dual is a chain of distinct multisets.
A319650 (program): a(n) = A073138(n) - n.
A319651 (program): Largest number having in its ternary representation the same number of 0’s, 1’s and 2’s as n.
A319654 (program): Write n in 6-ary, sort digits into increasing order.
A319658 (program): a(n) is the minimal number of successive ON cells that appears in n-th generation of rule-30 1D cellular automaton started from a single ON cell.
A319659 (program): 2-rank of the class group of imaginary quadratic field with discriminant -k, k = A003657(n).
A319660 (program): 2-rank of the class group of imaginary quadratic field with discriminant -k, k = A039957(n).
A319661 (program): 2-rank of the class group of imaginary quadratic field with discriminant -k, k = A191483(n).
A319663 (program): Irregular triangle read by rows: T(n,k) = 5^k mod 2^n, n >= 2, 0 <= k <= 2^(n-2) - 1.
A319664 (program): Irregular triangle read by rows: T(n,k) = (-3)^k mod 2^n, n >= 2, 0 <= k <= 2^(n-2) - 1.
A319665 (program): Irregular triangle read by rows: T(n,k) = log_5(4*k + 1) mod 2^n, n >= 2, 0 <= k <= 2^(n-2) - 1.
A319666 (program): Irregular triangle read by rows: T(n,k) = log_(-3)(4*k + 1) mod 2^n, n >= 2, 0 <= k <= 2^(n-2) - 1.
A319667 (program): Palindromes a(n) = (10^n + 1)*(10^(n+1) + 1).
A319674 (program): a(n) = 1 + 2 + 3 - 4 - 5 - 6 + 7 + 8 + 9 - 10 - 11 - 12 + … - (up to n).
A319675 (program): Sum of digits of prime(n) and digits of prime(n+1).
A319676 (program): Numerator of A047994(n)/n where A047994 is the unitary totient function.
A319677 (program): Denominator of A047994(n)/n where A047994 is the unitary totient function.
A319678 (program): Numbers with property that the first digit is the length of the number (written in base 10).
A319683 (program): Sum of A003415(d) over the proper divisors d of n, where A003415 is arithmetic derivative.
A319684 (program): Sum of A003415(d) over the divisors d of n, where A003415 is arithmetic derivative.
A319690 (program): Fully multiplicative with a(p^e) = (p mod 3)^e.
A319691 (program): a(n) = 1 if n is either 1 or divisible only by primes congruent to 1 mod 3, 0 otherwise.
A319693 (program): Filter sequence combining sopfr(d) from all proper divisors d of n, where sopfr(d) is A001414(d) = sum of primes dividing d with repetition.
A319697 (program): Sum of even squarefree divisors of n.
A319699 (program): a(n) = A001065(A252463(n)).
A319701 (program): Filter sequence for sequences that are constant for all odd terms >= 3.
A319702 (program): Filter sequence for sequences that are constant for all even terms >= 2.
A319703 (program): a(n) = A003415(A252463(n)).
A319710 (program): a(n) = 1 if n is divisible by the square of its smallest prime factor, 0 otherwise.
A319711 (program): Sum of A034968(d) over proper divisors d of n, where A034968 gives the sum of digits in factorial base.
A319712 (program): Sum of A034968(d) over divisors d of n, where A034968 gives the sum of digits in factorial base.
A319713 (program): Sum of A276150(d) over proper divisors d of n, where A276150 gives the sum of digits in primorial base.
A319715 (program): Sum of A276150(d) over divisors d of n, where A276150 gives the sum of digits in primorial base.
A319722 (program): Write n in 5-ary, sort digits into decreasing order.
A319723 (program): Write n in 6-ary, sort digits into decreasing order.
A319724 (program): Write n in 7-ary, sort digits into decreasing order.
A319743 (program): Row sums of A174158.
A319759 (program): Number of non-isomorphic intersecting multiset partitions of weight n with empty intersection.
A319762 (program): Number of non-isomorphic intersecting set multipartitions (multisets of sets) of weight n with empty intersection.
A319764 (program): Number of non-isomorphic intersecting set systems of weight n with empty intersection.
A319769 (program): Number of non-isomorphic intersecting set multipartitions (multisets of sets) of weight n whose dual is also an intersecting set multipartition.
A319773 (program): Number of non-isomorphic intersecting set systems of weight n whose dual is also an intersecting set system.
A319776 (program): Number of partitions of 2n in which any two distinct parts differ by at least n.
A319784 (program): Number of non-isomorphic intersecting T_0 set systems of weight n.
A319785 (program): a(n) = A073138(n) + A038573(n).
A319795 (program): a(n) = n^(n+1)/(n-1)^n for n>1, rounded to nearest integer.
A319796 (program): Even numbers that have middle divisors.
A319801 (program): Odd numbers without middle divisors.
A319802 (program): Even numbers without middle divisors.
A319803 (program): a(n) = A319651(n) + A038574(n).
A319806 (program): a(n) = A319723(n) + A319654(n).
A319812 (program): Square array read by antidiagonals: T(n,k) = (1 + i)-adic valuation of n + k*i, n >= 0, k >= 0, or -1 if n + k*i = 0.
A319813 (program): a(n) is the smallest a such that n is divisible by a^n + 1, or 0 if no such a exists.
A319840 (program): Table read by antidiagonals: T(n, k) is the number of elements on the perimeter of an n X k matrix.
A319842 (program): a(n) = 8 * A104720(n) + ceiling(n/2).
A319852 (program): Difference between 3^n and the product of primes less than or equal to n.
A319857 (program): Difference between 4^n and the product of primes less than or equal to n.
A319861 (program): Triangle read by rows, 0 <= k <= n: T(n,k) is the numerator of the k-th Bernstein basis polynomial of degree n evaluated at the interval midpoint t = 1/2; denominator is A319862.
A319862 (program): Triangle read by rows, 0 <= k <= n: T(n,k) is the denominator of the k-th Bernstein basis polynomial of degree n evaluated at the interval midpoint t = 1/2; numerator is A319861.
A319866 (program): a(n) = 2*1 + 4*3 + 6*5 + 8*7 + 10*9 + 12*11 + … + (up to the n-th term).
A319879 (program): a(n) = minimal number m of unit squares needed to make an figure formed from squares (joined edge to edge) which has n holes.
A319880 (program): Difference between 2^n and the product of primes less than or equal to n.
A319885 (program): a(n) = 2*1 - 4*3 + 6*5 - 8*7 + 10*9 - 12*11 + 14*13 - 16*15 + … - (up to the n-th term).
A319895 (program): a(n) is the number of partitions of n into consecutive parts, plus the total number of parts in those partitions.
A319905 (program): Decimal expansion of 4*(sqrt(2) - 1)/3.
A319923 (program): Quasi-primes: composite numbers k such that the least prime factor is greater than k^(1/(log log k)^2).
A319924 (program): a(n) = A143565(2n,n) for n > 0, a(0) = 1.
A319927 (program): Numbers k such that the sum of the squares of the odd non-unitary divisors of k divides the sum of the squares of the non-unitary divisors of k.
A319929 (program): Minimal arithmetic table similar to multiplication with different rules for odd and even products, read by antidiagonals.
A319930 (program): a(n) = (1/24)*n*(n - 1)*(n - 3)*(n - 14).
A319931 (program): a(n) = -(1/120)*n*(n - 3)*(n - 6)*(n^2 - 21*n + 8).
A319932 (program): a(n) = (1/720)*n*(n - 10)*(n - 1)*(n^3 - 34*n^2 + 181*n - 144).
A319948 (program): a(n) = Product_{i=1..n} floor(3*i/2).
A319949 (program): a(n) = Product_{i=1..n} floor(4*i/3).
A319950 (program): a(n) = Product_{i=1..n} floor(5*i/3).
A319951 (program): Take Golomb’s sequence A001462 and extend all the runs by 1; prepend an initial 0.
A319952 (program): Let M = A022342(n) be the n-th number whose Zeckendorf representation is even; then a(n) = A129761(M).
A319953 (program): List of binary words of lengths 0, 1, 2, etc., including empty word, each prefixed by a 2.
A319956 (program): Image of 3 under repeated application of the morphism 1 -> 1, 2 -> 22, 3 -> 312.
A319966 (program): a(n) = A003144(A003146(n)).
A319967 (program): a(n) = A003145(A003144(n)) where A003144 and A003145 are positions of ‘1’ and ‘2’ in the tribonacci word A092782.
A319968 (program): a(n) = A003145(A003145(n)).
A319969 (program): a(n) = A003145(A003146(n)).
A319970 (program): a(n) = A003146(A003144(n)).
A319971 (program): a(n) = A003146(A003145(n)).
A319972 (program): a(n) = A003146(A003146(n)).
A319974 (program): Expansion of (1-x^3+x^4+x^6)/(b(2)*b(3)*b(4)) where b(n) = 1-x^n.
A319981 (program): a(n) is the number of integer partitions of n with largest part <= 3 for which the index of the seaweed algebra formed by the integer partition paired with its weight is 0.
A319984 (program): Fully multiplicative with a(p^e) = prime(p mod 4)^e.
A319986 (program): Fully multiplicative with a(p^e) = prime(p mod 6)^e.
A319988 (program): a(n) = 1 if n is divisible by the square of its largest prime factor, 0 otherwise.
A319993 (program): a(n) = A319997(n) / A173557(n).
A319995 (program): Number of divisors of n of the form 6*k + 5.
A319997 (program): a(n) = Sum_{d|n, d is odd} mu(n/d)*d, where mu(n) is Moebius function A008683.
A319998 (program): a(n) = Sum_{d|n, d is even} mu(n/d)*d, where mu(n) is Moebius function A008683.
A320003 (program): Number of proper divisors of n of the form 6*k + 3.
A320005 (program): Number of proper divisors of n of the form 6*k + 5.
A320006 (program): a(n) = 1 if n encodes a nonnegative combinatorial game (in a style of A106486), otherwise 0; Characteristic function of A126001.
A320007 (program): If there is k >= 0 such that floor(n/4^k) is odd and A320006(k) is 1, then a(n) = 1, otherwise a(n) = 0.
A320008 (program): a(0) = 1; for n > 0, a(n) = A000120(n) * a(n-A000120(n)), where A000120(n) is the binary weight of n.
A320009 (program): a(0) = 1; for n > 0, a(n) = A000005(n) * a(n-A000005(n)), where A000005(n) gives the number of divisors of n.
A320014 (program): Filter sequence combining the binary expansions of proper divisors of n, grouped by their residue classes mod 3.
A320015 (program): Number of proper divisors of n that are either of the form 6*k+1 or 6*k + 5.
A320016 (program): a(1) = a(2) = 1; for n > 2, a(n) = A000005(n) * a(A000005(n)), where A000005(n) gives the number of divisors of n.
A320029 (program): Decimal expansion of sqrt(9 + sqrt(9 + sqrt(9 + sqrt(9 + …)))) = (sqrt(37) + 1)/2.
A320031 (program): Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of the e.g.f. exp(x)/(1 - k*x).
A320032 (program): Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of the e.g.f. exp(-x)/(1 - k*x).
A320037 (program): Write n in binary, then modify each run of 0’s by appending one 1, and modify each run of 1’s by appending one 0. a(n) is the decimal equivalent of the result.
A320038 (program): Write n in binary, then modify each run of 0’s by prepending one 1, and modify each run of 1’s by prepending one 0. a(n) is the decimal equivalent of the result.
A320039 (program): Write n in binary, then modify each run of 0’s and each run of 1’s by appending a 1. a(n) is the decimal equivalent of the result.
A320040 (program): Consider the Cantor matrix of rational numbers. This sequence reads the numerator, then the denominator as one moves through the matrix along alternate up and down antidiagonals.
A320042 (program): a(n) = a(floor(n/2)) + (-1)^(n*(n+1)/2) with a(1)=0.
A320043 (program): Row sums of the triangle A322550.
A320047 (program): Consider coefficients U(m,l,k) defined by the identity Sum_{k=1..l} Sum_{j=0..m} A302971(m,j)/A304042(m,j) * k^j * (T-k)^j = Sum_{k=0..m} (-1)^(m-k) * U(m,l,k) * T^k that holds for all positive integers l,m,T. This sequence gives 2-column table read by rows, where n-th row lists coefficients U(1,n,k) for k = 0, 1 and n >= 1.
A320048 (program): One half of composite numbers k with the property that the symmetric representation of sigma(k) has two parts.
A320049 (program): Expansion of (psi(x) / phi(x))^6 in powers of x where phi(), psi() are Ramanujan theta functions.
A320050 (program): Expansion of (psi(x) / phi(x))^7 in powers of x where phi(), psi() are Ramanujan theta functions.
A320052 (program): Number of product-sum knapsack partitions of n. Number of integer partitions y of n such that every product of sums of the parts of a multiset partition of any submultiset of y is distinct.
A320053 (program): Number of spanning sum-product knapsack partitions of n. Number of integer partitions y of n such that every sum of products of the parts of a multiset partition of y is distinct.
A320055 (program): Heinz numbers of sum-product knapsack partitions.
A320056 (program): Heinz numbers of product-sum knapsack partitions.
A320059 (program): Sum of divisors of n^2 that do not divide n.
A320062 (program): Nonprimes with odd digits only.
A320064 (program): The number of F_2 graphs on { 1, 2, …, n } with a unique cycle of weight 1, which corresponds to the number of reflectable bases of the root system of type D_n.
A320065 (program): a(n) is the smallest integer i such that binomial(2i,i) > n.
A320066 (program): Numbers k with the property that the symmetric representation of sigma(k) has five parts.
A320069 (program): Expansion of 1/(theta_3(q) * theta_3(q^2)), where theta_3() is the Jacobi theta function.
A320071 (program): Number of length n primitive (=aperiodic or period n) 6-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
A320072 (program): Number of length n primitive (=aperiodic or period n) 7-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
A320073 (program): Number of length n primitive (=aperiodic or period n) 8-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
A320074 (program): Number of length n primitive (=aperiodic or period n) 9-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
A320075 (program): Number of length n primitive (=aperiodic or period n) 10-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
A320085 (program): Triangle read by rows, 0 <= k <= n: T(n,k) is the numerator of the derivative of the k-th Bernstein basis polynomial of degree n evaluated at the interval midpoint t = 1/2; denominator is A320086.
A320087 (program): Number of primitive (=aperiodic) ternary words with length less than or equal to n which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
A320088 (program): Number of primitive (=aperiodic) 4-ary words with length less than or equal to n which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
A320089 (program): Number of primitive (=aperiodic) 5-ary words with length less than or equal to n which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
A320090 (program): Number of primitive (=aperiodic) 6-ary words with length less than or equal to n which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
A320091 (program): Number of primitive (=aperiodic) 7-ary words with length less than or equal to n which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
A320092 (program): Number of primitive (=aperiodic) 8-ary words with length less than or equal to n which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
A320093 (program): Number of primitive (=aperiodic) 9-ary words with length less than or equal to n which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
A320094 (program): Number of primitive (=aperiodic) 10-ary words with length less than or equal to n which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
A320106 (program): Möbius transform of A320107.
A320107 (program): a(n) = A001227(A252463(n)).
A320110 (program): Restricted growth sequence transform of function f: f(1) = 0, f(n) = A046523(A252463(n)) for n > 1.
A320111 (program): Number of divisors d of n that are not of the form 4k+2.
A320118 (program): a(1) = a(2) = 1; for n > 2, a(n) = A181819(n) * a(A181819(n)).
A320137 (program): Numbers that have only one middle divisor.
A320142 (program): Numbers that have exactly two middle divisors.
A320156 (program): Decimal expansion of the unique real root of x^3 - 3*x^2 + 8*x - 16 = 0, or equivalently, the unique positive root of x^4*(x + 5) - 4^4 = 0.
A320158 (program): Decimal expansion of real root of x^3 + 11x^2 + 27x - 27 = 0, x^2*(x + 5)^3 - 2^2*3^3 = 0.
A320222 (program): Number of unlabeled rooted trees with n nodes in which the non-leaf branches directly under any given node are all equal.
A320224 (program): a(1) = 1; a(n > 1) = Sum_{k = 1..n-1} Sum_{d|k, d < k} a(d).
A320225 (program): a(1) = 1; a(n > 1) = Sum_{k = 1…n} Sum_{d|k, d < k} a(d).
A320226 (program): Number of integer partitions of n whose non-1 parts are all equal.
A320235 (program): G.f.: Product_{k>=1, j>=1} (1 + x^(k*j))^2.
A320236 (program): G.f.: Product_{k>=1, j>=1} 1/(1 - x^(k*j))^2.
A320258 (program): a(n) = n! * [x^n] exp(x*exp(-n*x)).
A320259 (program): Terms that are on the y-axis of the square spiral built with 2*k, 2*k+1, 2*k+1 for k >= 0.
A320261 (program): Write n in binary, then modify each run of 0’s and each run of 1’s by prepending a 1. a(n) is the decimal equivalent of the result.
A320262 (program): Write n in binary, then modify each run of 0’s and each run of 1’s by appending a 0. a(n) is the decimal equivalent of the result.
A320263 (program): Write n in binary, then modify each run of 0’s and each run of 1’s by prepending a 0. a(n) is the decimal equivalent of the result.
A320268 (program): Number of unlabeled series-reduced rooted trees with n nodes where the non-leaf branches directly under any given node are all equal.
A320271 (program): Number of unlabeled semi-binary rooted trees with n nodes in which the non-leaf branches directly under any given node are all equal.
A320278 (program): a(n) is the number of positive integers 0 < i < n such that i + n is a square.
A320281 (program): Terms that are on the positive x-axis of the square spiral built with 2*k, 2*k+1, 2*k+1 for k >= 0.
A320283 (program): Lexicographical ordering of pure imaginary integers in the base (-1+i) numeral system.
A320287 (program): a(n) = n! * [x^n] Sum_{k>=0} exp(n^k*x)*x^k/k!.
A320298 (program): Differences between positions of 1’s in binary expansion of Pi.
A320299 (program): Lengths of runs of consecutive zeros in binary expansion of Pi.
A320300 (program): Positions of 0’s in binary expansion of Pi/4.
A320301 (program): Differences between positions of 0’s in binary expansion of Pi.
A320302 (program): Number of consecutive ones in binary expansion of Pi.
A320326 (program): a(n) = Sum_{i=0..n} binomial(2*i-1,i)*binomial(2*i,n-i).
A320327 (program): Triangle T(n,m) = C(2*n,m)*C(2*n-1,n), 0 <= m <= 2*n, n >= 0.
A320329 (program): Row sums of A174790.
A320342 (program): Maximum term in Cunningham chain of the first kind generated by the n-th prime.
A320344 (program): Expansion of e.g.f. log(1 + x)/(1 - log(1 + x))^2.
A320352 (program): Expansion of e.g.f. (exp(x) - 1)/(exp(x) - exp(2*x) + 1).
A320354 (program): Square array A(n,k), n >= 0, k >= 1, read by antidiagonals: A(n,k) = Product_{j=1..n} (k^j - 1).
A320366 (program): Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
A320389 (program): Product_i prime(i)^e(i), where e are the nonzero exponents in the prime factorization of n, sorted in increasing order.
A320390 (program): Prime signature of n (sorted in decreasing order), concatenated.
A320393 (program): First members of the Cunningham chains of the first kind whose length is a prime.
A320394 (program): Number of ones in binary expansion n^5.
A320410 (program): Continued fraction of a constant t with partial denominators {a(n), n>=0} such that the continued fraction of 4*t yields partial denominators {6*a(n), n>=0}.
A320427 (program): a(n) = floor(3*n/2) + ceiling(n/6) + 9.
A320429 (program): The length of the shortest prefix of the Thue-Morse word decomposable to not less than n palindromes.
A320431 (program): The number of tiles inside a regular n-gon created by lines that run from each of the vertices of the n edges orthogonal to these edges.
A320432 (program): Expansion of e.g.f. exp(3 * (1 - exp(x)) + x).
A320433 (program): Expansion of e.g.f. exp(4 * (1 - exp(x)) + x).
A320440 (program): Row sums of A225043.
A320448 (program): a(n) is the maximum number of distinct distances between n non-attacking rooks on an n X n chessboard.
A320453 (program): a(n) = (n^n + n*(-1)^n)/(n + 1).
A320465 (program): a(n) = 2^n - (2^(n-1) mod n), where “mod” is the nonnegative remainder operator.
A320468 (program): a(n) = a(n-1) + 20*a(n-2), n >= 2; a(0)=1, a(1)=41.
A320469 (program): a(n) = 3*a(n-1) + 10*a(n-2), n >= 2; a(0)=1, a(1)=1.
A320471 (program): a(n) = floor(sqrt(n)) mod ceiling(sqrt(n)).
A320508 (program): T(n,k) = binomial(n - k - 1, k), 0 <= k < n, and T(n,n) = (-1)^n, triangle read by rows.
A320511 (program): Numbers k with the property that the symmetric representation of sigma(k) has six parts.
A320519 (program): a(n) = 2*n^n*cos(n*arcsin(sqrt(4*n^2-1)/(2*n))) for n > 0 and a(0) = 2.
A320522 (program): Numbers k such that k^10 divides 10^k.
A320524 (program): Number of chiral pairs of a row of n colors using 6 or fewer colors.
A320531 (program): T(n,k) = n*k^(n - 1), k > 0, with T(n,0) = A063524(n), square array read by antidiagonals upwards.
A320534 (program): a(n) = ((1 + sqrt(4*n^2 + 1))^n + (1 - sqrt(4*n^2 + 1))^n)/2^n.
A320545 (program): Number of partitions of n into parts of exactly three sorts which are introduced in ascending order such that sorts of adjacent parts are different.
A320553 (program): Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most three elements and for at least one block c the smallest integer interval containing c has exactly three elements.
A320561 (program): Irregular table read by rows: T(n,k) = (2*k+1)^(2*k+1) mod 2^n, 0 <= k <= 2^(n-1) - 1.
A320563 (program): Expansion of Product_{k>=1} 1/(1 - x^k/(1 - x)^k)^k.
A320564 (program): Expansion of Product_{k>=1} (1 + x^k/(1 - x)^k)^k.
A320565 (program): a(n) = ((1 + sqrt(4*n^2 + 1))^n - (1 - sqrt(4*n^2 + 1))^n)/(2^n * sqrt(4*n^2 + 1)).
A320568 (program): a(n) = Sum_{k=1..n} (-1)^(n-k)*binomial(n,k)*sigma(k).
A320570 (program): a(n) = L_n(n), where L_n(x) is the Lucas polynomial.
A320576 (program): a(n) gives the number of configurations of non-attacking rooks up to symmetry on an n X n chessboard such that the number of distinct distances between the rooks is given by A319476(n).
A320577 (program): Number of isosceles triangles whose vertices are the vertices of a regular n-gon.
A320581 (program): a(n) is the number of closed factors of length n in the Fibonacci word.
A320584 (program): Numbers whose first digit is prime.
A320586 (program): Expansion of (1/(1 - x)) * Sum_{k>=1} k*x^k/(x^k + (1 - x)^k).
A320589 (program): Expansion of (1/(1 + x)) * Sum_{k>=1} k*x^k/(x^k + (1 + x)^k).
A320592 (program): Number of partitions of n with four parts in which no part occurs more than twice.
A320599 (program): Numbers k such that 4k + 1 and 8k + 1 are both primes.
A320601 (program): Exponents of powers of two having a digit zero in decimal.
A320603 (program): a(0) = 1; if n is odd, a(n) = Product_{i=0..n-1} a(i); if n is even, a(n) = Sum_{i=0..n-1} a(i).
A320604 (program): Chromatic number of the n-polygon diagonal intersection graph.
A320614 (program): Expansion of (1 + x^5) / ((1 - x^2) * (1 - x^3) * (1 - x^7)) in powers of x.
A320615 (program): Number of ordered set partitions of [n] where k = two is minimal such that for each block b the smallest integer interval containing b has at most k elements.
A320628 (program): Products of primes of nonprime index.
A320629 (program): Products of odd primes of nonprime index.
A320632 (program): Numbers k such that there exists a pair of factorizations of k into factors > 1 where no factor of one divides any factor of the other.
A320642 (program): Number of 1’s in the base-(-2) expansion of -n.
A320649 (program): Expansion of 1/(1 - Sum_{k>=1} k^2*x^k/(1 - x^k)).
A320650 (program): Expansion of 1/(1 - Sum_{k>=1} x^k/(1 - x^(2*k))).
A320651 (program): Expansion of 1/(1 - Sum_{k>=1} k*x^k/(1 + x^k)).
A320652 (program): Expansion of 1/(2 - Product_{k>=1} 1/(1 - k*x^k)).
A320654 (program): Expansion of 1/(2 - Product_{k>=1} (1 + x^k)/(1 - x^k)).
A320656 (program): Number of factorizations of n into squarefree semiprimes. Number of multiset partitions of the multiset of prime factors of n, into strict pairs.
A320661 (program): a(n) = 2^(n+3) - 6*n - 7.
A320667 (program): First differences of A066194.
A320674 (program): Positive integers m with binary expansion (b_1, …, b_k) (where k = A070939(m)) such that b_i = [m == 0 (mod prime(i))] for i = 1..k (where prime(i) denotes the i-th prime number and [] is an Iverson bracket).
A320687 (program): Sum of differences of the larger square and primes between two squares.
A320688 (program): Sum of the square excess A056892 of the primes between two squares.
A320689 (program): Number of partitions of n with up to two distinct kinds of 1.
A320690 (program): Number of partitions of n with up to three distinct kinds of 1.
A320691 (program): Number of partitions of n with up to four distinct kinds of 1.
A320698 (program): Numbers whose product of prime indices is a prime power (A246655).
A320701 (program): Indices of primes followed by a gap (distance to next larger prime) of 6.
A320702 (program): Indices of primes followed by a gap (distance to next larger prime) of 8.
A320703 (program): Indices of primes followed by a gap (distance to next larger prime) of 10.
A320704 (program): Indices of primes followed by a gap (distance to next larger prime) of 12.
A320705 (program): Indices of primes followed by a gap (distance to next larger prime) of 14.
A320706 (program): Indices of primes followed by a gap (distance to next larger prime) of 16.
A320707 (program): Indices of primes followed by a gap (distance to next larger prime) of 18.
A320708 (program): Indices of primes followed by a gap (distance to next larger prime) of 20.
A320709 (program): Indices of primes followed by a gap (distance to next larger prime) of 22.
A320710 (program): Indices of primes followed by a gap (distance to next larger prime) of 24.
A320711 (program): Indices of primes followed by a gap (distance to next larger prime) of 26.
A320712 (program): Indices of primes followed by a gap (distance to next larger prime) of 28.
A320713 (program): Indices of primes followed by a gap (distance to next larger prime) of 30.
A320714 (program): Indices of primes followed by a gap (distance to next larger prime) of 32.
A320715 (program): Indices of primes followed by a gap (distance to next larger prime) of 34.
A320716 (program): Indices of primes followed by a gap (distance to next larger prime) of 36.
A320717 (program): Indices of primes followed by a gap (distance to next larger prime) of 38.
A320718 (program): Indices of primes followed by a gap (distance to next larger prime) of 40.
A320719 (program): Indices of primes followed by a gap (distance to next larger prime) of 42.
A320730 (program): Integers k such that A086747(k) = 0, where A086747 is the Baum-Sweet sequence.
A320733 (program): Number of partitions of n with two sorts of part 1 which are introduced in ascending order.
A320752 (program): Primes of the form 5*n^2 - 5*n + 13.
A320753 (program): Number of partitions of n with seven kinds of 1.
A320754 (program): Number of partitions of n with eight kinds of 1.
A320755 (program): Number of partitions of n with nine kinds of 1.
A320756 (program): Number of partitions of n with ten kinds of 1.
A320758 (program): Number of ordered set partitions of [n] where the maximal block size equals two.
A320770 (program): a(n) = (-1)^floor(n/4) * 2^floor(n/2).
A320772 (program): Prime generating polynomial: a(n) = (4*n - 29)^2 + 58.
A320773 (program): Numbers (excluding squares) whose square root has a continued fraction with a period < 3.
A320816 (program): Number of partitions of n with exactly three sorts of part 1 which are introduced in ascending order.
A320826 (program): Expansion of x*(1 - 4*x)^(3/2)/(3*x - 1)^2.
A320827 (program): G.f.: -sqrt(1 - 4*x)*(2*x - 1)/(3*x - 1).
A320829 (program): Continued fraction of the positive constant t in (1,2) such that the partial denominators form the Beatty sequence {floor((n+1)*t), n >= 0}.
A320840 (program): Smallest N such that A092391(k) >= n for all k >= N.
A320857 (program): a(n) = Pi(8,5)(n) + Pi(8,7)(n) - Pi(8,1)(n) - Pi(8,3)(n) where Pi(a,b)(x) denotes the number of primes in the arithmetic progression a*k + b less than or equal to x.
A320858 (program): a(n) = A320857(prime(n)).
A320859 (program): Powers of 2 with initial digit 3.
A320860 (program): Powers of 2 with initial digit 4.
A320861 (program): Powers of 2 with initial digit 5.
A320862 (program): Powers of 2 with initial digit 6.
A320864 (program): Powers of 2 with initial digit 8.
A320866 (program): Primes such that p + digitsum(p, base 4) is again a prime.
A320877 (program): a(n) = 1 + Sum_{k=1..n} 2^prime(k).
A320889 (program): Number of set partitions of strict factorizations of n into factors > 1 such that all the blocks have the same product.
A320895 (program): a(n) = Sum_{k=1..n} k^3 * tau(k), where tau is A000005.
A320896 (program): a(n) = Sum_{k=1..n} k * tau(k)^2, where tau is A000005.
A320897 (program): a(n) = Sum_{k=1..n} k^2 * tau(k)^2, where tau is A000005.
A320898 (program): Expansion of e.g.f. exp(theta_3(x) - 1), where theta_3() is the Jacobi theta function.
A320899 (program): Expansion of e.g.f. exp(1/theta_4(x) - 1), where theta_4() is the Jacobi theta function.
A320900 (program): Expansion of Sum_{k>=1} x^k/(1 + x^k)^3.
A320901 (program): Expansion of Sum_{k>=1} x^k/(1 + x^k)^4.
A320903 (program): Row sums of A320902.
A320904 (program): T(n, k) = binomial(2*n + 1 - k, k)*hypergeom([1, 1, -k], [1, 2*(n - k + 1)], -1), triangle read by rows, T(n, k) for n >= 0 and 0 <= k <= n.
A320905 (program): T(n, k) = binomial(2*n - 1 - k, k - 1)*hypergeom([2, 2, 1-k], [1, 1 - 2*k + 2*n], -1), triangle read by rows, T(n, k) for n >= 1 and 1 <= k <= n.
A320906 (program): T(n, k) = binomial(2*n - k, k - 1)*hypergeom([2, 2, 1 - k], [1, 2*(1 - k + n)], -1), triangle read by rows, T(n,k) for n >= 0 and 0 <= k <= n.
A320907 (program): Row sums of A320906.
A320914 (program): One of the three successive approximations up to 13^n for 13-adic integer 5^(1/3). This is the 7 (mod 13) case (except for n = 0).
A320915 (program): One of the three successive approximations up to 13^n for 13-adic integer 5^(1/3). This is the 8 (mod 13) case (except for n = 0).
A320916 (program): Consider A010060 as a 2-adic number …100110010110, then a(n) is its approximation up to 2^n.
A320919 (program): Positive integers k such that binomial(k, 3) is divisible by 6.
A320926 (program): Concatenation of successive segments generated by the morphism {0 -> {0, 0, 1}, 1 -> {0}}, starting with 0.
A320927 (program): Concatenation of successive segments generated by the morphism {0 -> {0, 0, 1}, 1 -> {0,1,0}}, starting with 0.
A320928 (program): Positions of 0 in A320927.
A320929 (program): Positions of 1 in A320927.
A320933 (program): a(n) = 2^n - floor((n+3)/2).
A320934 (program): Number of chiral pairs of color patterns (set partitions) for a row of length n using 4 or fewer colors (subsets).
A320941 (program): Expansion of Sum_{k>=1} x^k*(1 + x^k)/(1 - x^k)^4.
A320942 (program): Expansion of Sum_{k>=1} (-1 + Product_{j>=1} (1 + x^(k*j))/(1 - x^(k*j))).
A320947 (program): a(n) is the number of dominoes, among all domino tilings of the 2 X n rectangle, sharing a length-2 side with the boundary of the rectangle.
A320956 (program): The exponential limit of sec + tan.
A320957 (program): a(n) = (1/6)*n!*[x^n] (2 + sec(3*x) + tan(3*x) + 3*sec(x) + 3*tan(x)).
A320958 (program): The exponential limit of arcsin (odd indices only).
A320959 (program): The exponential limit of arctanh (odd indices only).
A320962 (program): a(n) = (-1)^(n-1)*(n-1)!*Sum_{i=0..n} Stirling2(n, i) if n > 0 and 0 otherwise.
A320965 (program): Squares divisible by a single cube > 1.
A320985 (program): Complement of A092855.
A320986 (program): Fibonacci rabbit sequence number n coded in base four.
A320987 (program): Fibonacci rabbit sequence number n coded in base five.
A320988 (program): Fibonacci rabbit sequence number n coded in base six.
A320989 (program): Fibonacci rabbit sequence number n coded in base seven.
A320990 (program): Fibonacci rabbit sequence number n coded in base eight.
A320991 (program): Fibonacci rabbit sequence number n coded in base nine.
A320996 (program): Extremal values of Euler characteristics of polytopes.
A320997 (program): An absolute lower bound on the number of components in perfect systems of difference sets (PSDS).
A320999 (program): Related to the enumeration of pseudo-square convex polyominoes by semi-perimeter.
A321002 (program): a(0)=3; thereafter a(n) = 20*6^(n-1)-2^(n-1).
A321003 (program): a(n) = 2^n*(4*3^n-1).
A321013 (program): a(n) = how many of {6,7,8} divide n.
A321014 (program): Number of divisors of n which are greater than 3.
A321016 (program): Triangle read by rows: number of partitions of n into distinct and consecutive parts with largest part k (n >= 1, 1 <= k <= n)..
A321017 (program): a(n) = floor(pi(n)/2).
A321018 (program): a(n) = round(pi(n)/2).
A321019 (program): Coordination sequence for 3-D tiling (Cairo tiling) X Z, with respect to a 5-valent point.
A321020 (program): A hybrid of Kolakoski’s sequence A000002 and Golomb’s sequence A001462: if A001462(n) is odd replace it with 1, if even with 2.
A321025 (program): a(n) = sum of a(n-4) and a(n-5), with the lowest possible initial values that will generate a sequence where a(n) is always > a(n-1): 4, 5, 6, 7 and 8.
A321029 (program): Number of integers x such that 1 <= x <= n and gcd(x,n) = gcd(x+4,n) = gcd(x+6,n) = gcd(x+10,n) = gcd(x+12,n) = 1.
A321030 (program): Number of integers x such that 1 <= x <= n and gcd(x,n) = gcd(x+4,n) = gcd(x+6,n) = gcd(x+10,n) = gcd(x+12,n) = gcd(x+16,n) = 1.
A321032 (program): Number of words of length 3n such that all letters of the binary alphabet occur at least once and are introduced in ascending order and which can be built by repeatedly inserting triples into the initially empty word.
A321044 (program): Irregular table related to f[(a*x+b)/(c*x+d)]=c*x+d)^(2*n)*f[x], and f[x]=1/(x+1), f[x]=(a*x+b)/(c*x+d).
A321045 (program): a(n) is the value of the first entry in the matrix A^n where A = [{1,2,3}, {4,5,6}, {7,8,9}].
A321048 (program): Number of permutations of [n] with no fixed points where the maximal displacement of an element equals two.
A321069 (program): Greatest prime factor of n^3+2.
A321070 (program): Squares divisible by more than one cube > 1.
A321071 (program): Twice the Thue-Morse constant (A014571).
A321072 (program): One of the two successive approximations up to 11^n for 11-adic integer sqrt(3). Here the 5 (mod 11) case (except for n = 0).
A321073 (program): One of the two successive approximations up to 11^n for 11-adic integer sqrt(3). Here the 6 (mod 11) case (except for n = 0).
A321074 (program): Digits of one of the two 11-adic integers sqrt(3).
A321075 (program): Digits of one of the two 11-adic integers sqrt(3).
A321076 (program): One of the two successive approximations up to 11^n for 11-adic integer sqrt(5). Here the 4 (mod 11) case (except for n = 0).
A321077 (program): One of the two successive approximations up to 11^n for 11-adic integer sqrt(5). Here the 7 (mod 11) case (except for n = 0).
A321078 (program): Digits of one of the two 11-adic integers sqrt(5).
A321079 (program): Digits of one of the two 11-adic integers sqrt(5).
A321090 (program): Sequence {a(n), n>=0} satisfying the continued fraction relation: if z = [a(0) + 1; a(1) + 1, a(2) + 1, a(3) + 1, …, a(n) + 1, …], then 3*z = [a(0) + 9; a(1) + 11, a(2) + 11, a(3) + 11, …, a(n) + 11, …].
A321091 (program): Continued fraction expansion of the constant z that satisfies: CF(3*z, n) = CF(z, n) + 10, for n >= 0, where CF(z, n) denotes the n-th partial denominator in the continued fraction expansion of z.
A321093 (program): Continued fraction expansion of the constant z that satisfies: CF(4*z, n) = CF(z, n) + 21, for n >= 0, where CF(z, n) denotes the n-th partial denominator in the continued fraction expansion of z.
A321095 (program): Continued fraction expansion of the constant z that satisfies: CF(5*z, n) = CF(z, n) + 36, for n >= 0, where CF(z, n) denotes the n-th partial denominator in the continued fraction expansion of z.
A321097 (program): Continued fraction expansion of the constant z that satisfies: CF(6*z, n) = CF(z, n) + 55, for n >= 0, where CF(z, n) denotes the n-th partial denominator in the continued fraction expansion of z.
A321100 (program): Sequence {a(n), n>=0} satisfying the continued fraction relation: if z = [a(0) + 1; a(1) + 1, a(2) + 1, a(3) + 1, …, a(n) + 1, …], then 7*z = [a(0) + 9; a(1) + 11, a(2) + 11, a(3) + 11, …, a(n) + 11, …].
A321101 (program): Sequence generated by: a(3*n) = 0, a(3*n+2) = 3 - a(3*n+1), a(9*n+1) = 1, a(9*n+7) = 2, a(9*n+4) = 3 - a(3*n+1), for n >= 0.
A321102 (program): Sequence generated by: a(3*n) = 1, a(3*n+2) = 1 - a(3*n+1), a(9*n+1) = 1, a(9*n+7) = 0, a(9*n+4) = 1 - a(3*n+1), for n >= 0.
A321103 (program): Sequence generated by: a(3*n) = 1, a(3*n+2) = 2 - a(3*n+1), a(9*n+1) = 2, a(9*n+7) = 0, a(9*n+4) = 2 - a(3*n+1), for n >= 0.
A321104 (program): Sequence generated by: a(3*n) = 1, a(3*n+2) = 2 - a(3*n+1), a(9*n+1) = 0, a(9*n+7) = 2, a(9*n+4) = 2 - a(3*n+1), for n >= 0.
A321105 (program): One of the three successive approximations up to 13^n for 13-adic integer 5^(1/3). This is the 11 (mod 13) case (except for n = 0).
A321106 (program): Digits of one of the three 13-adic integers 5^(1/3) that is related to A320914.
A321107 (program): Digits of one of the three 13-adic integers 5^(1/3) that is related to A320915.
A321108 (program): Digits of one of the three 13-adic integers 5^(1/3) that is related to A321105.
A321119 (program): a(n) = ((1 - sqrt(3))^n + (1 + sqrt(3))^n)/2^floor((n - 1)/2); n-th row common denominator of A321118.
A321120 (program): Decimal expansion of (3 + sqrt(3))/12.
A321123 (program): a(n) = 2^n + 2*n^2 + 2*n + 1.
A321124 (program): a(n) = (4*n^3 - 6*n^2 + 14*n + 3)/3.
A321126 (program): T(n,k) = max(n + k - 1, n + 1, k + 1), square array read by antidiagonals (n >= 0, k >= 0).
A321129 (program): Numerator of Sum_{k=1..n} (k*sin((Pi*k)/3))/sqrt(3).
A321131 (program): Values of m (mod 25), where A317905(m) = 1. Values of m (mod 25) such that V(m) = 1, where V(m) indicates the constant convergence speed of the tetration base m.
A321133 (program): a(n) = 3*a(n-1) + 10*a(n-2), n >= 2; a(0)=-1, a(1)=23.
A321140 (program): a(n) = Sum_{d|n} sigma_3(d).
A321141 (program): a(n) = Sum_{d|n} sigma_n(d).
A321153 (program): Possible total numbers of pips when rolling two dice in backgammon.
A321162 (program): Maximum number of unbordered conjugates for a binary word of length n.
A321171 (program): a(n) is the total number of 1’s in binary that n shares with the positive integers less than n.
A321173 (program): a(n) = -2*a(n-1) + a(n-2) + a(n-3), a(0) = -1, a(1) = 3, a(2) = -9.
A321174 (program): a(n) = -2*a(n-1) + a(n-2) + a(n-3), a(0) = -1, a(1) = -4, a(2) = 5.
A321175 (program): a(n) = -a(n-1) + 2*a(n-2) + a(n-3), a(0) = -1, a(1) = -2, a(2) = 3.
A321176 (program): Number of integer partitions of n that are the vertex-degrees of some set system with no singletons.
A321177 (program): Heinz numbers of integer partitions that are the vertex-degrees of some set system with no singletons.
A321178 (program): One-half the sum of the first 2n + 1 primes.
A321180 (program): a(n) = 17*n^2 - 1.
A321184 (program): Number of integer partitions of n that are the vertex-degrees of some multiset of nonempty sets, none of which is a proper subset of any other, with no singletons.
A321185 (program): Number of integer partitions of n that are the vertex-degrees of some strict antichain of sets with no singletons.
A321189 (program): a(n) = n! * [x^n] 1 - 1/(n - 1/(exp(x) - 1)).
A321193 (program): Even numbers with no more than one odd prime factor, not counting multiplicity.
A321195 (program): Minimum number of monochromatic Schur triples over all 2-colorings of [n].
A321197 (program): a(n) gives the A-sequence for the Riordan matrix (1/(1 + x^2 - x^3), x/(1 + x^2 - x^3)) from A321196.
A321199 (program): Row sums of Riordan triangle A321198.
A321202 (program): Row sums of the irregular triangle A321201.
A321204 (program): Row sums of Riordan triangle A319203.
A321205 (program): Alternating row sums of Riordan triangle A319203.
A321207 (program): a(n) = (n*n!)^3.
A321212 (program): Numbers that are congruent to {2, 3} mod 16.
A321213 (program): a(n) is the number of divisors of n-th Fermat number (A000215).
A321220 (program): a(n) = n+2 if n is even, otherwise a(n) = 2*n+1 if n is odd.
A321222 (program): a(n) = Sum_{d|n} mu(d)*d^n.
A321228 (program): Number of non-isomorphic hypertrees of weight n with singletons.
A321232 (program): Length of n-th term of A321225.
A321233 (program): a(n) is the number of reflectable bases of the root system of type D_n.
A321234 (program): Denominator of series expansion of the hypergeometric series 3F2([1/2, 1, 1], [3/2, 3/2], x).
A321236 (program): a(n) = Sum_{d|n} mu(d)^2*d^n.
A321237 (program): Start with a square of dimension 1 X 1, and repeatedly append along the squares of the previous step squares with half their side length that do not overlap with any prior square; a(n) gives the number of squares appended at n-th step.
A321243 (program): a(n) is the product of n and all its decimal digits individually except the leftmost digit.
A321257 (program): Start with an equilateral triangle, and repeatedly append along the triangles of the previous step equilateral triangles with half their side length that do not overlap with any prior triangle; a(n) gives the number of triangles appended at n-th step.
A321259 (program): a(n) = sigma_n(n) - n^n.
A321262 (program): Expansion of 1/(1 - Sum_{k>=1} k*x^(2*k)/(1 - x^k)).
A321294 (program): a(n) = Sum_{d|n} mu(n/d)*d*sigma_n(d).
A321295 (program): a(n) = n * sigma_n(n).
A321298 (program): Triangle read by rows: T(n,k) is the number of the k-th eliminated person in the Josephus elimination process for n people and a count of 2, 1 <= k <= n.
A321322 (program): a(n) = Sum_{d|n} mu(n/d)*J_2(d), where J_2() is the Jordan function (A007434).
A321324 (program): a(n) = (n^2 - c(n)) / 7 + 1 where c(n) = c(-n) = c(n+7) for all n in Z and a(n) = 1 if 0 <= n <=3 except a(1) = 0.
A321327 (program): Expansion of Product_{k>=0} (1 - x^(2^k))^(2^k).
A321330 (program): Denominators of a Boas-Buck sequence for the triangular Sheffer matrix S2[3,1] = A282629.
A321333 (program): Compound sequence with a(n) = A319198(A278040(n)), for n >= 0.
A321334 (program): n such that all n - s are squarefree numbers where s is a squarefree number in range n/2 <= s < n.
A321335 (program): Expansion of 1/(1 - x) * Product_{k>=0} 1/(1 - x^(2^k))^(2^(k+1)).
A321336 (program): Expansion of Product_{k>=0} (1 - x^(2^k))^(2^(k+1)).
A321341 (program): An unbounded sequence which is 1 infinitely often, with the property that for any four consecutive terms the maximum term is the sum of the two minimum terms.
A321346 (program): Number of integer partitions of n containing no prime powers > 1.
A321348 (program): a(n) = Sum_{d|n} tau(d^n), where tau() is the number of divisors (A000005).
A321349 (program): a(n) = Sum_{d|n} phi(d^n), where phi() is the Euler totient function (A000010).
A321358 (program): a(n) = (2*4^n + 7)/3.
A321366 (program): a(n) is the least integer k greater than 1 such that n divides binomial(k, 2) = A000217(k-1).
A321369 (program): Coefficients of successive polynomials formed by iterating f(x) = -1 + 2x^2. Irregular triangle read by rows.
A321370 (program): n + [n*s/r] + [n*t/r], where r = 1, s = cos(2*Pi/5), t = sec(2*Pi/5).
A321371 (program): n + [n*r/s] + [n*t/s], where r = 1, s = cos(2*Pi/5), t = sec(2*Pi/5).
A321372 (program): n + [n*r/t] + [n*s/t], where r = 1, s = cos(2*Pi/5), t = sec(2*Pi/5).
A321373 (program): Array T(n,k) read by antidiagonals where the first row is (-1)^k*A140966(k) and each subsequent row is obtained by adding A001045(k) to the preceding one.
A321378 (program): Number of integer partitions of n containing no 1’s or prime powers.
A321383 (program): Numbers k such that the concatenation k21 is a square.
A321384 (program): a(1) = 1; a(n+1) = -Sum_{d|n} d*a(d).
A321385 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*d^d.
A321386 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*d^(d-1).
A321387 (program): Expansion of Product_{k>=1} (1 + x^k)^(k^(k-1)).
A321388 (program): Expansion of Product_{k>=1} (1 + x^k)^(k^(k-2)).
A321391 (program): Array read by antidiagonals: T(n,k) is the number of achiral rows of n colors using up to k colors.
A321394 (program): a(n) = (1/24)*n!*[x^n] (9 + sectan(4*x) + 6*sectan(2*x) + 8*sectan(x)) where sectan(x) = sec(x) + tan(x).
A321398 (program): a(n) = (-1)^(n+1)*n!* x^n.
A321401 (program): Number of non-isomorphic strict self-dual multiset partitions of weight n.
A321402 (program): Number of non-isomorphic strict self-dual multiset partitions of weight n with no singletons.
A321403 (program): Number of non-isomorphic self-dual set multipartitions (multisets of sets) of weight n.
A321404 (program): Number of non-isomorphic self-dual set multipartitions (multisets of sets) of weight n with no singletons.
A321405 (program): Number of non-isomorphic self-dual set systems of weight n.
A321406 (program): Number of non-isomorphic self-dual set systems of weight n with no singletons.
A321411 (program): Number of non-isomorphic self-dual multiset partitions of weight n with no singletons, with aperiodic parts whose sizes are relatively prime.
A321412 (program): Number of non-isomorphic self-dual multiset partitions of weight n with no singletons and with aperiodic parts.
A321416 (program): Number of n element multisets of the 10th roots of unity with zero sum.
A321421 (program): a(n) = 10*(4^n - 1)/3 + 1.
A321438 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*d^n.
A321461 (program): a(n) = -a(n-1) + 2*a(n-2) + a(n-3), a(0) = -1, a(1) = -2, a(2) = -4.
A321463 (program): Decimal expansion of 36*Pi.
A321480 (program): Zeroless analog of triangular numbers (version 2): a(0) = 0, and for any n > 0, a(n) = noz(1 + noz(2 + … + noz((n-1) + n))), where noz(n) = A004719(n) omits the zeros from n.
A321481 (program): Expansion of Sum_{n>=1} q^(n*(n-1)) / (1-q)^n.
A321483 (program): a(n) = 7*2^n + (-1)^n.
A321484 (program): Number of non-isomorphic self-dual connected multiset partitions of weight n.
A321490 (program): Triangular table T[n,k] = (n+k)(n^2+k^2), 1 <= k <= n = 1, 2, 3, …; read by rows.
A321499 (program): Numbers of the form (x - y)(x^2 - y^2) with x > y > 0.
A321500 (program): Triangular table T(n,k) = (n+k)*(n^2+k^2), n >= k >= 0; read by rows n = 0, 1, 2, …
A321501 (program): Numbers not of the form (x - y)(x^2 - y^2) with x > y > 0; complement of A321499.
A321510 (program): Primes p for which there exists a prime q < p such that 3*q == 1 (mod p).
A321512 (program): Characteristic function of the reverse in the shuffle (perfect faro shuffle with cut): 1 if the sequence of shuffles of n cards contains the reverse of the original order of cards, 0 if not.
A321516 (program): Number of composite divisors of n that are < n.
A321519 (program): Let d(n,i), i = 1..k be the k divisors of n^2 + 1 (the number 1 is not counted). a(n) is the number of ordered pairs d(n,i) < d(n,j) such that gcd(d(n,i), d(n,j)) = 1.
A321521 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*d!.
A321522 (program): Expansion of Product_{k>=1} (1 + x^k)^((k-1)!).
A321526 (program): Number of partitioned graphs on n labeled nodes.
A321531 (program): a(n) is the maximum number of distinct directions between n non-attacking rooks on an n X n chessboard.
A321539 (program): 3^n with digits rearranged into nonincreasing order.
A321540 (program): 3^n with digits rearranged into nondecreasing order.
A321541 (program): a(0)=1; thereafter a(n) = 3*a(n-1) with digits rearranged into nonincreasing order.
A321542 (program): a(0)=1; thereafter a(n) = 3*a(n-1) with digits rearranged into nondecreasing order.
A321543 (program): a(n) = Sum_{d|n} (-1)^(d-1)*d^2.
A321544 (program): a(n) = Sum_{d|n} (-1)^(d-1)*d^5.
A321545 (program): a(n) = Sum_{d|n} (-1)^(d-1)*d^6.
A321546 (program): a(n) = Sum_{d|n} (-1)^(d-1)*d^7.
A321547 (program): a(n) = Sum_{d|n} (-1)^(d-1)*d^8.
A321548 (program): a(n) = Sum_{d|n} (-1)^(d-1)*d^9.
A321549 (program): a(n) = Sum_{d|n} (-1)^(d-1)*d^10.
A321550 (program): a(n) = Sum_{d|n} (-1)^(d-1)*d^11.
A321551 (program): a(n) = Sum_{d|n} (-1)^(d-1)*d^12.
A321552 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*d^7.
A321553 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*d^8.
A321554 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*d^9.
A321555 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*d^10.
A321556 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*d^11.
A321557 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*d^12.
A321558 (program): a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^2.
A321559 (program): a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^3.
A321560 (program): a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^4.
A321561 (program): a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^5.
A321562 (program): a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^6.
A321563 (program): a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^7.
A321564 (program): a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^8.
A321565 (program): a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^9.
A321573 (program): Row sums of A321624.
A321574 (program): Row sums of A321623.
A321577 (program): a(n) = F_n mod M_n, where F_n = 2^(2^n) + 1 and M_n = 2^n - 1.
A321578 (program): a(n) is the maximum value of k such that A007504(k) <= prime(n).
A321579 (program): Number of n-tuples of 4 elements excluding reverse duplicates and those consisting of repetitions of the same element only.
A321580 (program): Numbers k such that it is possible to reverse a deck of k cards by a sequence of perfect Faro shuffles with cut.
A321598 (program): a(n) = Sum_{d|n} d*binomial(d+2,3).
A321601 (program): G.f.: A(x,y) = Sum_{n=-oo…+oo} (x^n + y)^n = Sum_{n>=0} Sum_{k>=0} T(n,k) * x^(n^2 + n*k) * y^k, written here as a rectangle of coefficients T(n,k) read by antidiagonals.
A321613 (program): Partial products of the unitary totient function (A047994): a(n) = Product_{k=1..n} uphi(k).
A321622 (program): The Riordan square of the Fine numbers, triangle read by rows, T(n, k) for 0 <= k<= n.
A321628 (program): Row sums of A321627.
A321631 (program): Row sums of A321630.
A321632 (program): Expansion of e.g.f. (1 + sin(x))/exp(x).
A321643 (program): a(n) = 5*2^n - (-1)^n.
A321647 (program): Number of distinct row/column permutations of the Ferrers diagram of the integer partition with Heinz number n.
A321648 (program): Number of permutations of the conjugate of the integer partition with Heinz number n.
A321655 (program): Number of distinct row/column permutations of strict plane partitions of n.
A321663 (program): a(n) = prime(n)^prime(n+2).
A321664 (program): A sequence consisting of three disjoint copies of the Fibonacci sequence, one shifted, with the property that for any four consecutive terms the maximum term is the sum of the two minimum terms.
A321672 (program): Number of chiral pairs of rows of length 5 using up to n colors.
A321697 (program): T(j,k) = binomial(j^k,k)/j, j <= m, k <= j, written as triangle T(j,k).
A321702 (program): Numbers that are still valid after a horizontal reflection on a calculator display.
A321703 (program): a(n) = 3*a(n-1) + 4*a(n-2) + a(n-3), a(0) = 1, a(1) = 1, a(2) = 5.
A321715 (program): a(n) = 3*a(n-1) + 4*a(n-2) + a(n-3), a(0) = 1, a(1) = -1, a(2) = -1 .
A321728 (program): Number of integer partitions of n whose Young diagram cannot be partitioned into vertical sections of the same sizes as the parts of the original partition.
A321729 (program): Number of integer partitions of n whose Young diagram can be partitioned into vertical sections of the same sizes as the parts of the original partition.
A321740 (program): Number of representations of n as a truncated triangular number.
A321741 (program): Product of the first n terms of A007318 (Pascal), read as a sequence.
A321747 (program): Sum of coefficients of elementary symmetric functions in the monomial symmetric function of the integer partition with Heinz number n.
A321753 (program): Sum of coefficients of elementary symmetric functions in the power sum symmetric function indexed by the integer partition with Heinz number n.
A321764 (program): Sum of coefficients of Schur functions in the monomial symmetric function of the integer partition with Heinz number n.
A321773 (program): Number of compositions of n into parts with distinct multiplicities and with exactly three parts.
A321774 (program): Number of compositions of n into parts with distinct multiplicities and with exactly four parts.
A321789 (program): Factorials of terms of Pascal’s triangle by row.
A321798 (program): G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^4).
A321799 (program): G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^5).
A321807 (program): a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^10.
A321808 (program): a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^11.
A321809 (program): a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^12.
A321810 (program): Sum of 6th powers of odd divisors of n.
A321811 (program): Sum of 7th powers of odd divisors of n.
A321812 (program): Sum of 8th powers of odd divisors of n.
A321813 (program): Sum of 9th powers of odd divisors of n.
A321814 (program): Sum of 10th powers of odd divisors of n.
A321815 (program): Sum of 11th powers of odd divisors of n.
A321816 (program): Sum of 12th powers of odd divisors of n.
A321817 (program): a(n) = Sum_{d|n, n/d odd} d^6 for n > 0.
A321818 (program): a(n) = Sum_{d|n, n/d odd} d^8 for n > 0.
A321819 (program): a(n) = Sum_{d|n, n/d odd} d^10 for n > 0.
A321820 (program): a(n) = Sum_{d|n, n/d odd} d^12 for n > 0.
A321821 (program): a(n) = Sum_{d|n, d==1 mod 4} d^5 - Sum_{d|n, d==3 mod 4} d^5.
A321822 (program): a(n) = Sum_{d|n, d==1 mod 4} d^6 - Sum_{d|n, d==3 mod 4} d^6.
A321823 (program): a(n) = Sum_{d|n, d==1 mod 4} d^7 - Sum_{d|n, d==3 mod 4} d^7.
A321824 (program): a(n) = Sum_{d|n, d==1 mod 4} d^8 - Sum_{d|n, d==3 mod 4} d^8.
A321825 (program): a(n) = Sum_{d|n, d==1 (mod 4)} d^9 - Sum_{d|n, d==3 (mod 4)} d^9.
A321826 (program): a(n) = Sum_{d|n, d==1 mod 4} d^10 - Sum_{d|n, d==3 mod 4} d^10.
A321827 (program): a(n) = Sum_{d|n, d==1 (mod 4)} d^11 - Sum_{d|n, d==3 (mod 4)} d^11.
A321828 (program): a(n) = Sum_{d|n, d==1 mod 4} d^12 - Sum_{d|n, d==3 mod 4} d^12.
A321829 (program): a(n) = Sum_{d|n, n/d==1 mod 4} d^5 - Sum_{d|n, n/d==3 mod 4} d^5.
A321830 (program): a(n) = Sum_{d|n, n/d==1 mod 4} d^6 - Sum_{d|n, n/d==3 mod 4} d^6.
A321831 (program): a(n) = Sum_{d|n, n/d==1 mod 4} d^7 - Sum_{d|n, n/d==3 mod 4} d^7.
A321832 (program): a(n) = Sum_{d|n, n/d==1 (mod 4)} d^8 - Sum_{d|n, n/d==3 (mod 4)} d^8.
A321833 (program): a(n) = Sum_{d|n, n/d==1 mod 4} d^9 - Sum_{d|n, n/d==3 mod 4} d^9.
A321834 (program): a(n) = Sum_{d|n, n/d==1 mod 4} d^10 - Sum_{d|n, n/d==3 mod 4} d^10.
A321835 (program): a(n) = Sum_{d|n, n/d==1 mod 4} d^11 - Sum_{d|n, n/d==3 mod 4} d^11.
A321836 (program): a(n) = Sum_{d|n, n/d==1 mod 4} d^12 - Sum_{d|n, n/d==3 mod 4} d^12.
A321837 (program): Expansion of e.g.f.: exp(x/(1-3*x)).
A321838 (program): Number of words w of length n such that each letter of the binary alphabet is used at least once and for every prefix z of w we have #(z,a_i) = 0 or #(z,a_i) >= #(z,a_j) for all j>i and #(z,a_i) counts the occurrences of the i-th letter in z.
A321847 (program): E.g.f.: exp(x/(1 - 4*x)).
A321848 (program): E.g.f.: exp(x/(1-5*x)).
A321849 (program): Expansion of e.g.f.: exp(x/(1-6*x)).
A321850 (program): E.g.f.: exp(x/(1-7*x)).
A321853 (program): a(n) is the sum of the fill times of all 1-dimensional fountains given by the permutations in S_n.
A321858 (program): a(n) = Pi(12,5)(n) + Pi(12,7)(n) - Pi(12,1)(n) - Pi(12,11)(n) where Pi(a,b)(x) denotes the number of primes in the arithmetic progression a*k + b less than or equal to x.
A321861 (program): a(n) = A071838(prime(n)).
A321862 (program): a(n) = A321857(prime(n)).
A321863 (program): a(n) = A321858(prime(n)).
A321875 (program): a(n) = Sum_{d|n} d*d!.
A321879 (program): Partial sums of the Jordan function J_2(k), for 1 <= k <= n.
A321882 (program): a(n) is the least base b > 1 such that the sum n + n can be computed without carry.
A321883 (program): Nonnegative integers n for which n! + 1 is not a square.
A321885 (program): a(1) = 1, a(n) = n + d(a(n-1)).
A321890 (program): Primes of the form p^2 + 16 where p is prime.
A321893 (program): Sum of coefficients of forgotten symmetric functions in the Schur function of the integer partition with Heinz number n.
A321898 (program): Sum of coefficients of power sums symmetric functions in h(y) * Product_i y_i! where h is homogeneous symmetric functions and y is the integer partition with Heinz number n.
A321901 (program): Irregular table read by rows: T(n,k) = (2*k+1)^(-(2*k+1)) mod 2^n, 0 <= k <= 2^(n-1) - 1.
A321902 (program): Irregular table read by rows: T(n,k) = (2*k+1)^(1/(2*k+1)) mod 2^n, 0 <= k <= 2^(n-1) - 1.
A321903 (program): Irregular table read by rows: T(n,k) = (2*k+1)^(-1/(2*k+1)) mod 2^n, 0 <= k <= 2^(n-1) - 1.
A321904 (program): Irregular table read by rows: T(n,k) is the smallest m such that m^(-m) == 2*k + 1 (mod 2^n), 0 <= k <= 2^(n-1) - 1.
A321905 (program): Irregular table read by rows: T(n,k) is the smallest m such that m^(1/m) == 2*k + 1 (mod 2^n), 0 <= k <= 2^(n-1) - 1.
A321906 (program): Irregular table read by rows: T(n,k) is the smallest m such that m^(-1/m) == 2*k + 1 (mod 2^n), 0 <= k <= 2^(n-1) - 1.
A321907 (program): If n > 1 is the k-th prime number, then a(n) = k!, otherwise a(n) = 0.
A321909 (program): a(n) is the least base b > 1 in which the additive persistence of n is <= 1.
A321942 (program): A sequence related to the Euler-Gompertz constant.
A321944 (program): Starting from n, repeatedly compute the sum of the prime divisors until a fixed point or 0 is reached; a(n) is the number of terms, including n.
A321946 (program): Number of divisors for the automorphism group size having the largest number of divisors for a binary self-dual code of length 2n.
A321957 (program): a(n) = binomial(3*n, n + 1)*hypergeom([1, 1 - 2*n], [2 + n], -1).
A321959 (program): a(n) = [x^n] ((1 - x)*x)/((1 - 2*x)^2*(2*x^2 - 2*x + 1)).
A321963 (program): Stieltjes generated from the sequence m, m+1, m+2, m+3, …. where m = 4.
A321965 (program): a(n) = n! [x^n] exp((1/(x - 1)^2 - 1)/2)/(1 - x).
A321968 (program): a(n) = 2^n*n!*[x^n] -sqrt(exp(LambertW(-x)))*(LambertW(-x) + 1).
A321973 (program): Partial sums of the Dedekind psi_2(k) function, for 1 <= k <= n.
A321984 (program): Decimal expansion of number of kilograms (kg) in 1 international avoirdupois ounce (oz).
A321986 (program): Number of integer pairs (x,y) with x+y < 3*n/4, x-y < 3*n/4 and -x/2 < y < 2*x.
A321999 (program): Sum of digits of n minus the number of digits of n.
A322003 (program): Indices where A028897(A322000(n)) increases. Partial sums of A072170(n,10).
A322008 (program): 1/(1 - Integral_{x=0..1} x^(x^n) dx), rounded to the nearest integer.
A322014 (program): Heinz numbers of integer partitions with an even number of even parts.
A322015 (program): If A003188(n+1) < A003188(n), then a(n) = n+1, otherwise a(n) = 0.
A322016 (program): a(0) = 0; for n > 0, if A003188(n) > A003188(n-1) then a(n) = n-1, otherwise a(n) = 0.
A322018 (program): a(n) = A006068(A129760(A003188(n))).
A322026 (program): Lexicographically earliest such sequence a that a(i) = a(j) => A007814(i) = A007814(j) and A007949(i) = A007949(j), for all i, j, where A007814 and A007949 give the 2-adic and 3-adic valuation of n.
A322029 (program): Denominator of least value of the squared diameters of the enclosing circles of all strictly convex lattice n-gons with minimal area given by A070911. Numerators are A321693.
A322031 (program): (Sum_{t=0..oo} ((-1)^t*(2*t+1)*q^((2*t+1)^2)))^3 * (Sum_{t=0..oo} q^((2*t+1)^2)) = Sum_{k=0..oo} a(k)*q^(8*k+4).
A322034 (program): Let p1 <= p2 <= … <= pk be the prime factors of n, with repetition; let s = 1/p1 + 1/(p1*p2) + 1/(p1*p2*p3) + … + 1/(p1*p2*…*pk); a(n) = numerator of s. a(1)=0 by convention.
A322035 (program): Let p1 <= p2 <= … <= pk be the prime factors of n, with repetition; let s = 1/p1 + 1/(p1*p2) + 1/(p1*p2*p3) + … + 1/(p1*p2*…*pk); a(n) = denominator of s. a(1)=1 by convention.
A322036 (program): a(n) = A322035(n) - A322034(n).
A322037 (program): a(n) = 2^b(n), where b(n) = A000031(n).
A322039 (program): Expansion of (1 + x)^2 / ((1 - x)^2*(1 + 2*x)^2).
A322040 (program): Expansion of (1 + x)^2 / ((1 - x)^2*(1 + 2*x + 2*x^2)^2).
A322042 (program): Maximum edge-distance of a point in the quotient graph E/nE from the origin (see A322041 for further information).
A322043 (program): Numbers k such that the coefficient of x^k in the expansion of Product_{m >= 1} (1-x^m)^15 is zero.
A322048 (program): Final elements in rows when A322050 is displayed as a triangle.
A322051 (program): a(n) is the number of initial terms in the row of length 2^n of A322050 that agree with the limiting sequence A322049.
A322052 (program): Number of decimal strings of length n that contain a specific string xy where x and y are distinct digits.
A322053 (program): Number of decimal strings of length n that contain a specific string xx (where x is a single digit).
A322054 (program): Number of decimal strings of length n that do not contain a specific string xx (where x is a single digit).
A322062 (program): Sums of pairs of consecutive terms of Pascal’s triangle read by row.
A322068 (program): a(n) = (1/2)*Sum_{p prime <= n} floor(n/p) * floor(1 + n/p).
A322071 (program): Triangle read by rows: T(n, k) is the largest integer m such that m*k^k <= 2*n^k.
A322072 (program): Row sums of the triangle A322071.
A322075 (program): Number of factorizations of n into nonprime squarefree numbers > 1.
A322078 (program): a(n) = n^2 * Sum_{p|n} 1/p^2, where p are primes dividing n.
A322079 (program): a(n) = n^2 * Sum_{ p^k | n } k / p^2, where p are primes dividing n with multiplicity k.
A322085 (program): One of the two successive approximations up to 13^n for 13-adic integer sqrt(3). Here the 4 (mod 13) case (except for n = 0).
A322086 (program): One of the two successive approximations up to 13^n for 13-adic integer sqrt(3). Here the 9 (mod 13) case (except for n = 0).
A322087 (program): Digits of one of the two 13-adic integers sqrt(3).
A322088 (program): Digits of one of the two 13-adic integers sqrt(3).
A322089 (program): One of the two successive approximations up to 13^n for 13-adic integer sqrt(-3). Here the 6 (mod 13) case (except for n = 0).
A322090 (program): One of the two successive approximations up to 13^n for 13-adic integer sqrt(3). Here the 7 (mod 13) case (except for n = 0).
A322091 (program): Digits of one of the two 13-adic integers sqrt(-3).
A322092 (program): Digits of one of the two 13-adic integers sqrt(-3).
A322108 (program): Distance of n-th iteration in an alternating rectangular spiral.
A322111 (program): Number of non-isomorphic self-dual connected multiset partitions of weight n with multiset density -1.
A322112 (program): Number of non-isomorphic self-dual connected multiset partitions of weight n with no singletons and multiset density -1.
A322113 (program): Number of non-isomorphic self-dual connected antichains of multisets of weight n.
A322116 (program): Main diagonal of triangle A321600; a(n) = A321600(n,n-1) for n >= 1.
A322121 (program): Composite numbers m such that b^(m-1) == 1 (mod (b^2-1)*m) has a solution b.
A322127 (program): Triangular array, read by rows: T(n,k) = numerator of binomial(n-1, n-k)/k!, 1 <= k <= n.
A322128 (program): Triangular array, read by rows: T(n,k) = denominator of binomial(n-1, n-k)/k!, 1 <= k <= n.
A322129 (program): Digital roots of A057084.
A322135 (program): Table of truncated square pyramid numbers, read by antidiagonals.
A322136 (program): Numbers whose number of prime factors counted with multiplicity exceeds half their sum of prime indices by at least 1.
A322141 (program): a(n) is also the sum of the even-indexed terms of the n-th row of the triangle A237591.
A322144 (program): a(n) = Sum_{i=1..phi(n)-1} (r(i+1)-r(i))^2 where r(1) = 1 < … < n-1 = r(phi(n)) are the phi(n) integers relatively prime to n.
A322157 (program): The successive approximations up to 5^n for 5-adic integer 7^(1/5).
A322159 (program): Decimal expansion of 1 - 1/sqrt(5).
A322171 (program): Expansion of x*(3 + 5*x + x^2 + x^3)/((1 - x)^2*(1 + x^2)).
A322175 (program): Determinant of the symmetric n X n matrix M defined by M(i,j) = mu(gcd(i,j)) for 1 <= i,j <= n where mu is the Moebius function.
A322185 (program): a(n) = sigma(2*n) * binomial(2*n,n)/2, for n >= 1.
A322186 (program): G.f.: exp( Sum_{n>=1} A322185(n)*x^n/n ), where A322185(n) = sigma(2*n) * binomial(2*n,n)/2.
A322201 (program): Main diagonal of square table A322200.
A322202 (program): G.f.: exp( Sum_{n>=1} A322201(n)*x^n/n ), where A322201(n) is the coefficient of x^n*y^n/(2*n) in Sum_{n>=1} -log(1 - (x^n + y^n)).
A322203 (program): a(n) = coefficient of x^n*y^n/n in Sum_{n>=1} -log(1 - (x^n + y^n)), for n >= 1.
A322204 (program): G.f.: exp( Sum_{n>=1} A322203(n)*x^n/n ), where A322203(n) is the coefficient of x^n*y^n/n in Sum_{n>=1} -log(1 - (x^n + y^n)).
A322205 (program): a(n) = coefficient of x^(2*n)*y^n/n in Sum_{n>=1} -log(1 - (x^n + y^n)) for n >= 1.
A322206 (program): G.f.: exp( Sum_{n>=1} A322205(n)*x^n/n ), where A322205(n) is the coefficient of x^(2*n)*y^n/n in Sum_{n>=1} -log(1 - (x^n + y^n)).
A322216 (program): G.f.: Product_{n>=1} (1 - 2*x^n)^3.
A322217 (program): Expansion of the 2-adic integer sqrt(17) that ends in 01.
A322240 (program): a(n) = A084605(n)^2, the square of the central coefficient in (1 + x + 4*x^2)^n.
A322241 (program): G.f.: exp( Sum_{n>=1} A084605(n)^2 * x^n/n ), where A084605(n) is the central coefficient in (1 + x + 4*x^2)^n.
A322242 (program): G.f.: 1/sqrt(1 - 6*x - 7*x^2).
A322243 (program): a(n) = A322242(n)^2, the square of the central coefficient in (1 + 3*x + 4x^2)^n.
A322244 (program): G.f.: 1/sqrt(1 - 6*x - 55*x^2).
A322245 (program): a(n) = A322244(n)^2, the square of the central coefficient in (1 + 3*x + 16x^2)^n.
A322246 (program): Expansion of g.f.: 1/sqrt(1 - 10*x - 11*x^2).
A322247 (program): a(n) = A322246(n)^2, the square of the central coefficient in (1 + 5*x + 9*x^2)^n.
A322248 (program): G.f.: 1/sqrt( (1 + 3*x)*(1 - 13*x) ).
A322249 (program): a(n) = A322248(n)^2, the square of the central coefficient in (1 + 5*x + 16*x^2)^n.
A322250 (program): Take binary expansion of 2n-1 and delete the trailing block of 1’s, except if the number is 11…1, leave a single 1.
A322252 (program): a(0) = 1 and a(n) = (5*n)!/(5!*n!^5) for n > 0.
A322260 (program): Numbers k such that the poset of multiset partitions of a multiset whose multiplicities are the prime indices of k is a lattice.
A322264 (program): Square array A(n,k), n >= 1, k >= 0, read by antidiagonals: A(n,k) = denominator of Sum_{d|n} 1/d^k.
A322284 (program): Number of nonequivalent ways to place n nonattacking kings on a 2 X 2n chessboard under all symmetry operations of the rectangle.
A322303 (program): a(n) = Fibonacci(semiprime(n)).
A322306 (program): Number of connected divisors of n. Number of connected submultisets of the n-th multiset multisystem (A302242).
A322307 (program): Number of multisets in the swell of the n-th multiset multisystem.
A322309 (program): Largest automorphism group size for a binary self-dual code of length 2n
A322312 (program): a(n) = Product_{d|n, d+1 is prime} prime(1+A286561(n,d+1)), where A286561(n,k) gives the k-valuation of n (for k > 1).
A322321 (program): a(n) = lcm(A003557(n), A173557(n)).
A322325 (program): Number of nondecreasing Motzkin paths of length n.
A322327 (program): a(n) = A005361(n) * A034444(n).
A322328 (program): a(n) = A005361(n) * 4^A001221(n) for n > 0.
A322351 (program): a(n) = min(A003557(n), A173557(n)).
A322352 (program): a(n) = max(A003557(n), A173557(n)).
A322354 (program): Greatest common divisor of product p and product (p+2), where p ranges over distinct prime divisors of n; a(n) = gcd(A007947(n), A166590(A007947(n))).
A322359 (program): Least common multiple of product (p-1) and product (p+1), where p ranges over distinct prime divisors of n.
A322360 (program): Multiplicative with a(p^e) = p^2 - 1.
A322361 (program): a(n) = gcd(n, A003961(n)), where A003961 is completely multiplicative with a(prime(k)) = prime(k+1).
A322362 (program): a(n) = gcd(n, A166590(n)), where A166590 is completely multiplicative with a(p) = p+2 for prime p.
A322368 (program): Heinz numbers of disconnected integer partitions.
A322371 (program): a(n) is the least practical number that is divisible by prime(n).
A322372 (program): Least positive integer c such that c*prime(n) is practical.
A322373 (program): Let d_i be the i-th divisor of n. Then a(n) is the largest k such that gcd(d_k, …, d_tau(n)) = 1.
A322382 (program): a(n) = p*a(n/p) + 1, where p is the smallest prime divisor of n; a(1)=0.
A322405 (program): Number of compositions of n into parts 1, 8, 9.
A322406 (program): a(n) = n + n*n^n.
A322407 (program): Compound sequence a(n) = A319198(A278039(n)), for n >= 0.
A322408 (program): Compound sequence with a(n) = A319198(A278041(n)), for n >= 0.
A322409 (program): Compound tribonacci sequence with a(n) = A278040(A278040(n)), for n >= 0.
A322410 (program): Compound tribonacci sequence with a(n) = A278040(A278039(n)), for n >= 0.
A322411 (program): Compound tribonacci sequence with a(n) = A278040(A278041(n)), for n >= 0.
A322412 (program): Compound tribonacci sequence with a(n) = A278041(A278040(n)), for n >= 0.
A322413 (program): Compound tribonacci sequence with a(n) = A278041(A278039(n)), for n >= 0.
A322414 (program): Compound tribonacci sequence with a(n) = A278041(A278041(n)), for n >= 0.
A322417 (program): a(n) - 2*a(n-1) = period 2: repeat [3, 0] for n > 0, a(0)=5, a(1)=13.
A322420 (program): Sum of the first n*(n+1) primes.
A322430 (program): Numbers k such that the coefficient of x^k in the expansion of Product_{j>=1} (1-x^j)^8 is zero.
A322431 (program): Numbers k such that the coefficient of x^k in the expansion of Product_{j>=1} (1-x^j)^10 is zero.
A322432 (program): Numbers k such that the coefficient of x^k in the expansion of Product_{j>=1} (1-x^j)^14 is zero.
A322438 (program): Number of unordered pairs of factorizations of n into factors > 1 where no factor of one properly divides any factor of the other.
A322450 (program): Number of permutations of [2n] in which the size of the last cycle is n and the cycles are ordered by increasing smallest elements.
A322453 (program): Number of factorizations of n into factors > 1 using only primes and perfect powers.
A322458 (program): Sum of n-th powers of the roots of x^3 - 49*x + 49.
A322459 (program): Sum of n-th powers of the roots of x^3 + 7*x^2 + 14*x + 7.
A322462 (program): Numbers on the 0-1-12 line in a spiral on a grid of equilateral triangles.
A322465 (program): Numbers on the 0-9-10-line in a spiral on an equilateral triangular lattice.
A322483 (program): The number of semi-unitary divisors of n.
A322489 (program): Numbers k such that k^k ends with 4.
A322490 (program): Numbers k such that k^k ends with 7.
A322492 (program): Records in the number of ways to represent a number as truncated triangular number A008912.
A322496 (program): Number of tilings of a 3 X n rectangle using V (2m+1)-ominoes (m >= 0) in standard orientation.
A322504 (program): a(n) = -4*a(n-1) - 3*a(n-2) + a(n-3), a(0) = 1, a(1) = -2, a(2) = 4.
A322518 (program): Binomial transform of the Apéry numbers (A005259).
A322519 (program): Inverse binomial transform of the Apéry numbers (A005259).
A322533 (program): Position of 1/3^n in the sequence of all numbers 1/2^m, 1/3^m, 2/3^m arranged in decreasing order.
A322534 (program): Position of 2/3^n in the sequence of all numbers 1/2^m, 1/3^m, 2/3^m arranged in decreasing order.
A322544 (program): a(n) is the reciprocal of the coefficient of x^n in the power series of the function defined by ((1+2x)*exp(x) + 3*exp(-x) - 4)/ (4x^2).
A322546 (program): Numbers k such that every integer partition of k contains a 1 or a prime power.
A322550 (program): Table read by ascending antidiagonals: T(n, k) is the minimum number of cubes necessary to fill a right square prism with base area n^2 and height k.
A322551 (program): Primes indexed by squarefree semiprimes.
A322553 (program): Odd numbers whose product of prime indices is a prime power.
A322556 (program): The number of eigenvectors with eigenvalue 1 summed over all linear operators on the vector space GF(2)^n.
A322558 (program): a(0)=1, a(1)=1; for n>1, a(n)=a(n-1)+a(n-2) if a(n-1) is less than or equal to n-1, otherwise a(n)=a(n-1)-(n-1).
A322559 (program): One of the two successive approximations up to 17^n for 17-adic integer sqrt(2). This is the 6 (mod 17) case (except for n = 0).
A322560 (program): One of the two successive approximations up to 17^n for 17-adic integer sqrt(2). This is the 11 (mod 17) case (except for n = 0).
A322561 (program): Digits of one of the two 17-adic integers sqrt(2) that is related to A322559.
A322562 (program): Digits of one of the two 17-adic integers sqrt(2) that is related to A322560.
A322563 (program): One of the two successive approximations up to 17^n for 17-adic integer sqrt(-2). This is the 7 (mod 17) case (except for n = 0).
A322564 (program): One of the two successive approximations up to 17^n for 17-adic integer sqrt(-2). This is the 10 (mod 17) case (except for n = 0).
A322565 (program): Digits of one of the two 17-adic integers sqrt(-2) that is related to A322563.
A322566 (program): Digits of one of the two 17-adic integers sqrt(-2) that is related to A322564.
A322573 (program): G.f. = g(f(x)), where f(x) = g.f. of Fibonacci sequence A000045 and g(x) = g.f. of Jacobsthal sequence A001045.
A322577 (program): a(n) = Sum_{d|n} psi(n/d) * phi(d).
A322581 (program): Sum of A003958 and its Dirichlet inverse: a(n) = A003958(n) + A097945(n).
A322582 (program): a(n) = n - A003958(n), where A003958 is fully multiplicative with a(p) = (p-1).
A322584 (program): Number of divisors of n that area product of primorial numbers (terms of A025487).
A322585 (program): a(n) = 1 if n is a product of primorial numbers (A002110), 0 otherwise.
A322586 (program): a(n) = 1 if n is a highly composite number (A002182), 0 otherwise.
A322590 (program): Lexicographically earliest such positive sequence a that a(i) = a(j) => A007947(i) = A007947(j) for all i, j.
A322593 (program): a(n) = 2^n + 2*n^2 + 1.
A322594 (program): a(n) = (4*n^3 + 12*n^2 - 4*n + 3)/3.
A322595 (program): a(n) = (n^3 + 9*n + 14*n + 9)/3.
A322596 (program): Square array read by descending antidiagonals (n >= 0, k >= 0): let b(n,k) = (n+k)!/((n+1)!*k!); then T(n,k) = b(n,k) if b(n,k) is an integer, and T(n,k) = floor(b(n,k)) + 1 otherwise.
A322597 (program): a(n) = (4*n^3 - 6*n^2 + 20*n + 3)/3.
A322598 (program): a(n) is the number of unlabeled rank-3 graded lattices with 3 coatoms and n atoms.
A322615 (program): Nearest integer to 4*Pi*n^2.
A322623 (program): E.g.f.: (1 + sinh(x)) / (1 - sinh(x)).
A322628 (program): Number of n-digit decimal numbers containing a fixed 2-digit integer with distinct digits as a substring.
A322630 (program): Arithmetic table similar to multiplication with different rules for odd and even products, read by antidiagonals. T(n,k) = (n*k + A319929(n,k))/2.
A322631 (program): a(n) = 2*binomial(7*n-1,2*n)/(7*n-1).
A322655 (program): Numerator of (Sum_{d|n} sigma(d)) / sigma(n).
A322656 (program): Denominator of (Sum_{d|n} sigma(d)) / sigma(n).
A322661 (program): Number of graphs with loops spanning n labeled vertices.
A322665 (program): Partial sums of A089451.
A322666 (program): a(n) is the smallest positive integer k such that there does not exist an m such that floor(m^2/10^n) = k.
A322667 (program): a(n) is the smallest positive integer k such that floor((k + 1)^2/10^n) - floor(k^2/10^n) = 2.
A322671 (program): a(n) = Sum_{d|n} (pod(d)/d), where pod(k) is the product of the divisors of k (A007955).
A322672 (program): a(n) = Product_{d|n} (pod(d)/d) where pod(k) is the product of the divisors of k (A007955).
A322673 (program): a(n) = numerator of Product_{d|n} (sigma(d)/d) where sigma(k) = the sum of the divisors of k (A000203).
A322675 (program): a(n) = n * (4*n + 3)^2.
A322677 (program): a(n) = 16 * n * (n+1) * (2*n+1)^2.
A322699 (program): Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where A(n,k) is 1/2 * (-1 + Sum_{j=0..k} binomial(2*k,2*j)*(n+1)^(k-j)*n^j).
A322701 (program): The successive approximations up to 2^n for 2-adic integer 3^(1/3).
A322702 (program): a(n) is the product of primes p such that p+1 divides n.
A322707 (program): a(0)=0, a(1)=5 and a(n) = 22*a(n-1) - a(n-2) + 10 for n > 1.
A322708 (program): a(0)=0, a(1)=6 and a(n) = 26*a(n-1) - a(n-2) + 12 for n > 1.
A322709 (program): a(0)=0, a(1)=7 and a(n) = 30*a(n-1) - a(n-2) + 14 for n > 1.
A322744 (program): Array T(n,k) = (3*n*k - A319929(n,k))/2, n >= 1, k >= 1, read by antidiagonals.
A322745 (program): a(n) = n * (16*n^2+20*n+5)^2.
A322746 (program): a(n) = 1/2 * (-1 + Sum_{k=0..n} binomial(2*n,2*k)*(n+1)^(n-k)*n^k).
A322747 (program): a(n) = sqrt(1 + A322746(2*n)).
A322753 (program): Expansion of x*(1 + 2*x - 3*x^2 + 4*x^3) / (1 - x - x^2 + x^3 - x^4).
A322755 (program): Numerator of expected payoff in the “Guessing Card Colors” game with a 2n-card deck, using an optimal strategy.
A322756 (program): Denominator of expected payoff in the “Guessing Card Colors” game with a 2n-card deck, using an optimal strategy.
A322761 (program): Irregular triangle read by rows in which n-th row lists all partitions of n, in graded reverse lexicographic ordering, using a compressed notation.
A322780 (program): First differences of A237262.
A322783 (program): a(n) = 1 - n + (2^(n+2) - (-1)^n)/3.
A322790 (program): Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where A(n,k) is Sum_{j=0..k} binomial(2*k,2*j)*(n+1)^(k-j)*n^j.
A322796 (program): a(n) = Kronecker symbol (6/n).
A322798 (program): Number of compositions (ordered partitions) of n into hexagonal numbers (A000384).
A322801 (program): Number of compositions (ordered partitions) of n into centered pentagonal numbers (A005891).
A322802 (program): Number of compositions (ordered partitions) of n into centered hexagonal numbers (A003215).
A322809 (program): Lexicographically earliest such sequence a that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n) = -1 if n is an odd prime, and f(n) = floor(n/2) for all other numbers.
A322813 (program): a(n) = A001227(A122111(n)).
A322819 (program): a(n) = A000593(A122111(n)).
A322820 (program): a(n) = A052126(n) * A006530(A052126(n)).
A322821 (program): a(1) = 0; for n > 1, a(n) = A000265(A048675(n)).
A322825 (program): A variant of A322827.
A322827 (program): A permutation of A025487: Sequence of least representatives of distinct prime signatures obtained from the run lengths present in the binary expansion of n.
A322829 (program): a(n) = Jacobi (or Kronecker) symbol (n/21).
A322830 (program): a(n) = 32*n^3 + 48*n^2 + 18*n + 1.
A322832 (program): Values x + y, where the ordered pairs (x,y) are sorted first by maximal coordinate and then lexicographically.
A322836 (program): Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where A(n,k) is Chebyshev polynomial of the first kind T_{n}(x), evaluated at x=k.
A322839 (program): Numbers n with more prime factors (counted with multiplicity) than n+1.
A322840 (program): Positive integers n with fewer prime factors (counted with multiplicity) than n + 1.
A322844 (program): a(n) = (1/12)*n^2*(3*(1 + n^2) - 2*(2 + n^2)*(n mod 2)).
A322860 (program): If n is practical (in A005153), a(n) = 1, otherwise a(n) = 0.
A322865 (program): a(n) = A000265(A122111(n)).
A322867 (program): a(n) = A000120(A122111(n)).
A322869 (program): a(n) = A000120(A048675(n)).
A322885 (program): Number of 3-generated Abelian groups of order n.
A322888 (program): Chebyshev T-polynomials T_n(16).
A322889 (program): Chebyshev T-polynomials T_n(18).
A322890 (program): a(n) = value of Chebyshev T-polynomial T_n(20).
A322899 (program): a(n) = T_{2*n}(n+1) where T_{n}(x) is a Chebyshev polynomial of the first kind.
A322904 (program): a(n) = Sum_{k=0..n} binomial(2*n+1,2*k+1)*(n^2-1)^(n-k)*n^(2*k).
A322907 (program): Entry points for the 3-Fibonacci numbers A006190.
A322908 (program): The determinant of an n X n Toeplitz matrix M(n) whose first row consists of successive positive integer numbers 1, …, n and whose first column consists of 1, n + 1, …, 2*n - 1.
A322914 (program): a(0)=0; for n>0, a(n) is the number of rooted 4-regular maps on the torus having n vertices.
A322918 (program): a(n) is the number of rooted 6-regular maps with n vertices on the torus.
A322921 (program): From Goldbach’s conjecture: a(n) is the number of decompositions of 6n into a sum of two primes.
A322923 (program): Primes of the form 3*p + 4, where p is a prime.
A322924 (program): Sum of n-th Bell number and n-th Bell number written backwards.
A322925 (program): Expansion of x*(1 + 2*x + 10*x^2)/((1 - x^2)*(1 - 10*x^2)).
A322926 (program): The successive approximations up to 2^n for 2-adic integer 5^(1/3).
A322927 (program): Expansion of x*(1 + 5*x + 40*x^2)/((1 - x^2)*(1 - 10*x^2)).
A322931 (program): Digits of the 8-adic integer 3^(1/3).
A322932 (program): Digits of the 8-adic integer 5^(1/3).
A322933 (program): Digits of the 8-adic integer 7^(1/3).
A322934 (program): The successive approximations up to 2^n for 2-adic integer 7^(1/3).
A322938 (program): a(n) = binomial(2*n + 2, n + 2) - 1.
A322939 (program): a(n) = [x^n] (4*x^2 + x - 1)/(4*x^3 + 3*x^2 + 2*x - 1).
A322940 (program): a(n) = [x^n] (4*x^2 + x - 1)/(2*x^2 + 3*x - 1).
A322943 (program): a(n) = n! [x^n] -exp(-1/(3*(x - 1)^3) - 1/3)/(x - 1).
A322970 (program): Coefficient triangle of polynomials recursively defined by P(n,x) = (n+1)*(n+1)! + x*Sum_{k=1..n} k^2*n!/(n+1-k)!*P(n-k,x) with P(0,x) = 1.
A322975 (program): Number of divisors d of n such that d-2 is prime.
A322976 (program): Number of divisors d of n such that d+2 is prime.
A322977 (program): Number of even divisors d of n such that d-1 is prime.
A322978 (program): Number of even divisors d of 2n such that d-1 is prime.
A322979 (program): a(n) = Sum A009191(d) over the divisors d of n, where A009191(x) = gcd(x, A000005(x)), and A000005(x) gives the number of divisors of x.
A322980 (program): a(n) = 1 if n and d(n) are coprime, 0 otherwise. Here d(n) is the number of divisors of n, A000005.
A322981 (program): If n is the k-th prime power > 1, a(n) = k, otherwise a(n) = 0.
A322982 (program): If n is a noncomposite, then a(n) = 2*n - 1, otherwise a(n) = A032742(n), the largest proper divisor of n.
A322983 (program): Number of iterations of A011371(x) = x - A000120(x) needed to reach an odd number, when starting from x = n.
A322984 (program): Number of iterations of A011371(x) = x - A000120(x) needed to reach an odd number, when starting from x = 2n.
A322987 (program): Number of iterations of A049820(x) = x - A000005(x) needed to reach a square, when starting from x = n.
A322993 (program): a(1) = 0; for n > 1, a(n) = A000265(A156552(n)).
A322996 (program): Number of iterations of A049820(x) = x - A000005(x) needed to reach an odd number or zero, when starting from x = n.
A322997 (program): Number of iterations of A049820(x) = x - A000005(x) needed to reach an odd number or zero, when starting from x = 2n.
A322999 (program): The successive approximations up to 2^n for 2-adic integer 9^(1/3).
A323000 (program): Digits of the 2-adic integer 3^(1/3).
A323011 (program): a(n) = A172103(n) - A172104(n).
A323012 (program): a(n) = (1/sqrt(n^2+1)) * T_{2*n+1}(sqrt(n^2+1)) where T_{n}(x) is a Chebyshev polynomial of the first kind.
A323014 (program): a(1) = 0; a(prime) = 1; otherwise a(n) = 1 + a(A181819(n)).
A323045 (program): Digits of the 2-adic integer 5^(1/3).
A323048 (program): Sums of no more than two 5-smooth numbers.
A323055 (program): Numbers with exactly two distinct exponents in their prime factorization, or two distinct parts in their prime signature.
A323066 (program): Numbers whose binary complement (A035327) is a square.
A323071 (program): a(n) = gcd(n, 1+A060681(n)).
A323072 (program): a(n) = n/A323071(n) = n/gcd(n, 1+A060681(n)).
A323075 (program): The fixed point reached when map x -> 1+(x-(largest divisor d < x)) is iterated, starting from x = n.
A323076 (program): Number of iterations of map x -> 1+(x-(largest divisor d < x)), starting from x=n, needed to reach a fixed point, which is always either a prime or 1.
A323077 (program): Number of iterations of map x -> (x - (largest divisor d < x)) needed to reach 1 or a prime, when starting at x = n.
A323095 (program): Digits of the 2-adic integer 7^(1/3).
A323096 (program): Digits of the 2-adic integer 9^(1/3).
A323099 (program): Number T(n,k) of colored set partitions of [n] where exactly k colors are used for the elements; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
A323100 (program): Square array read by ascending antidiagonals: T(p,q) is the number of bases e such that e^2 = -1 in Clifford algebra Cl(p,q)(R).
A323116 (program): Fixed point of the morphism 1->221, 2->2211.
A323117 (program): a(n) = T_{n}(n-1) where T_{n}(x) is a Chebyshev polynomial of the first kind.
A323118 (program): a(n) = U_{n}(n) where U_{n}(x) is a Chebyshev polynomial of the second kind.
A323129 (program): a(1) = 1, and for any n > 1, let p be the greatest prime factor of n, and e be its exponent, then a(n) = p^a(e).
A323139 (program): Integers that are not multiples of 6 and are the sum of two consecutive primes.
A323152 (program): a(n) = 1 if sigma(n) is divisible by all proper divisors of n, 0 otherwise.
A323153 (program): a(n) = 1 if n is either a prime or a perfect number, 0 otherwise.
A323158 (program): If n is a square, a(n) = 1-(n mod 2), otherwise a(n) = (n mod 2); a(n) = A049820(n) mod 2, where A049820(n) = n - number of divisors of n.
A323159 (program): Greatest common divisor of product (1+(p^e)) and product (1+p), where p ranges over prime factors of n, with e corresponding exponent; a(n) = gcd(A034448(n), A048250(n)).
A323160 (program): a(n) = gcd(n, A323159(n)) = gcd(n, A034448(n), A048250(n)).
A323161 (program): Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n<=3) = -n, f(n) = 0 if n-1 is an odd prime, and f(n) = floor((n-1)/2) for all other numbers.
A323162 (program): a(n) = 1 if both n and n-1 are composite, 0 otherwise.
A323164 (program): a(n) = A000720(A323075(n)).
A323166 (program): Greatest common divisor of Product (1+(p_i^e_i)) and n, when n = Product (p_i^e_i); a(n) = gcd(A034448(n), n).
A323167 (program): a(n) = A294898(A122111(n)).
A323170 (program): a(n) = 1 if (2*phi(n)) < n, 0 otherwise, where phi is Euler totient function (A000010).
A323171 (program): Numerator of the average of distinct prime factors of n (A008472(n)/A001221(n)).
A323173 (program): Sum of divisors computed for conjugated prime factorization: a(n) = A000203(A122111(n)).
A323174 (program): Deficiency computed for conjugated prime factorization: a(n) = A033879(A122111(n)).
A323178 (program): a(n) = 1 + 100*n^2 for n >= 0.
A323181 (program): a(n) = U_{2*n-1}(n)/(2*n) where U_{n}(x) is a Chebyshev polynomial of the second kind.
A323182 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) is Chebyshev polynomial of the second kind U_{n}(x), evaluated at x=k.
A323186 (program): a(0) = 0, a’(0) = 0, a’‘(0) = 1, a’‘(1) = -1, a(n) = a(n-1) + a’(n), a’(n) = a’(n-1) + a’‘(n), a’‘(n) = -a’‘(n-1) if a(n-2) = 0, or else a’‘(n-1).
A323191 (program): Expansion of (1 - x^5) / ((1 + x) * (1 + x^4)) in powers of x.
A323202 (program): Expansion of (1 - x) * (1 - x^3) / (1 - x^4) in powers of x.
A323208 (program): a(n) = hypergeometric([-n - 1, n + 2], [-n - 2], n).
A323209 (program): a(n) = hypergeometric([-n, n + 1], [-n - 1], n).
A323210 (program): a(n) = 9*J(n)^2 where J(n) are the Jacobsthal numbers A001045 with J(0) = 1.
A323211 (program): Level 1 of Pascal’s pyramid. T(n, k) triangle read by rows for n >= 0 and 0 <= k <= n.
A323217 (program): a(n) = hypergeometric([-n, n + 1], [-n - 1], n + 1).
A323218 (program): a(n) = (4*n^3 + 30*n^2 + 50*n)/3 + 1.
A323219 (program): a(n) = [x^n] (1 - 4*x)^(-n/2)*x/(1 - x).
A323220 (program): a(n) = n*(n + 5)*(n + 7)*(n + 10)/24 + 1.
A323221 (program): a(n) = n*(n + 5)*(n + 7)/6 + 1.
A323222 (program): A(n, k) = [x^k] (1 - 4*x)^(-n/2)*x/(1 - x), square array read by ascending antidiagonals with n >= 0 and k >= 0.
A323223 (program): a(n) = [x^n] x/((1 - x)*(1 - 4*x)^(5/2)).
A323224 (program): A(n, k) = [x^k] C^n*x/(1 - x) where C = 2/(1 + sqrt(1 - 4*x)), square array read by ascending antidiagonals with n >= 0 and k >= 0.
A323225 (program): a(n) = ((2^n*n + i*(1 - i)^n - i*(1 + i)^n))/4, where i is the imaginary unit.
A323227 (program): a(n) = [x^n] (-x^4 + 2*x^3 - x^2 + 2*x - 1)/((x - 1)^2*(2*x - 1)).
A323228 (program): a(n) = binomial(n + 4, n - 1) + 1.
A323229 (program): a(n) = binomial(2*n, n+1) + 1.
A323230 (program): a(n) = binomial(2*(n - 1), n - 1) + 1.
A323231 (program): A(n, k) = [x^k] (1/(1-x) + x/(1-x)^n), square array read by descending antidiagonals for n, k >= 0.
A323232 (program): a(n) = 2^n*J(n, 1/2) where J(n, x) are the Jacobsthal polynomials as defined in A322942.
A323239 (program): a(n) = 1 if n is odd and squarefree, otherwise a(n) = 0.
A323243 (program): a(1) = 0; for n > 1, a(n) = A000203(A156552(n)).
A323244 (program): a(1) = 0; and for n > 1, a(n) = A033879(A156552(n)).
A323247 (program): a(n) = A005187(A156552(n)).
A323248 (program): a(n) = A323247(n) - A323243(n).
A323254 (program): The determinant of an n X n Toeplitz matrix M(n) whose first row consists of successive positive integer numbers 2*n - 1, n - 1, …, 1 and whose first column consists of 2*n - 1, 2*n - 2, …, n.
A323274 (program): Ceiling(1/(e - 1/0! - 1/1! - 1/2! - … - 1/n!).
A323277 (program): G.f. = (x/6)*( 1/(1-12*x)^(3/2) - 1/(1-12*x) ).
A323280 (program): a(n) = Sum_{k=0..n} binomial(n,k) * k^(2*k).
A323290 (program): Numerator of the sum of inverse products of cycle sizes in all permutations of [n].
A323291 (program): Denominator of the sum of inverse products of cycle sizes in all permutations of [n].
A323294 (program): Number of 3-uniform hypergraphs spanning n labeled vertices where every two edges have two vertices in common.
A323295 (program): Number of ways to fill a matrix with the first n positive integers.
A323300 (program): Number of ways to fill a matrix with the parts of the integer partition with Heinz number n.
A323304 (program): Heinz numbers of integer partitions that cannot be arranged into a matrix with equal row-sums and equal column-sums.
A323305 (program): Number of divisors of the number of prime factors of n counted with multiplicity.
A323306 (program): Heinz numbers of integer partitions that can be arranged into a matrix with equal row-sums and equal column-sums.
A323308 (program): The number of exponential semiproper divisors of n.
A323309 (program): The sum of exponential semiproper divisors of n.
A323325 (program): Coefficients a(n) of x^n*y^n*z^n in function A = A(x,y,z) such that A = 1 + x*B*C, B = 1 + y*C*A, and C = 1 + z*A*B, for n >= 0.
A323332 (program): The Dedekind psi function values of the powerful numbers, A001615(A001694(n)).
A323333 (program): The Euler phi function values of the powerful numbers, A000010(A001694(n)).
A323339 (program): Numerator of the sum of inverse products of parts in all compositions of n.
A323340 (program): Denominator of the sum of inverse products of parts in all compositions of n.
A323346 (program): Square array read by ascending antidiagonals: T(p,q) is the number of bases e such that e^2 = 1 (including e = 1) in Clifford algebra Cl(p,q)(R).
A323350 (program): Nonprime numbers > 1 whose number of prime factors counted with multiplicity is a perfect square.
A323351 (program): Number of ways to fill a (not necessarily square) matrix with n zeros and ones.
A323363 (program): Dirichlet inverse of Dedekind’s psi, A001615.
A323364 (program): Sum of Dedekind’s psi, A001615, and its Dirichlet inverse, A323363.
A323385 (program): Expansion of AGM(1,1-16*x) (where AGM denotes the arithmetic-geometric mean).
A323397 (program): a(n) = (4^n + 15*n - 1)/9.
A323398 (program): Lexicographically first 3-free sequence on nonnegative integers not containing the Stanley sequence S(0,1), which is A005836.
A323399 (program): Sum of Jordan function J_2(n), A007434 and its Dirichlet inverse, A046970.
A323403 (program): Sum of sigma and its Dirichlet inverse: a(n) = A000203(n) + A046692(n).
A323406 (program): Greatest common divisor of Product (p_i^e_i)-1 and Product (p_i^e_i)+1, when n = Product (p_i^e_i): a(n) = gcd(A047994(n), A034448(n)).
A323407 (program): Dirichlet inverse of A047994, unitary phi.
A323409 (program): Greatest common divisor of Product (p_i^e_i)-1 and n, when n = Product (p_i^e_i); a(n) = gcd(n, A047994(n)).
A323410 (program): Unitary analog of cototient function A051953: a(n) = n - A047994(n).
A323413 (program): Infinitary analog of cototient function A051953: a(n) = n - A091732(n).
A323416 (program): a(n) = (n-1)! * (10^n - 1) / 9.
A323420 (program): Lexicographically earliest sequence of positive integers such that for any n > 0, a(n + a(n)) > a(n).
A323425 (program): Number of ways n people in a line can each choose two others both on the same side of them.
A323437 (program): Number of semistandard Young tableaux whose entries are the prime indices of n.
A323439 (program): Number of ways to fill a Young diagram with the prime indices of n such that all rows and columns are strictly increasing.
A323444 (program): Sum of exponents in prime-power factorization of Product_{k=0..n} binomial(n,k) (A001142).
A323462 (program): Smallest number that can be obtained from the “Choix de Bruxelles”, version 2 (A323460) operation applied to n.
A323466 (program): Number of terms in row n of A323465.
A323467 (program): Smallest number in row n of A323465.
A323495 (program): Irregular table read by rows: T(n,k) = (2*k+1)^(-1) mod 2^n, 0 <= k <= 2^(n-1) - 1.
A323505 (program): Mirror image of (denominators of) Bernoulli tree, A106831.
A323506 (program): a(n) = A323505(n) / A246660(n).
A323508 (program): a(n) = A323505(A156552(n)).
A323512 (program): a(n) = A079559(A156552(n)).
A323519 (program): a(n) is the number of ways to fill a square matrix with the multiset of prime factors of n, if the number of prime factors (counted with multiplicity) is a perfect square, and a(n) = 0 otherwise.
A323520 (program): Numbers of the form p^(k^2) where p is prime and k >= 0.
A323521 (program): Numbers whose number of prime factors counted with multiplicity (A001222) is not a perfect square.
A323526 (program): One and prime numbers whose prime index is a perfect square.
A323540 (program): a(n) = Product_{k=0..n} (k^2 + (n-k)^2).
A323541 (program): a(n) = Product_{k=0..n} (k^3 + (n-k)^3).
A323542 (program): a(n) = Product_{k=0..n} (k^4 + (n-k)^4).
A323543 (program): a(n) = Product_{k=0..n} (k^5 + (n-k)^5).
A323544 (program): a(n) = Product_{k=0..n} (k^6 + (n-k)^6).
A323545 (program): a(n) = Product_{k=0..n} (k^7 + (n-k)^7).
A323547 (program): n-th digit in the base-2 expansion of 1/n.
A323553 (program): Irregular table read by rows: T(n,k) = (2*k+1)^(-1/3) mod 2^n, 0 <= k <= 2^(n-1) - 1.
A323554 (program): Irregular table read by rows: T(n,k) = (2*k+1)^(-1/5) mod 2^n, 0 <= k <= 2^(n-1) - 1.
A323555 (program): Irregular table read by rows: T(n,k) = (2*k+1)^(1/5) mod 2^n, 0 <= k <= 2^(n-1) - 1.
A323556 (program): Irregular table read by rows: T(n,k) = (2*k+1)^(1/3) mod 2^n, 0 <= k <= 2^(n-1) - 1.
A323576 (program): Primes p such that 2 is a primitive root modulo p while 128 is not.
A323577 (program): Primes p such that 2 is a primitive root modulo p while 2048 is not.
A323583 (program): Number of ways to split an integer partition of n into consecutive subsequences.
A323590 (program): Primes p such that 2 is a primitive root modulo p while 8192 is not.
A323591 (program): n-th digit after the radix point in the base-3 expansion of 1/n.
A323592 (program): n-th digit in the base-4 expansion of 1/n.
A323599 (program): Dirichlet convolution of the identity function with omega.
A323600 (program): Dirichlet convolution of sigma with omega.
A323608 (program): The position function the fractalization of which yields A323607.
A323610 (program): List of 5-powerful numbers (for the definition of k-powerful see A323395).
A323613 (program): Antidiagonal sums of A323182.
A323614 (program): List of 7-powerful numbers (for the definition of k-powerful see A323395).
A323618 (program): Expansion of e.g.f. (1 + x)*log(1 + x)*(2 + log(1 + x))/2.
A323620 (program): Expansion of e.g.f. 2*sqrt(1 + x)*sinh(sqrt(5)*log(1 + x)/2)/sqrt(5).
A323622 (program): The first row of the order of square grid cells touched by a circle expanding from the middle of a cell.
A323623 (program): The second row of the order of square grid cells touched by a circle expanding from the middle of a cell.
A323629 (program): List of 6-powerful numbers (for the definition of k-powerful see A323395).
A323630 (program): Expansion of e.g.f. exp(log(1 - x)^2/2)/(1 - x). This is also the transform of the involution numbers given by the signless Stirling cycle numbers.
A323631 (program): Stirling transform of Pell numbers (A000129).
A323632 (program): Stirling transform of Jacobsthal numbers (A001045).
A323633 (program): Expansion of 1/Sum_{k>=0} x^(k^3).
A323634 (program): Expansion of Product_{k>=1} 1/(1 - k^(k-1)*x^k).
A323639 (program): a(n) = 3*(10^n - 4)/9.
A323641 (program): Triangle read by rows in which row n lists the first 2^n terms of A323642, n >= 1.
A323642 (program): Row n of triangle A323641 when n -> infinity.
A323643 (program): a(n) is the sum of the noncentral divisors of n.
A323644 (program): Numbers with 3 or 4 divisors.
A323648 (program): Numbers k such that the largest Dyck path of the symmetric representation of sigma(k) does not share any line segment with the largest Dyck path of the symmetric representation of sigma(k+1).
A323649 (program): Corner sequence of the cellular automaton of A323650.
A323650 (program): Flower garden sequence (see Comments for precise definition).
A323651 (program): Number of elements added at n-th stage to the toothpick structure of A323650.
A323663 (program): Square array A(n,k), n >= 1, k >= 1, read by antidiagonals, where A(n,k) is Sum_{j=1..n} binomial(j*k, k).
A323665 (program): a(n) is the number of vertices in the binary tree the root of which is assigned the value n and built recursively by the rule: write node’s value as (2^c)*(2k+1); if c>0, create a left child with value c; if k>0, create a right child with value k.
A323669 (program): Decimal expansion of 15/(2*Pi^2) = 1/((4/5)*zeta(2)).
A323703 (program): Number of values of (X^3 + X) mod prime(n).
A323704 (program): Number of cubic residues (including 0) modulo the n-th prime.
A323715 (program): a(n) = Product_{k=0..n} (2^k + 3^k).
A323716 (program): a(n) = Product_{k=0..n} (3^k + 1).
A323723 (program): a(n) = (-2 - (-1)^n*(-2 + n) + n + 2*n^3)/4.
A323724 (program): a(n) = n*(2*(n - 2)*n + (-1)^n + 3)/4.
A323728 (program): a(n) is the smallest number k such that both k-2*n and k+2*n are squares.
A323735 (program): a(n) is the largest minimal distance of a binary LCD [n,2] code.
A323739 (program): a(n) is the number of residues modulo (4*primorial(n)) of the squares of primes greater than or equal to prime(n+1).
A323741 (program): a(n) = m-p where m = (2n+1)^2 and p is the largest prime < m.
A323756 (program): a(1) = 2; for n >= 2, if a(n-1) has not yet been assigned, then a(n-1) = 1 and a(2*n-1) = 2, otherwise a(2*n) = 3.
A323760 (program): Numerator of Product_{d|n} (pod(d)/tau(d)) where pod(k) = the product of the divisors of k and tau(k) = the number of the divisors of k.
A323761 (program): Denominator of Product_{d|n} (pod(d)/tau(d)) where pod(k) = the product of the divisors of k and tau(k) = the number of the divisors of k.
A323768 (program): a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k)^k.
A323769 (program): a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k)^n.
A323770 (program): Expansion of e.g.f. x*(2 - x)*exp(x/(1 - x))/(2*(1 - x)^2).
A323771 (program): Expansion of e.g.f. 2*exp(x/(2 - 2*x))*sinh(sqrt(5)*x/(2 - 2*x))/sqrt(5).
A323772 (program): Expansion of e.g.f. 1 - LambertW(-x/(1 - x))*(2 + LambertW(-x/(1 - x)))/2.
A323775 (program): a(n) = Sum_{k = 1…n} k^(2^(n - k)).
A323776 (program): a(n) = Sum_{k = 1…n} binomial(k + 2^(n - k) - 1, k - 1).
A323812 (program): a(n) = n*Fibonacci(n-2) + ((-1)^n + 1)/2.
A323824 (program): a(0) = 6; thereafter a(n) = 4*a(n-1) + 1.
A323833 (program): A Seidel matrix A(n,k) read by antidiagonals upwards.
A323834 (program): A Seidel matrix A(n,k) read by antidiagonals downwards.
A323842 (program): Number of n-node Stanley graphs without isolated nodes.
A323847 (program): a(n) = (n-1)*(n-2)*(n^2+9*n+12)/24.
A323868 (program): Number of matrices of size n whose entries cover an initial interval of positive integers.
A323885 (program): Sum of A001511 and its Dirichlet inverse.
A323901 (program): a(n) = A002487(A163511(n)).
A323902 (program): a(n) = A002487(A156552(n)).
A323903 (program): a(n) = A002487(A122111(n)).
A323907 (program): Lexicographically earliest positive sequence such that a(i) = a(j) => A004718(i) = A004718(j), for all i, j >= 0.
A323908 (program): Reversing binary representation of A004718, Per Nørgård’s “infinity sequence”.
A323915 (program): a(n) = A023900(A005940(1+n)).
A323921 (program): a(n) = (4^(valuation(n, 4) + 1) - 1) / 3.
A323950 (program): Number of ways to split an n-cycle into connected subgraphs, none having exactly two vertices.
A323951 (program): Number of ways to split an n-cycle into connected subgraphs, all having at least three vertices.
A323952 (program): Regular triangle read by rows where if k > 1 then T(n, k) is the number of connected subgraphs of an n-cycle with any number of vertices other than 2 through k - 1, n >= 1, 1 <= k <= n - 1. Otherwise T(n, 1) = n.
A323956 (program): Triangle read by rows: T(n, k) = 1 + n * (n - k) for 1 <= k <= n.
A323967 (program): Number of 3 X n integer matrices (m_{i,j}) such that m_{1,1}=0, m_{3,n}=2, and all rows, columns, and falling diagonals are (weakly) monotonic without jumps of 2.
A323976 (program): Records for the number of ‘Reverse and Add’ steps, needed for a Lychrel number to join the trajectory of a smaller Lychrel number (i.e., its seed).
A323988 (program): a(n) = 2^(n - 1) + binomial(n, floor(n/2))*(n + 1)/2.
A323989 (program): Partial alternating sums modulo 3 of the Kolakoski sequence A000002.
A324015 (program): Number of nonempty subsets of {1, …, n} containing no two cyclically successive elements.
A324023 (program): One of the two successive approximations up to 5^n for 5-adic integer sqrt(6). This is the 1 (mod 5) case (except for n = 0).
A324024 (program): One of the two successive approximations up to 5^n for 5-adic integer sqrt(6). This is the 4 (mod 5) case (except for n = 0).
A324025 (program): Digits of one of the two 5-adic integers sqrt(6) that is related to A324023.
A324026 (program): Digits of one of the two 5-adic integers sqrt(6) that is related to A324024.
A324027 (program): One of the two successive approximations up to 5^n for 5-adic integer sqrt(-6). This is the 2 (mod 5) case (except for n = 0).
A324028 (program): One of the two successive approximations up to 5^n for 5-adic integer sqrt(-6). This is the 3 (mod 5) case (except for n = 0).
A324029 (program): Digits of one of the two 5-adic integers sqrt(-6) that is related to A324027.
A324030 (program): Digits of one of the two 5-adic integers sqrt(-6) that is related to A324028.
A324036 (program): Modified reduced Collatz map fs acting on positive odd integers.
A324044 (program): a(n) = A003958(n) - A033879(n).
A324045 (program): a(n) = A000010(n) - A106316(n).
A324046 (program): a(n) = gcd(n, A106316(n)).
A324047 (program): a(n) = A000203(n) - A106316(n).
A324048 (program): a(n) = A000203(n) - A083254(n) = n + sigma(n) - 2*phi(n).
A324050 (program): Numbers satisfying Korselt’s criterion: squarefree numbers n such that for every prime divisor p of n, p-1 divides n-1.
A324052 (program): a(n) = A083254(A005940(1+n)).
A324054 (program): a(n) = A000203(A005940(1+n)).
A324055 (program): Deficiency of Doudna-sequence: a(n) = A033879(A005940(1+n)).
A324056 (program): a(n) = A000593(A005940(1+n)).
A324057 (program): a(n) = A106315(A005940(1+n)).
A324058 (program): a(n) = A324121(A005940(1+n)) = gcd(A324054(n), A005940(1+n)*A106737(n)).
A324074 (program): Total number of distorted ancestor-successor pairs in all defective (binary) heaps on n elements.
A324077 (program): One of the four successive approximations up to 13^n for 13-adic integer 3^(1/4).This is the 2 (mod 13) case (except for n = 0).
A324082 (program): One of the four successive approximations up to 13^n for 13-adic integer 3^(1/4).This is the 3 (mod 13) case (except for n = 0).
A324083 (program): One of the four successive approximations up to 13^n for 13-adic integer 3^(1/4).This is the 10 (mod 13) case (except for n = 0).
A324084 (program): One of the four successive approximations up to 13^n for 13-adic integer 3^(1/4).This is the 11 (mod 13) case (except for n = 0).
A324085 (program): Digits of one of the four 3-adic integers 3^(1/4) that is congruent to 2 mod 13.
A324086 (program): Digits of one of the four 3-adic integers 3^(1/4) that is congruent to 3 mod 13.
A324087 (program): Digits of one of the four 3-adic integers 3^(1/4) that is congruent to 10 mod 13.
A324101 (program): Numbers whose “unary-binary encoded prime factorization” (A156552) is not A000120-deficient.
A324103 (program): a(1) = 0; for n > 1, a(n) = A083254(A156552(n)).
A324104 (program): a(1) = 0; for n > 1, a(n) = A000010(A156552(n)).
A324105 (program): a(1) = 0; for n > 1, a(n) = A000005(A156552(n)).
A324116 (program): a(n) = A002487(1+A323247(n)) = A324288(A156552(n)).
A324117 (program): Number of odd divisors in A156552(n): a(1) = 0, for n > 1, a(n) = A001227(A156552(n)) = A000005(A322993(n)).
A324118 (program): Sum of odd divisors in A156552(n): a(1) = 0, for n > 1, a(n) = A000593(A156552(n)) = A000203(A322993(n)).
A324119 (program): a(n) = A001221(A156552(n)).
A324121 (program): a(n) = gcd(n*d(n), sigma(n)), where d(n) = number of divisors of n (A000005) and sigma(n) = sum of divisors of n (A000203).
A324122 (program): a(n) = sigma(n) - gcd(n*d(n), sigma(n)), where d(n) = number of divisors of n (A000005) and sigma(n) = sum of divisors of n (A000203).
A324127 (program): Partial sums of A175046.
A324128 (program): a(n) = 2*n*Fibonacci(n) + (-1)^n + 1.
A324129 (program): a(n) = n*Fibonacci(n) + ((-1)^n + 1)/2.
A324133 (program): Number of permutations of [n] that avoid the shuffle pattern s-k-t, where s = 12 and t = 12.
A324140 (program): Define b(n) and c(n) by b(0)=0, b(1)=c(0)=c(1)=1; b(n)=c(n-1)*c(n-2), c(n) = (b(n-1)+c(n-1)*(b(n-2)+c(n-2)); sequence gives b(n).
A324141 (program): Define b(n) and c(n) by b(0)=0, b(1)=c(0)=c(1)=1; b(n)=c(n-1)*c(n-2), c(n) = (b(n-1)+c(n-1)*(b(n-2)+c(n-2)); sequence gives c(n).
A324143 (program): This sequence and A324142 are a pair of complementary sequences studied by Bode, Harborth, and Kimberling (2007).
A324151 (program): a(n) = (2/((n+1)*(n+2)))*multinomial(3*n;n,n,n).
A324152 (program): a(0)=1; for n>0, a(n) = (3/((n+1)*(n+2)*(n+3))) * multinomial(4*n;n,n,n,n).
A324153 (program): Digits of one of the four 13-adic integers 3^(1/4) that is congruent to 11 mod 13.
A324158 (program): Expansion of Sum_{k>=1} x^k / (1 - k * x^k)^k.
A324159 (program): Expansion of Sum_{k>=1} k * x^k / (1 - k * x^k)^k.
A324161 (program): Number of zerofree nonnegative integers <= n.
A324169 (program): Number of labeled graphs covering the vertex set {1,…,n} with no crossing edges.
A324172 (program): Number of subsets of {1,…,n} that cross their complement.
A324174 (program): Integers k such that 2*floor(sqrt(k)) divides k.
A324182 (program): a(n) = A083254(A163511(n)).
A324183 (program): a(n) = d(A163511(n)), where d(n) is A000005, the number of divisors of n.
A324184 (program): a(n) = sigma(A163511(n)).
A324185 (program): Deficiency of n permuted by A163511: a(n) = A033879(A163511(n)) = 2*A163511(n) - sigma(A163511(n)).
A324186 (program): Sum of odd divisors permuted by A163511: a(n) = A000593(A163511(n)).
A324187 (program): a(n) = A106315(A163511(n)).
A324188 (program): a(n) = A324121(A163511(n)).
A324189 (program): a(n) = A324122(A163511(n)).
A324198 (program): a(n) = gcd(n, A276086(n)).
A324225 (program): Total number T(n,k) of 1’s in falling diagonals with index k in all n X n permutation matrices; triangle T(n,k), n>=1, 1-n<=k<=n-1, read by rows.
A324245 (program): The modified Collatz map considered by Vaillant and Delarue.
A324265 (program): a(n) = 5*343^n.
A324266 (program): a(n) = 2*49^n.
A324267 (program): a(n) = 11*7^(5*n).
A324268 (program): a(n) = 31*11^(5*n).
A324269 (program): a(n) = 3*11^(2*n).
A324270 (program): a(n) = 13*7^(7*n).
A324272 (program): a(n) = 2*13^(2*n).
A324275 (program): Numbers k for which A324274(k) is 0, i.e., starting squares in A324274 that yield a path of infinite length.
A324285 (program): a(n) = A002487(A297168(n)).
A324286 (program): a(n) = A002487(A048675(n)).
A324287 (program): a(n) = A002487(A005187(n)).
A324288 (program): a(n) = A002487(1+A005187(n)).
A324289 (program): a(n) = A276086(A283477(n)).
A324290 (program): a(n) = 1 if for every prime divisor p of n, p-1 divides n-1, 0 otherwise; characteristic function of A087441.
A324293 (program): a(n) = A002487(sigma(n)).
A324294 (program): a(n) = A002487(1+sigma(n)).
A324306 (program): G.f.: Sum_{n>=0} (2^n + 1)^n * x^n / (1 + 2^n*x)^(n+1).
A324331 (program): a(n) = (n-1)^2 - phi(n)*sigma(n), where phi is A000010 and sigma is A000203.
A324335 (program): a(n) = A323363(A005940(1+n)), where A005940 is the Doudna sequence and A323363 is the Dirichlet inverse of Dedekind’s psi.
A324337 (program): a(n) = A002487(A006068(n)).
A324338 (program): a(n) = A002487(1+A006068(n)).
A324340 (program): a(n) = A046692(A005940(1+n)), where A005940 is the Doudna sequence and A046692 is the Dirichlet inverse of sigma function.
A324342 (program): If 2n = 2^e1 + … + 2^ek [e1 .. ek distinct], then a(n) is the minimal number of primorials (A002110) that add to A002110(e1) * … * A002110(ek).
A324348 (program): a(n) = A294898(A005940(1+n)), where A294898(k) = A005187(k) - A000203(k).
A324349 (program): a(n) = A324122(A005940(1+n)), where A005940 is the Doudna sequence and A324122(n) = sigma(n) - gcd(n*d(n), sigma(n)).
A324352 (program): Total number of occurrences of 2 in the (signed) displacement sets of all permutations of [n+2] divided by 2!.
A324353 (program): Total number of occurrences of 3 in the (signed) displacement sets of all permutations of [n+3] divided by 3!.
A324354 (program): Total number of occurrences of 4 in the (signed) displacement sets of all permutations of [n+4] divided by 4!.
A324355 (program): Total number of occurrences of 5 in the (signed) displacement sets of all permutations of [n+5] divided by 5!.
A324356 (program): Total number of occurrences of 6 in the (signed) displacement sets of all permutations of [n+6] divided by 6!.
A324357 (program): Total number of occurrences of 7 in the (signed) displacement sets of all permutations of [n+7] divided by 7!.
A324358 (program): Total number of occurrences of 8 in the (signed) displacement sets of all permutations of [n+8] divided by 8!.
A324359 (program): Total number of occurrences of 9 in the (signed) displacement sets of all permutations of [n+9] divided by 9!.
A324360 (program): Total number of occurrences of 10 in the (signed) displacement sets of all permutations of [n+10] divided by 10!.
A324361 (program): Total number of occurrences of n in the (signed) displacement sets of all permutations of [2n] divided by n!.
A324362 (program): Total number of occurrences of k in the (signed) displacement sets of all permutations of [n+k] divided by k!; square array A(n,k), n>=0, k>=0, read by antidiagonals.
A324368 (program): Number of partitions of n that contain {1,2} minus number of partitions of n that contain neither 1 nor 2.
A324377 (program): a(0) = 0; for n > 0, a(n) = A000265(A005187(n)).
A324378 (program): a(n) = A000265(1+A005187(n)).
A324379 (program): a(n) = A007814(A005187(n)).
A324383 (program): a(n) is the minimal number of primorials that add to A322827(n).
A324384 (program): a(n) = gcd(n, A276154(n)), where A276154 is the primorial base left shift.
A324386 (program): a(n) = A324383(A006068(n)).
A324388 (program): If n is a prime power (in A000961), then a(n) = n, otherwise a(n) is the greatest proper unitary divisor of n.
A324391 (program): Fully multiplicative with a(p^e) = A070939(p)^e, where A070939(p) gives the length of the binary representation of p.
A324394 (program): a(n) = A009194(A005940(1+n)), where A005940 is the Doudna sequence and A009194(n) = gcd(n,sigma(n)).
A324395 (program): a(n) = A017666(A005940(1+n)), where A005940 is the Doudna sequence and A017666(n) = n/gcd(n,sigma(n)).
A324396 (program): a(1) = 0; for n > 1, a(n) = A009194(A156552(n)).
A324398 (program): a(1) = 0; for n > 1, a(n) = A318458(A156552(n)).
A324400 (program): Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j) for all i, j >= 1, where f(n) = -1 if n = 2^k and k > 0, and f(n) = n for all other numbers.
A324445 (program): Number of labeled cyclic chord diagrams with n chords such that the minimal chord length equals one.
A324465 (program): Exponent of highest power of 2 that divides A324152(n).
A324466 (program): Exponent of highest power of 2 that divides multinomial(3*n;n,n,n).
A324467 (program): Three times the binary weight of n: 3*A000120(n).
A324468 (program): a(n) = r(n) + r(n+1) + r(n+2), where r(n) is the ruler sequence A007814.
A324469 (program): Exponent of highest power of 3 that divides multinomial(4*n;n,n,n,n).
A324470 (program): Partial sums of ternary tribonacci word A092782.
A324471 (program): a(n) = 10 mod n.
A324472 (program): a(n) = 1000 mod n.
A324476 (program): Packing numbers for n-tripods.
A324478 (program): a(n) = (6/((n+1)*(n+2)*(n+3))) * multinomial(4*n;n,n,n,n).
A324482 (program): Symmetric inflation orbit counts (b-bar)_{2n} for 1D cut and project patterns with inversion symmetric tau-inflation.
A324483 (program): Expansion of (1-x-x^2)^2*(1+x-x^2)^2/((1-3*x+x^2)*(1-x)^2*(1+x)^4).
A324486 (program): G.f. = (1-3*x+x^2)^3*(1+3*x+x^2)^3*(1-x^2)^10/((1-4*x-x^2)*(1-x-x^2)^6*(1+x-x^2)^9).
A324487 (program): a(n) = A001350(n)^3.
A324490 (program): A324487(3*n).
A324493 (program): Expansion of (1-18*x+x^2)^3*(1+18*x+x^2)^3*(1-x^2)^10/((1-76*x-x^2)*(1-4*x-x^2)^6*(1+4*x-x^2)^9).
A324498 (program): Decimal expansion of the real solution to x^2*(x-1)^3 = 1.
A324502 (program): a(n) = denominator of Sum_{d|n} (1/pod(d)) where pod(k) = the product of the divisors of k (A007955).
A324506 (program): a(n) = numerator of Product_{d|n} (d/tau(d)) where tau(k) = the number of divisors of k (A000005).
A324507 (program): a(n) = denominator of Product_{d|n} (d/tau(d)) where tau(k) = the number of divisors of k (A000005).
A324509 (program): a(n) = numerator of Product_{d|n} (sigma(d)/tau(d)) where sigma(k) = the sum of the divisors of k (A000203) and tau(k) = the number of divisors of k (A000005).
A324510 (program): a(n) = denominator of Product_{d|n} (sigma(d)/tau(d)) where sigma(k) = the sum of the divisors of k (A000203) and tau(k) = the number of divisors of k (A000005).
A324511 (program): Numbers m such that Product_{d|m} (sigma(d)/tau(d)) is an integer h where sigma(k) = the sum of the divisors of k (A000203) and tau(k) = the number of divisors of k (A000005).
A324521 (program): Numbers > 1 where the maximum prime index is less than or equal to the number of prime factors counted with multiplicity.
A324522 (program): Numbers > 1 where the minimum prime index is equal to the number of prime factors counted with multiplicity.
A324528 (program): a(n) = lcm(tau(n), pod(n)) where tau(k) = the number of divisors of k (A000005) and pod(n) = the product of divisors of k (A007955).
A324529 (program): a(n) = lcm(sigma(n), pod(n)) where sigma(k) = the sum of divisors of k (A000203) and pod(n) = the product of divisors of k (A007955).
A324534 (program): The smallest common prime factor of sigma(n) and A276086(n), or 1 if no such prime exists.
A324560 (program): Numbers > 1 where the minimum prime index is less than or equal to the number of prime factors counted with multiplicity.
A324562 (program): Numbers > 1 where the maximum prime index is greater than or equal to the number of prime factors counted with multiplicity.
A324568 (program): a(n) = Sum_{i=0..n, j=0..n} (binomial(2*i, j) + binomial(2*j, i)).
A324573 (program): a(1) = 0; for n > 1, a(n) = sigma(A048675(n)).
A324574 (program): a(1) = 0; for n > 1, a(n) = A033879(A087207(n)).
A324575 (program): a(1) = 0; for n > 1, a(n) = A033879(A048675(n)).
A324580 (program): a(n) = n * A276086(n).
A324583 (program): Numbers k such that k and A276086(k) are coprime, where A276086 is the primorial base exp-function.
A324584 (program): Numbers n that share a prime factor with A276086(n).
A324591 (program): E.g.f.: exp(2 * (x + x^2 / 2 + x^3 / 3)).
A324600 (program): a(n) = (k(n)*(k(n) + 1))/2 with k = A018252 (nonprime numbers), for n >= 1.
A324644 (program): a(n) = gcd(sigma(n), A276086(n)).
A324645 (program): a(n) = gcd(d(n), A276086(n)), where d(n) gives the number of divisors (A000005).
A324646 (program): a(n) = gcd(n, A276086(n-1)).
A324648 (program): a(n) = n - A318458(n), where A318458(n) is bitwise-AND of n and the sum of proper divisors of n (sigma(n)-n).
A324649 (program): Numbers k such that A318458(k) (bitwise-AND of k and sigma(k)-k) is equal to k.
A324650 (program): a(n) = A000010(A276086(n)).
A324651 (program): Bisection of A324650: a(n) = A000010(A276086(2*n)).
A324652 (program): Numbers k such that A318468(k) (bitwise-AND of 2*k and sigma(k)) is equal to 2*k.
A324653 (program): a(n) = A000203(A276086(n)).
A324654 (program): a(n) = A033879(A276086(n)).
A324655 (program): a(n) = A000005(A276086(n)).
A324658 (program): a(n) = n - A324659(n), where A324659(n) is half of bitwise-AND of 2*n and sigma(n).
A324659 (program): a(n) = (1/2)*A318468(n), where A318468(n) is bitwise-AND of 2*n and sigma(n).
A324713 (program): a(n) = 2*A156552(n) XOR A323243(n).
A324716 (program): a(n) = 2*A156552(n) - bitand(2*A156552(n), A323243(n)), where bitand is bitwise-AND, A004198.
A324721 (program): Positions of positive terms in A323244; numbers n for which 2*A156552(n) > A323243(n).
A324729 (program): a(n) = A000120(A323243(n)).
A324732 (program): Characteristic function of A324721: a(n) = 1 if 2*A156552(n) > A323243(n), and 0 otherwise.
A324740 (program): Number of simple graphs on n unlabeled nodes with maximum degree exactly 2.
A324758 (program): Heinz numbers of integer partitions containing no prime indices of the parts.
A324761 (program): Heinz numbers of integer partitions not containing 1 or any prime indices of the parts.
A324772 (program): The “Octanacci” sequence: Trajectory of 0 under the morphism 0->{0,1,0}, 1->{0}.
A324795 (program): a(n) = 2*p(n)*p(n+2)-p(n+1)^2 where p(k) = k-th prime.
A324798 (program): a(n) = floor(sqrt(2)*prime(n)) - prime(n+1).
A324815 (program): a(n) = 2*A156552(n) AND A323243(n), where AND is bitwise-and, A004198.
A324816 (program): Binary weight of A324815; number of 1-bits in common positions in 2*A156552(n) and A323243(n).
A324819 (program): a(n) = 2*A156552(n) OR A323243(n), where OR is bitwise-OR, A003986.
A324822 (program): a(n) = 1 if A156552(n) is a square, 0 otherwise.
A324823 (program): a(n) = 1 if n > 1 and A156552(n) is a square or a twice a square, 0 otherwise.
A324824 (program): a(n) = 1 if n>1 and sigma(A156552(n)) is congruent to 2 modulo 4, otherwise a(n) = 0.
A324825 (program): Number of divisors d of n such that A323243(d) is odd; number of terms of A324813 larger than 1 that divide n.
A324863 (program): Binary length of A324866(n), where A324866(n) = A156552(n) OR (A323243(n) - A156552(n)).
A324865 (program): a(n) = A323243(n) - A156552(n).
A324866 (program): a(n) = A156552(n) OR A324865(n), where OR is bitwise-OR, A003986.
A324867 (program): a(n) = A156552(n) XOR A324865(n), where XOR is bitwise-xor, A003987.
A324868 (program): Binary weight of A324398(n).
A324873 (program): a(n) = gcd(n, A060968(n)).
A324874 (program): a(n) is the binary length of A324398(n), where A324398(n) = A156552(n) AND (A323243(n) - A156552(n)).
A324881 (program): Number of nonleading zeros in binary representation of A324398, where A324398(n) = A156552(n) AND (A323243(n) - A156552(n)).
A324882 (program): a(1) = 0; for n > 1, a(n) = A001511(A324866(n)), where A324866(n) = A156552(n) OR (A323243(n) - A156552(n)).
A324883 (program): a(n) = 1 if A055396(n) < A324885(n), otherwise 0.
A324884 (program): a(1) = 0; for n > 1, a(n) = A001511(A324819(n)), where A324819(n) = 2*A156552(n) OR A323243(n).
A324885 (program): a(1) = 0; for n > 1, a(n) = A001511(A323243(n)).
A324886 (program): a(n) = A276086(A108951(n)).
A324887 (program): a(n) = A108951(n) * A276086(A108951(n)).
A324888 (program): Minimal number of primorials (A002110) that add to A108951(n).
A324891 (program): a(n) = sigma(A170818(n)), where A170818(n) is the part of n composed of prime factors of form 4k+1.
A324893 (program): a(n) = sigma(A097706(n)), where A097706(n) is the part of n composed of prime factors of form 4k+3.
A324895 (program): Largest proper divisor of A276086(n); a(0) = 1.
A324896 (program): Largest proper divisor of A324886(n).
A324899 (program): Odd numbers n for which sigma(n) == 3 (mod 4).
A324902 (program): The 2-adic valuation of A318456(n), where A318456(n) = n OR (sigma(n)-n).
A324903 (program): a(n) = 1 if A007814(sigma(n)) > A007814(n), 0 otherwise. Here A007814(n) gives the 2-adic valuation of n.
A324904 (program): The 2-adic valuation of A318466(n), where A318466(n) = 2*n OR sigma(n).
A324905 (program): a(n) = A007895(A003965(n)).
A324906 (program): Number of trailing 1-bits in the binary representation of A318466(n), where A318466(n) = 2*n OR sigma(n).
A324908 (program): a(n) = 1 if n is an odd number which is not a square, 0 otherwise.
A324909 (program): Odd numbers n for which sigma(n^2) == 3 (mod 4).
A324910 (program): Multiplicative with a(p^e) = (2^e)-1.
A324912 (program): Binary weight of A324911(n).
A324913 (program): a(n) = Sum_{k=1..n} 2^k * phi(k), where phi is the Euler totient function A000010.
A324914 (program): a(n) = Sum_{k=1..n} 2^k * tau(k), where tau(k) = A000005(k).
A324915 (program): a(n) = Sum_{k=1..n} 2^k * sigma(k), where sigma(k) = A000203(k).
A324920 (program): a(n) is the number of iterations of the integer splitting function (A056737) necessary to reach zero.
A324922 (program): a(n) = unique m such that m/A003963(m) = n, where A003963 is product of prime indices.
A324923 (program): Number of distinct factors in the factorization of n into factors q(i) = prime(i)/i, i > 0.
A324927 (program): Matula-Goebel numbers of rooted trees of depth 2. Numbers that are not powers of 2 but whose prime indices are all powers of 2.
A324928 (program): Matula-Goebel numbers of rooted trees of depth 3.
A324929 (program): Numbers whose product of prime indices is even.
A324930 (program): Total weight of the multiset of multisets of multisets with MMM number n. Totally additive with a(prime(n)) = A302242(n).
A324932 (program): Numerator in the division of n by the product of prime indices of n.
A324933 (program): Denominator in the division of n by the product of prime indices of n.
A324937 (program): Triangle read by rows: T(n, k) = 2*n*k + n + k - 8.
A324940 (program): Numbers of the form x^2+7*y^2+7*z^2.
A324964 (program): a(n) = A000139(n) mod 2; Characteristic function of odd fibbinary numbers (A022341).
A324965 (program): Partial sums of A324964.
A324966 (program): Number of distinct odd prime indices of n.
A324967 (program): Number of distinct even prime indices of n.
A324969 (program): Number of unlabeled rooted identity trees with n vertices whose non-leaf terminal subtrees are all different.
A324980 (program): a(n) = Product_{d|n} (d*sigma(d)) where sigma(k) = the sum of the divisors of k (A000203).
A324981 (program): a(n) = Product_{d|n} (d*pod(d)) where pod(k) = the product of the divisors of k (A007955).
A324986 (program): a(n) = Sum_{d|n} (tau(d)*sigma(d)) where tau(k) = the number of divisors of k (A000005) and sigma(k) = the sum of the divisors of k (A000203).
A324987 (program): a(n) = Product_{d|n} (tau(d)*sigma(d)) where tau(k) = the number of divisors of k (A000005) and sigma(k) = the sum of the divisors of k (A000203).
A324999 (program): Array read by descending antidiagonals: A(n,k) is the number of oriented colorings of the facets (or vertices) of a regular n-dimensional simplex using up to k colors.
A325000 (program): Array read by descending antidiagonals: T(n,k) is the number of unoriented colorings of the facets (or vertices) of a regular n-dimensional simplex using up to k colors.
A325001 (program): Array read by descending antidiagonals: A(n,k) is the number of achiral colorings of the facets (or vertices) of a regular n-dimensional simplex using up to k colors.
A325002 (program): Triangle read by rows: T(n,k) is the number of oriented colorings of the facets (or vertices) of a regular n-dimensional simplex using exactly k colors.
A325003 (program): Triangle read by rows: T(n,k) is the number of achiral colorings of the facets (or vertices) of a regular n-dimensional simplex using exactly k colors.
A325005 (program): Array read by descending antidiagonals: A(n,k) is the number of unoriented colorings of the facets of a regular n-dimensional orthotope using up to k colors.
A325006 (program): Array read by descending antidiagonals: A(n,k) is the number of chiral pairs of colorings of the facets of a regular n-dimensional orthotope using up to k colors.
A325029 (program): a(n) = Sum_{d|n} (sigma(d)*pod(d)) where sigma(k) = the sum of the divisors of k (A000203) and pod(k) = the product of the divisors of k (A007955).
A325030 (program): a(n) = Product_{d|n} (sigma(d)*pod(d)) where sigma(k) = the sum of the divisors of k (A000203) and pod(k) = the product of the divisors of k (A007955).
A325032 (program): Product of products of the multisets of prime indices of each prime index of n.
A325033 (program): Sum of sums of the multisets of prime indices of each prime index of n.
A325034 (program): Sum of products of the multisets of prime indices of each prime index of n.
A325036 (program): Difference between product and sum of prime indices of n.
A325037 (program): Heinz numbers of integer partitions whose product of parts is greater than their sum.
A325042 (program): Heinz numbers of integer partitions whose product of parts is one fewer than their sum.
A325050 (program): a(n) = Product_{k=0..n} (k!^2 + 1).
A325095 (program): Number of subsets of {1…n} with no binary carries.
A325100 (program): Heinz numbers of strict integer partitions with no binary carries.
A325101 (program): Number of divisible binary-containment pairs of positive integers up to n.
A325102 (program): Number of ordered pairs of positive integers up to n with no binary carries.
A325103 (program): Number of increasing pairs of positive integers up to n with no binary carries.
A325104 (program): Number of increasing pairs of positive integers up to n with at least one binary carry.
A325106 (program): Number of divisible binary-containment pairs of positive integers up to n.
A325114 (program): Integers such that no nonzero subsequence of decimal representation is divisible by 7.
A325120 (program): Sum of binary lengths of the prime indices of n.
A325121 (program): Sum of binary digits of the prime indices of n.
A325126 (program): a(1) = 1; a(n) = -Sum_{d|n, d<n} rad(n/d) * a(d), where rad = A007947.
A325128 (program): Numbers in whose prime factorization the exponent of prime(k) is less than k for all prime indices k.
A325131 (program): Heinz numbers of integer partitions where the set of distinct parts is disjoint from the set of distinct multiplicities.
A325133 (program): Heinz number of the integer partition obtained by removing the inner lining, or, equivalently, the largest hook, of the integer partition with Heinz number n.
A325134 (program): a(1) = 1; a(n) = number of prime factors of n counted with multiplicity plus the largest prime index of n.
A325136 (program): The product of primes <= 2n that are strongly prime to 2n, bisection of A181836.
A325138 (program): a(n) = Sum_{k=0..n} Sum_{j=0..n-k} binomial(j+k, k)*|Stirling1(n, j+k)|*(k+1)^j.
A325140 (program): a(n) = Sum_{k=0..n} Sum_{j=0..n-k} binomial(j+k, k)*|Stirling1(n, j+k)|*(k+2)^j.
A325144 (program): a(n) = - Sum_{d | n} (-1)^d *a(d) if n != 1, a(1) = 1.
A325153 (program): A column of triangle A322220; a(n) = A322220(n,1) for n >= 1.
A325156 (program): G.f.: A(x) = Sum_{n>=0} x^n * (1 + (-1)^n * sqrt(A(x)))^n / (1 - (-1)^n * x*sqrt(A(x)))^(n+1).
A325157 (program): G.f.: A(x) = Sum_{n>=0} x^n * (1 + (-1)^n * A(x))^n / (1 - (-1)^n * x*A(x))^(n+1).
A325160 (program): Products of distinct, non-consecutive primes. Squarefree numbers not divisible by any two consecutive primes.
A325161 (program): Nonprime squarefree numbers not divisible by any two consecutive primes.
A325164 (program): Heinz numbers of integer partitions with Durfee square of length 2.
A325168 (program): Number of integer partitions of n with origin-to-boundary graph-distance equal to 2.
A325169 (program): Origin-to-boundary graph-distance of the Young diagram of the integer partition with Heinz number n.
A325170 (program): Heinz numbers of integer partitions with origin-to-boundary graph-distance equal to 2.
A325171 (program): Down-integers: integers k such that w_(s+1) = floor(phi*k) for some k-slow Fibonacci walk, with phi=(1+sqrt(5))/2. See comments for further explanation.
A325172 (program): Up-integers: integers k such that w_(s+1) = ceiling(phi*k) for some k-slow Fibonacci walk, with phi=(1+sqrt(5))/2. See comments for further explanation.
A325173 (program): Perfect squares of the form a + b^2 + c^3, where a,b,c are consecutive numbers.
A325181 (program): Number of integer partitions of n such that the difference between the length of the minimal square containing and the maximal square contained in the Young diagram is 1.
A325191 (program): Number of integer partitions of n such that the difference between the length of the minimal triangular partition containing and the maximal triangular partition contained in the Young diagram is 1.
A325223 (program): Sum of the prime indices of n minus the greater of the number of prime factors of n counted with multiplicity and the largest prime index of n.
A325224 (program): Sum of prime indices of n minus the lesser of the number of prime factors of n counted with multiplicity and the maximum prime index of n.
A325225 (program): Lesser of the number of prime factors of n counted with multiplicity and the maximum prime index of n.
A325226 (program): Number of prime factors of n that are less than the largest, counted with multiplicity.
A325229 (program): Heinz numbers of integer partitions such that lesser of the maximum part and the number of parts is 2.
A325230 (program): Numbers of the form p^k * q, p and q prime, p > q, k > 0.
A325231 (program): Numbers of the form 2 * p or 3 * 2^k, p prime, k > 1.
A325233 (program): Heinz numbers of integer partitions with Dyson rank 1.
A325234 (program): Heinz numbers of integer partitions with Dyson rank -1.
A325235 (program): Heinz numbers of integer partitions with Dyson rank 1 or -1.
A325240 (program): Numbers whose minimum prime exponent is 2.
A325247 (program): Numbers whose omega-sequence is strict (no repeated parts).
A325249 (program): Sum of the omega-sequence of n.
A325251 (program): Numbers whose omega-sequence covers an initial interval of positive integers.
A325259 (program): Numbers with one fewer distinct prime exponents than distinct prime factors.
A325261 (program): Numbers whose omega-sequence does not cover an initial interval of positive integers.
A325264 (program): Numbers whose omega-sequence sums to 7.
A325265 (program): Numbers with sum of omega-sequence > 4.
A325266 (program): Numbers whose adjusted frequency depth equals their number of prime factors counted with multiplicity.
A325269 (program): Number of integer partitions of n with 2 distinct parts or at least 3 parts.
A325281 (program): Numbers of the form a*b, a*a*b, or a*a*b*c where a, b, and c are distinct primes. Numbers with sorted prime signature (1,1), (1,2), or (1,1,2).
A325282 (program): Maximum adjusted frequency depth among integer partitions of n.
A325284 (program): Numbers whose prime indices form an initial interval with a single hole: (1, 2, …, x, x + 2, …, m - 1, m), where x can be 0 but must be less than m - 1.
A325299 (program): a(n) = 9 * sigma(n).
A325313 (program): a(n) = A048250(n) - n, where A048250(n) is the sum of squarefree divisors of n.
A325314 (program): a(n) = n - A162296(n), where A162296(n) is the sum of divisors of n that have a square factor.
A325321 (program): a(n) = 1 if cototient of n is a square, 0 otherwise.
A325334 (program): Number of integer partitions of n with adjusted frequency depth 3 whose parts cover an initial interval of positive integers.
A325337 (program): Numbers whose prime exponents are distinct and cover an initial interval of positive integers.
A325339 (program): Number of divisors of n^3 that are <= n.
A325359 (program): Numbers of the form p^y * 2^z where p is an odd prime, y >= 2, and z >= 0.
A325370 (program): Numbers whose prime signature has multiplicities covering an initial interval of positive integers.
A325371 (program): Numbers whose prime signature has multiplicities of its parts all distinct and covering an initial interval of positive integers.
A325385 (program): a(n) = gcd(n-A048250(n), n-A162296(n)).
A325392 (program): Number of permutations of the multiset of prime factors of n whose first part is not 2.
A325395 (program): Heinz numbers of integer partitions whose augmented differences are strictly increasing.
A325401 (program): minflip(n) = min(n, r(n)) where r(n) is the binary reverse of n.
A325402 (program): maxflip(n) = max(n, r(n)) where r(n) is the binary reverse of n.
A325403 (program): Number of permutations of the multiset of prime factors of 2n whose first part is not 2.
A325411 (program): Numbers whose omega-sequence has repeated parts.
A325413 (program): Largest sum of the omega-sequence of an integer partition of n.
A325424 (program): Complement of A036668: numbers not of the form 2^i*3^j*k, i + j even, (k,6) = 1.
A325431 (program): a(n) is the least number not 3*a(m) or 4*a(m) for any m < n.
A325432 (program): Complement of A325431.
A325435 (program): Numbers m such that m! / sigma(m) is an integer.
A325437 (program): Final digit of primes of the form k^2 + 1.
A325446 (program): The unitary version of Kalmár’s function: number of ordered factorizations of n into powers of distinct primes.
A325454 (program): a(n) is the digit sum of the n-th Niven number (or Harshad number).
A325459 (program): Sum of numbers of nontrivial divisors (greater than 1 and less than k) of k for k = 1..n.
A325469 (program): a(n) is the number of divisors d of n such that d divides sigma(d).
A325470 (program): a(n) is the sum of divisors d of n such that d divides sigma(d).
A325473 (program): Number of compositions of n with no part divisible by 3 and an even number of parts congruent to 4 or 5 modulo 6.
A325475 (program): a(n) = (24*n)^2.
A325482 (program): Number of colored set partitions of [n] where colors of the elements of subsets are distinct and in increasing order and exactly two colors are used.
A325483 (program): Numbers whose sum of their decimal digits is less than or equal to the sum of the digits of their binary representation.
A325484 (program): One of the four successive approximations up to 5^n for the 5-adic integer 6^(1/4). This is the 1 (mod 5) case (except for n = 0).
A325485 (program): One of the four successive approximations up to 5^n for the 5-adic integer 6^(1/4). This is the 2 (mod 5) case (except for n = 0).
A325486 (program): One of the four successive approximations up to 5^n for the 5-adic integer 6^(1/4). This is the 3 (mod 5) case (except for n = 0).
A325487 (program): One of the four successive approximations up to 13^n for the 13-adic integer 6^(1/4). This is the 4 (mod 5) case (except for n = 0).
A325488 (program): Dimensions of space of harmonic polynomials of each degree invariant under the full icosahedral group.
A325489 (program): Digits of one of the four 5-adic integers 6^(1/4) that is congruent to 1 mod 5.
A325490 (program): Digits of one of the four 5-adic integers 6^(1/4) that is congruent to 2 mod 5.
A325491 (program): Digits of one of the four 5-adic integers 6^(1/4) that is congruent to 3 mod 5.
A325492 (program): Digits of one of the four 5-adic integers 6^(1/4) that is congruent to 4 mod 5.
A325498 (program): Difference sequence of A036668.
A325499 (program): Difference sequence of A325424.
A325511 (program): Numbers whose prime signature is that of a factorial number.
A325516 (program): Triangle read by rows: T(n, k) = (1/4)*n*(1 - (-1)^(n - k) + 2*(n - k)^2), with 0 <= k < n.
A325517 (program): a(n) = n*((2*n + 1)*(2*n^2 + 2*n + 3) - 3*(-1)^n)/24.
A325524 (program): Difference sequence of A325431.
A325525 (program): Difference sequence of A325432.
A325543 (program): Width (number of leaves) of the rooted tree with Matula-Goebel number n!.
A325544 (program): Number of nodes in the rooted tree with Matula-Goebel number n!.
A325580 (program): G.f.: A(x,y) = Sum_{n>=0} x^n * ((1+x)^n + y)^n, where A(0) = 0, as a triangle of coefficients T(n,k) of x^n*y^k in A(x,y) = Sum_{n>=0} x^n * Sum_{k=0..n} T(n,k)*x^n*y^k, read by rows.
A325581 (program): G.f.: Sum_{n>=0} (n+1) * x^n * (1+x)^(n*(n+1)).
A325586 (program): G.f.: Sum_{n>=0} (n+1)*(n+2)/2 * x^n * (1+x)^(n*(n+2)).
A325587 (program): G.f.: Sum_{n>=0} (n+1)*(n+2)*(n+3)/3! * x^n * (1+x)^(n*(n+3)).
A325596 (program): a(n) = Sum_{d|n} mu(n/d) * (-1)^(d + 1) * d.
A325597 (program): a(n) is the least number not 2a(m) + a(m-1) for any m < n.
A325598 (program): Complement of A325597.
A325599 (program): Difference sequence of A325597.
A325600 (program): Positions of 1 in A325599.
A325601 (program): Positions of 2 in A325599.
A325617 (program): Multinomial coefficient of the prime signature of n!.
A325636 (program): a(n) = gcd(2n, sigma(n)).
A325644 (program): “Sloping quaternary numbers”: write numbers in quaternary under each other (right-justified), read diagonals in upward direction, convert to decimal.
A325645 (program): “Sloping quinary numbers”: write numbers in quinary under each other (right-justified), read diagonals in upward direction, convert to decimal.
A325646 (program): Number of separable partitions of n in which the number of distinct (repeatable) parts is 2.
A325656 (program): a(n) = (1/24)*n*((4*n + 3)*(2*n^2 + 1) - 3*(-1)^n).
A325657 (program): a(n) = (1/2)*(-1 + (-1)^n)*(n-1) + n^2.
A325660 (program): Number of ones in the q-signature of n.
A325661 (program): q-powerful numbers. Numbers whose factorization into factors prime(i)/i has no factor of multiplicity 1.
A325664 (program): First term of n-th difference sequence of (floor[k*r]), r = sqrt(2), k >= 0.
A325665 (program): First term of n-th difference sequence of (floor(k*r)), r = -sqrt(2), k >= 0.
A325666 (program): First term of n-th difference sequence of (floor(k*r)), r = sqrt(3), k >= 0.
A325667 (program): First term of n-th difference sequence of (floor(k*r)), r = -sqrt(3), k >= 0.
A325668 (program): First term of n-th difference sequence of (floor(k*r)), r = sqrt(5), k >= 0.
A325669 (program): First term of n-th difference sequence of (floor(k*r)), r = -sqrt(5), k >= 0.
A325670 (program): First term of n-th difference sequence of (floor(k*r)), r = sqrt(6), k >= 0.
A325671 (program): First term of n-th difference sequence of (floor(k*r)), r = -sqrt(6), k >= 0.
A325672 (program): First term of n-th difference sequence of (floor(k*r)), r = sqrt(7), k >= 0.
A325673 (program): First term of n-th difference sequence of (floor(k*r)), r = -sqrt(7), k >= 0.
A325674 (program): First term of n-th difference sequence of (floor(k*r)), r = sqrt(8), k >= 0.
A325675 (program): First term of n-th difference sequence of (floor(k*r)), r = -sqrt(8), k >= 0.
A325685 (program): Number of compositions of n whose distinct consecutive subsequences have different sums, and such that these sums cover an initial interval of positive integers.
A325688 (program): Number of length-3 compositions of n such that every distinct consecutive subsequence has a different sum.
A325689 (program): Number of length-3 compositions of n such that no part is the sum of the other two.
A325690 (program): Number of length-3 integer partitions of n whose largest part is not the sum of the other two.
A325691 (program): Number of length-3 integer partitions of n whose largest part is not greater than the sum of the other two.
A325692 (program): “Sloping senary numbers”: write numbers in senary (that is, base 6) under each other (right-justified), read diagonals in upward direction, convert to decimal.
A325693 (program): “Sloping septenary numbers”: write numbers in septenary under each other (right-justified), read diagonals in upward direction, convert to decimal.
A325695 (program): Number of length-3 strict integer partitions of n such that the largest part is not the sum of the other two.
A325696 (program): Number of length-3 strict compositions of n such that no part is the sum of the other two.
A325698 (program): Numbers with as many even as odd prime indices, counted with multiplicity.
A325699 (program): Number of distinct even prime indices of n minus the number of distinct odd prime indices of n.
A325700 (program): Numbers with as many distinct even as distinct odd prime indices.
A325711 (program): Number of separable partitions of n in which the number of distinct (repeatable) parts <= 2.
A325729 (program): First term of n-th difference sequence of (floor(k*r)), r = sqrt(1/2), k >= 0.
A325730 (program): First term of n-th difference sequence of (floor(k*r)), r = sqrt(1/3), k >= 0.
A325732 (program): First term of n-th difference sequence of (floor(k*r)), r = sqrt(3/4), k >= 0.
A325733 (program): First term of n-th difference sequence of (floor(k*r)), r = 1/2 + sqrt(2), k >= 0.
A325734 (program): First term of n-th difference sequence of (floor(k*e)), k >= 0.
A325735 (program): First term of n-th difference sequence of (floor(-k*e)), k >= 0.
A325736 (program): First term of n-th difference sequence of (floor(2e*k)), k >= 0.
A325737 (program): First term of n-th difference sequence of (floor(3e*k)), k >= 0.
A325738 (program): First term of n-th difference sequence of (floor(e*k/2)), k >= 0.
A325739 (program): First term of n-th difference sequence of (floor(Pi*k)), k >= 0.
A325740 (program): First term of n-th difference sequence of (floor(2*Pi*k)), k >= 0.
A325741 (program): First term of n-th difference sequence of (floor(Pi*k/2)), k >= 0.
A325742 (program): First term of n-th difference sequence of (floor(Pi*k/3)), k >= 0.
A325743 (program): First term of n-th difference sequence of (floor(Pi*k/4)), k >= 0.
A325744 (program): First term of n-th difference sequence of (floor(Pi*k/6)), k >= 0.
A325745 (program): First term of n-th difference sequence of (floor(r*k)), r = (1+sqrt(5))/2, k >= 0.
A325746 (program): First term of n-th difference sequence of (floor(r*k)), r = -(1+sqrt(5))/2, k >= 0.
A325747 (program): First term of n-th difference sequence of (floor(r*k)), r = (3+sqrt(5))/2, k >= 0.
A325748 (program): First term of n-th difference sequence of (floor(k/e)), k >= 0.
A325749 (program): First term of n-th difference sequence of (floor(e*k/(e-1))), k >= 0.
A325750 (program): First term of n-th difference sequence of (floor(r*k)), r = (1+sqrt(3))/2, k >= 0.
A325755 (program): Numbers n divisible by their prime shadow A181819(n).
A325759 (program): Number of distinct frequencies in the frequency span of n.
A325760 (program): Heinz number of the frequency span of n.
A325765 (program): Number of integer partitions of n with a unique consecutive subsequence summing to every positive integer from 1 to n.
A325770 (program): Number of distinct nonempty contiguous subsequences of the integer partition with Heinz number n.
A325784 (program): Reading the first row of this array or its successive antidiagonals is the same as reading this sequence.
A325785 (program): Reading the first column of this array or its successive antidiagonals is the same as reading this sequence.
A325794 (program): Number of divisors of n minus the sum of prime indices of n.
A325795 (program): Numbers with more divisors than the sum of their prime indices.
A325796 (program): Numbers with at least as many divisors as the sum of their prime indices.
A325797 (program): Numbers with fewer divisors than the sum of their prime indices.
A325798 (program): Numbers with at most as many divisors as the sum of their prime indices.
A325803 (program): Nonzero terms of Product_{k=0..floor(log_2(n))} (1 + A004718(floor(n/(2^k)))).
A325804 (program): Positions of nonzero terms of Product_{k=0..floor(log_2(n))} (1 + A004718(floor(n/(2^k)))).
A325805 (program): “Sloping octal numbers”: write numbers in octal under each other (right-justified), read diagonals in upward direction, convert to decimal.
A325813 (program): a(n) = gcd(A034448(n)-n, n-A048146(n)), where A034448 and A048146 are respectively the sum of unitary and non-unitary divisors of n.
A325814 (program): a(n) = n - A048146(n), where A048146 is the sum of non-unitary divisors of n.
A325829 (program): “Sloping nonary numbers”: write numbers in nonary under each other (right-justified), read diagonals in upward direction, convert to decimal.
A325837 (program): The number of exponentially odd divisors of n.
A325838 (program): a(n) is the product of divisors of the n-th triangular number.
A325840 (program): First term of n-th difference sequence of (round(k*sqrt(2))), k >= 0.
A325841 (program): First term of n-th difference sequence of (round(k*sqrt(3))), k >= 0.
A325842 (program): First term of n-th difference sequence of (round(k*sqrt(5))), k >= 0.
A325843 (program): First term of n-th difference sequence of (round(k*sqrt(6))), k >= 0.
A325844 (program): First term of n-th difference sequence of (round(k*tau)), tau = golden ratio = (1+sqrt(5))/2, k >= 0.
A325845 (program): First term of n-th difference sequence of round((k*e)), k >= 0.
A325846 (program): First term of n-th difference sequence of round((k*Pi)), k >= 0.
A325887 (program): Excess of sum of odd integers up to n and coprime to n over sum of even integers up to n and coprime to n.
A325892 (program): The successive approximations up to 2^n for the 2-adic integer 3^(1/5).
A325893 (program): The successive approximations up to 2^n for 2-adic integer 5^(1/5).
A325894 (program): The successive approximations up to 2^n for the 2-adic integer 7^(1/5).
A325895 (program): The successive approximations up to 2^n for the 2-adic integer 9^(1/5).
A325896 (program): Digits of the 2-adic integer 3^(1/5).
A325897 (program): Digits of the 2-adic integer 5^(1/5).
A325898 (program): Digits of the 2-adic integer 7^(1/5).
A325899 (program): Digits of the 2-adic integer 9^(1/5).
A325905 (program): Decimal expansion of 2/e^2.
A325909 (program): Lexicographically earliest sequence of distinct positive terms such that for any n > 0, n divides Sum_{k = 1..n} (-1)^k * a(k).
A325911 (program): Screaming numbers in base 16: numbers whose hexadecimal representation is AAAAAAA…
A325913 (program): Integers m such that there are exactly two powers of 2 between 3^m and 3^(m+1).
A325931 (program): Signs of first differences of A076042.
A325937 (program): Expansion of Sum_{k>=1} (-1)^(k + 1) * x^(2*k) / (1 - x^k).
A325938 (program): a(n) = omega(n)^tau(n), where omega=A001221 and tau=A000005.
A325939 (program): Expansion of Sum_{k>=1} x^(2*k) / (1 + x^k).
A325940 (program): Expansion of Sum_{k>=1} x^(2*k) / (1 + x^k)^2.
A325941 (program): Expansion of Sum_{k>=1} k * x^(2*k) / (1 + x^k)^2.
A325943 (program): a(n) = floor(n / omega(n)) where omega = A001221.
A325946 (program): Maximum number of intercardinal adjacencies among all n-celled polyplets.
A325947 (program): a(n) = 4^n * [x^n] 1/sqrt(1-x) * Product_{k>=1} 1/(1 - x^k).
A325948 (program): a(n) = 4^n * [x^n] sqrt(1-x) * Product_{k>=1} 1/(1 - x^k).
A325951 (program): G.f.: 1/(1-x)^3 * Product_{k>=1} (1 + x^k).
A325952 (program): G.f.: 1/(1-x)^4 * Product_{k>=1} (1 + x^k).
A325958 (program): Sum of the corners of a 2n+1 X 2n+1 square spiral.
A325964 (program): a(n) = 1 if n and sigma(n) are relatively prime, 0 otherwise, where sigma(n) = sum of divisors of n, A000203; Characteristic function of A014567.
A325973 (program): Arithmetic mean of {sum of unitary divisors} and {sum of squarefree divisors}: a(n) = (1/2) * (A034448(n) + A048250(n)).
A325974 (program): Arithmetic mean of {sum of non-unitary divisors} and {sum of nonsquarefree divisors}: a(n) = (1/2)*(A048146(n) + A162296(n)).
A325975 (program): a(n) = gcd(A325977(n), A325978(n)).
A325977 (program): a(n) = (1/2)*(A034460(n) + A325313(n)).
A325978 (program): a(n) = (1/2)*(A325314(n) + A325814(n)).
A325988 (program): Number of covering (or complete) factorizations of n.
A325989 (program): Number of perfect factorizations of n.
A325997 (program): G.f.: Sum_{n>=0} (n+1) * (x + x^n)^n.
A325998 (program): G.f.: Sum_{n>=0} (n+1)*(n+2)/2 * (x + x^n)^n.
A325999 (program): G.f.: Sum_{n>=0} (n+1)*(n+2)*(n+3)/3! * (x + x^n)^n.
A326002 (program): G.f.: Sum_{n>=0} (n+1) * x^n * (1 + x^n)^n.
A326003 (program): G.f.: Sum_{n>=0} (n+1)*(n+2)/2 * x^n * (1 + x^n)^n.
A326004 (program): G.f.: Sum_{n>=0} (n+1)*(n+2)*(n+3)/3! * x^n * (1 + x^n)^n.
A326005 (program): G.f.: Sum_{n>=0} (n+1)*(n+2)*(n+3)*(n+4)/4! * x^n * (1 + x^n)^n.
A326011 (program): a(n) = (n+1) * (2^n + 1)^n.
A326012 (program): a(n) = (n+1)*(n+2)/2 * (2^n + 1)^n.
A326013 (program): a(n) = (n+1) * (3^n + 1)^n.
A326031 (program): Weight of the set-system with BII-number n.
A326032 (program): a(2^x + … + 2^z) = w(x) + … + w(z), where x…z are distinct nonnegative integers and w = A000120.
A326034 (program): Number of knapsack partitions of n with largest part 3.
A326038 (program): Square root of the largest square dividing the sum of divisors of n: a(n) = A000188(sigma(n)).
A326039 (program): Largest square dividing the sum of divisors of n: a(n) = A008833(sigma(n)).
A326040 (program): a(n) = sigma(n) - A008833(sigma(n)).
A326041 (program): a(n) = sigma(A064989(n)).
A326042 (program): a(n) = A064989(sigma(A003961(n))), where A003961 shifts the prime factorization of n one step towards larger primes, and A064989 shifts it back towards smaller primes.
A326044 (program): a(n) = n - {the largest square dividing its sum of divisors}: a(n) = n - A008833(sigma(n)).
A326045 (program): a(n) is the sum of divisors of n, minus the largest square dividing that sum, minus n: a(n) = sigma(n) - A008833(sigma(n)) - n.
A326046 (program): a(n) = gcd(n-A326039(n), A326040(n)-n).
A326047 (program): a(n) = gcd(n-A050449(n), n-A050452(n)), where A050449 and A050452 give the sum of divisors of the form 4k+1 and of the form 4k+3, respectively.
A326048 (program): a(n) = gcd(n-A050449(n), A082052(n)-n), where A050449 and A082052 give the sum of divisors of the form 4k+1, and not of that form, respectively.
A326049 (program): a(n) = n - A050449(n), where A050449 is the sum of divisors of the form 4k+1.
A326050 (program): a(n) = A082052(n) - n, where A082052 is the sum of divisors of n that are not of the form 4k+1.
A326052 (program): a(n) = n - A050452(n), where A050452 is the sum of divisors of the form 4k+3.
A326053 (program): Sum of all other divisors of n except the largest square divisor: a(n) = sigma(n) - A008833(n).
A326054 (program): a(n) = A326053(n) - n, where A326053 gives the sum of all other divisors of n except the largest square divisor.
A326055 (program): a(n) = n - {the largest square that divides n}.
A326056 (program): a(n) = gcd(sigma(n)-A008833(n)-n, n-A008833(n)), where sigma is the sum of divisors of n, and A008833 is the largest square dividing n.
A326057 (program): a(n) = gcd(A003961(n)-2n, A003961(n)-sigma(n)), where A003961(n) is fully multiplicative function with a(prime(k)) = prime(k+1).
A326058 (program): a(n) = n - {the sum of square divisors of n}.
A326059 (program): a(n) = A285309(n) - n, where A285309 gives the sum of nonsquare divisors of n.
A326060 (program): a(n) = gcd(n-A035316(n), A285309(n)-n), where A035316 and A285309 give respectively the sums of square and nonsquare divisors of n.
A326061 (program): Sum of all other divisors of n except the largest proper divisor. a(1) = 0 by convention.
A326062 (program): a(1) = gcd((sigma(n)-A032742(n))-n, n-A032742(n)), where A032742 gives the largest proper divisor of n.
A326065 (program): Sum of divisors of the largest proper divisor of n: a(n) = sigma(A032742(n)).
A326066 (program): a(n) = sigma(n) - sigma(A032742(n)), where A032742 gives the largest proper divisor of n.
A326067 (program): a(n) = sigma(n) - sigma(A032742(n)) - n, where A032742 gives the largest proper divisor of n, and sigma is the sum of divisors of n.
A326068 (program): a(n) = n - sigma(A032742(n)), where sigma is the sum of divisors of n and A032742 gives the largest proper divisor of n.
A326069 (program): a(n) = gcd((sigma(n) - sigma(A032742(n))) - n, n - sigma(A032742(n))), where A032742 gives the largest proper divisor of n.
A326073 (program): a(n) = gcd(1+n-A020639(n), 1+sigma(n)-A020639(n)-n), where A020639 gives the smallest prime factor of n (and 1 for 1), and sigma is the sum of divisors of n.
A326118 (program): a(n) is the largest number of squares of unit area connected only at corners and without holes that can be inscribed in an n X n square.
A326120 (program): a(n) is the concatenation of n^1, n^2, …, n^n.
A326121 (program): Expansion of Sum_{k>=1} k^2 * x^(2*k) / (1 - k * x^k).
A326122 (program): a(n) = 10 * sigma(n).
A326123 (program): a(n) is the sum of all divisors of the first n odd numbers.
A326124 (program): a(n) is the sum of all divisors of the first n positive even numbers.
A326125 (program): Expansion of Sum_{k>=1} k^2 * x^k / (1 + x^k)^2.
A326126 (program): Sum of all other divisors of n except the squarefree part of n: a(n) = sigma(n) - A007913(n).
A326127 (program): a(n) = A326126(n) - n, where A326126 gives the sum of all other divisors of n except the squarefree part of n.
A326128 (program): a(n) = n - A007913(n), where A007913 gives the squarefree part of n.
A326129 (program): a(n) = gcd(A326127(n), A326128(n)).
A326130 (program): a(n) = gcd(A000120(n), A294898(n)) = gcd(A000120(n), sigma(n)-A005187(n)).
A326135 (program): a(n) = sigma(A028234(n)), where sigma is the sum of divisors of n, and A028234 gives n without any occurrence of its smallest prime factor.
A326136 (program): a(n) = sigma(n) - sigma(A028234(n)), where sigma is the sum of divisors of n, and A028234 gives n without any occurrence of its smallest prime factor.
A326140 (program): a(n) = gcd(A318878(n), A318879(n)).
A326142 (program): Sum of all other divisors of n except its largest squarefree divisor: a(n) = sigma(n) - A007947(n).
A326143 (program): a(n) = A326142(n) - n, where A326142 gives the sum of all other divisors of n except its largest squarefree divisor.
A326144 (program): a(n) = gcd(A066503(n), A326143(n)) = gcd(n - A007947(n), sigma(n) - A007947(n) - n).
A326146 (program): a(n) = sigma(n) - A020639(n) - n, where A020639 gives the smallest prime factor of n, and sigma is the sum of divisors of n.
A326147 (program): a(n) = gcd(n-A020639(n), sigma(n)-A020639(n)-n), where A020639 gives the smallest prime factor of n, and sigma is the sum of divisors of n.
A326178 (program): Number of subsets of {1..n} whose product is equal to their sum.
A326184 (program): a(n) = sigma(n) - A057521(n), where A057521 gives the powerful part of n, and sigma gives the sum of divisors of n.
A326185 (program): a(n) = sigma(n) - A057521(n) - n.
A326186 (program): a(n) = n - A057521(n), where A057521 gives the powerful part of n.
A326187 (program): a(n) = sigma(n) - A003557(n).
A326188 (program): a(n) = A001065(n) - A003557(n), where A001065(n) = the sum of proper divisors of n, and A003557(n) = n divided by its largest squarefree divisor.
A326194 (program): Number of iterations of x -> A009194(x) needed to reach a fixed point when starting from x = n, where A009194(x) = gcd(x, sigma(x)).
A326195 (program): Number of iterations of x -> A009195(x) needed to reach 1 when starting from x = n, where A009195(x) = gcd(x, phi(x)).
A326238 (program): Expansion of Sum_{k>=1} k * x^k * (1 - x^k) / (1 + x^k)^3.
A326243 (program): Number of capturing set partitions of {1..n}.
A326244 (program): Number of labeled n-vertex simple graphs without crossing or nesting edges.
A326247 (program): Number of labeled n-vertex 2-edge multigraphs that are neither crossing nor nesting.
A326249 (program): Number of capturing set partitions of {1..n} that are not nesting.
A326251 (program): Number of digraphs with vertices {1..n} whose increasing edges are not crossing.
A326254 (program): Number of non-capturing set partitions of {1..n}.
A326278 (program): Number of n-vertex, 2-edge multigraphs that are not nesting. Number of n-vertex, 2-edge multigraphs that are not crossing.
A326289 (program): a(0) = 0, a(n) = 2^binomial(n,2) - 2^(n - 1).
A326290 (program): Number of non-crossing n-vertex graphs with loops.
A326296 (program): Triangle of numbers T(n,k) = 2*floor(k/2)*(n-k) + ceiling((k-1)^2/2), 1<=k<=n.
A326297 (program): If n = Product (p_j^k_j) then a(n) = Product ((p_j - 1)^(k_j - 1)).
A326299 (program): a(n) = floor(n*log_2(n)).
A326300 (program): Steinhaus sums.
A326305 (program): Dirichlet g.f.: zeta(s-1) * (1 - 2^(-s)) / zeta(s).
A326306 (program): Dirichlet g.f.: zeta(s) * zeta(s-1) * Product_{p prime} (1 - p^(1 - s) + p^(-s)).
A326324 (program): a(n) = A_{5}(n) where A_{m}(x) are the Eulerian polynomials as defined in A326323.
A326325 (program): a(n) = 2^n*n!*([z^n] exp(x*z)*tanh(z)))(1/2).
A326328 (program): a(n) = (2*n)! [x^(2*n)] cosh(x)^(-3).
A326329 (program): Number of simple graphs covering {1..n} with no crossing or nesting edges.
A326345 (program): a(n) is the number of arm movements when expressing n in flag semaphore, counting the movement of each arm separately.
A326347 (program): Number of unordered pairs of 4-colorings of an n-cycle that differ in the coloring of exactly one vertex.
A326354 (program): a(n) is the number of fractions reduced to lowest terms with numerator and denominator less than or equal to n in absolute value.
A326355 (program): Number of permutations of length n with at most two descents.
A326367 (program): Number of tilings of an equilateral triangle of side length n with unit triangles (of side length 1) and exactly two unit “lozenges” or “diamonds” (also of side length 1).
A326394 (program): Expansion of Sum_{k>=1} x^k * (1 + x^(2*k)) / (1 - x^(3*k)).
A326395 (program): Expansion of Sum_{k>=1} x^(2*k) * (1 + x^k) / (1 - x^(3*k)).
A326398 (program): a(n) is the smallest k > 0 such that the concatenation prime(n)k is composite.
A326399 (program): Expansion of Sum_{k>=1} k * x^k / (1 - x^(3*k)).
A326400 (program): Expansion of Sum_{k>=1} k * x^(2*k) / (1 - x^(3*k)).
A326401 (program): Expansion of Sum_{k>=1} k * x^k / (1 + x^k + x^(2*k)).
A326415 (program): Dirichlet g.f.: zeta(2*s) / zeta(s)^3.
A326417 (program): Dirichlet g.f.: zeta(s)^4 * (1 - 2^(-s)).
A326419 (program): a(n) is the number of distinct Horadam sequences of period n.
A326420 (program): Fixed point of the morphism 1->13, 2->132, 3->1322.
A326422 (program): Numbers k such that A000045(k) mod 5 is prime.
A326440 (program): a(n) = 1 - tau(1) + tau(2) - tau(3) + … + (-1)^n tau(n), where tau = A000005 is number of divisors.
A326464 (program): Sum of all the parts in the partitions of n into 9 parts.
A326465 (program): Sum of the smallest parts of the partitions of n into 9 parts.
A326478 (program): a(n) = n*denominator(n*Bernoulli(n-1))/denominator(Bernoulli(n-1)).
A326481 (program): a(n) = E2_{n}(0) with E2_{n} the polynomials defined in A326480.
A326482 (program): a(n) = E2_{n}(-1) with E2_{n} the polynomials defined in A326480.
A326483 (program): a(n) = 2^n*E2_{n}(1/2) with E2_{n} the polynomials defined in A326480.
A326494 (program): Number of subsets of {1..n} containing all differences and quotients of pairs of distinct elements.
A326501 (program): a(n) = Sum_{k=0..n} (-k)^k.
A326503 (program): Expansion of Sum_{k>=1} x^k * (1 - x^(2*k)) / (1 + x^k + x^(2*k))^2.
A326504 (program): Number of (binary) max-heaps on n elements from the set {0,1} containing exactly three 0’s.
A326555 (program): a(n) = (2^n + 3^n)^n for n>= 0.
A326564 (program): O.g.f. A(x) satisfies: 0 = Sum_{n>=1} (b(n) - A(x))^n * (2*x)^n / n, where b(n) = 1 if n is odd or b(n) = 2 if n is even.
A326567 (program): Numerator of the average of the multiset of prime indices of n.
A326575 (program): Expansion of Sum_{k>=1} k * x^k * (1 + x^(2*k)) / (1 + x^(2*k) + x^(4*k)).
A326577 (program): a(n) = (2*n - 1) / A326478(2*n - 1).
A326578 (program): a(n) = n^2*denominator(n*Bernoulli(n-1))/denominator(Bernoulli(n-1)) = n*A326478(n).
A326579 (program): a(n) = n*denominator(n*Bernoulli(n-1)) for n >= 1 and a(0) = 0.
A326580 (program): a(n) = (2*n+1)*denominator((2*n+1)*Bernoulli(2*n)).
A326581 (program): Odd integers which are prime or square.
A326583 (program): Integers k >= 0 such that 2*k + 1 is prime or square.
A326584 (program): a(n) = gcd(n*N(n-1), D(n-1)), with N(n)/D(n) = B(n) the n-th Bernoulli number.
A326586 (program): Odd numbers which do not satisfy Korselt’s criterion, complement of A324050.
A326618 (program): a(n) = n^18 + n^9 + 1.
A326619 (program): Numerator of the average of the set of distinct prime indices of n.
A326657 (program): a(n) = 4*floor(n/2) + ceiling((n-1)^2/2).
A326658 (program): a(n) = 6*floor(n/2) + ceiling((n-1)^2/2).
A326659 (program): T(n,k) = [0<k<=n] * n*(T(n-1,k-1)+T(n-1,k)) + [k=0 and n>=0]; triangle T(n,k), n >= 0, 0 <= k <= n, read by rows.
A326663 (program): Column 3 of the array at A309157; see Comments.
A326664 (program): Column 3 of the array at A326661 see Comments.
A326669 (program): Numbers k such that the average position of the ones in the binary expansion of k is an integer.
A326674 (program): GCD of the set of positions of 1’s in the reversed binary expansion of n.
A326689 (program): Numerator of the fraction (Sum_{prime p | n} 1/p - 1/n).
A326690 (program): Denominator of the fraction (Sum_{prime p | n} 1/p - 1/n).
A326691 (program): a(n) = n/denominator(Sum_{prime p | n} 1/p - 1/n).
A326692 (program): Values of n for which the denominator of (Sum_{prime p | n} 1/p - 1/n) is n.
A326699 (program): Numerator of the average position of a 1 in the reversed binary expansion of n.
A326700 (program): Denominator of the average position of a 1 in the reversed binary expansion of n.
A326703 (program): BII-numbers of chains of nonempty sets.
A326708 (program): Non-Brazilian squares of primes.
A326712 (program): Numbers with a record sum of divisors, weighted by divisor multiplicity (A168512).
A326713 (program): Numbers m that are neither arithmetic (A003601) nor RMS numbers (A140480).
A326714 (program): a(n) = binomial(n,2) + (2-adic valuation of n).
A326715 (program): Values of n for which the denominator of (Sum_{prime p | n} 1/p - 1/n) is 1.
A326719 (program): a(n) = n! * [x^n] (x * tanh(x) * sech(x)) / 2.
A326725 (program): a(n) = (1/2)*n*(5*n - 7); row 5 of A326728.
A326728 (program): A(n, k) = n*(k - 1)*k/2 - k, square array for n >= 0 and k >= 0 read by ascending antidiagonals.
A326729 (program): a(0) = 0; for n >= 1, a(n) is the result of inverting s-th bit (from right) in n, where s is the number of ones in the binary representation of n.
A326730 (program): Number of iterations of A326729(x) starting at x = n to reach 0.
A326731 (program): a(0) = 0; for n >= 1, a(n) = result of inverting s-th bit (from left) in n, where s is the number of ones in the binary representation of n.
A326732 (program): Number of iterations of A326731(x) starting at x = n to reach 0.
A326781 (program): No position of a 1 in the reversed binary expansion of n is a power of 2.
A326790 (program): The rank of the group of functions on the units of Z/nZ generated by the functions f(u) = u*k mod n.
A326810 (program): The smallest prime that does not divide the prime product form (A276086) of the primorial base expansion of n.
A326812 (program): Expansion of Sum_{k>=1} (2^k - 1) * x^(2^k - 1) / (1 - x^(2^k - 1)).
A326813 (program): Dirichlet g.f.: zeta(2*s) / (1 - 2^(-s)).
A326814 (program): Dirichlet g.f.: (1/zeta(s)) * Product_{p prime} (1 - 2 * p^(-s)).
A326815 (program): Dirichlet g.f.: zeta(s)^3 * Product_{p prime} (1 - 2 * p^(-s)).
A326822 (program): T(n, k) = k^0 if k = 1 else 0^n. Triangle read by rows, T(n, k) for 0 <= k <= n.
A326826 (program): a(n) = (1/2) * Sum_{d|n} (sigma_1(d) + sigma_2(d)), where sigma_1 = A000203 and sigma_2 = A001157.
A326827 (program): Expansion of 1 / (chi(-x)^10 * chi(-x^2)^4) in powers of x where chi() is a Ramanujan theta function.
A326828 (program): a(n) = (1/2) * Sum_{d|n} mu(n/d) * phi(d) * (psi(d) + 1), where mu = A008683, phi = A000010 and psi = A001615.
A326829 (program): G.f. A(x) satisfies: A(x) = 1 - x * (1 - A(x/(1 + x)) / (1 + x)).
A326833 (program): Numbers whose sum of digits is a power of 10.
A326845 (program): Sum times maximum of the integer partition with Heinz number n.
A326846 (program): Length times maximum of the integer partition with Heinz number n.
A326917 (program): Nonnegative numbers of the form 8*T(x) - T(y) with 0 <= x, 0 <= y, where T() denotes a triangular number.
A326925 (program): Irregular triangular array read by rows: row n shows the coefficients of this polynomial of degree n: (1/n!)*(numerator of n-th derivative of (1-x)/(1-x-x^2)).
A326926 (program): Triangular array read by rows: row n shows the coefficients of this polynomial of degree n: (1/n!)*(numerator of n-th derivative of 1/(1-x+x^2)).
A326933 (program): Number of nonconstant irreducible polynomial divisors of the n-th polynomial given in A326926.
A326934 (program): Table of A(n,k) read by antidiagonals, where A(n,k)=(n*k) mod (n+1).
A326937 (program): Dirichlet g.f.: (2^s - 1) / (zeta(s-1) * (2^s - 2)).
A326938 (program): Dirichlet g.f.: 1 / (zeta(s) * zeta(s-1) * (1 - 2^(-s))).
A326953 (program): a(n) = A001222(A028906(n)).
A326956 (program): Characteristic function of A228354.
A326963 (program): Number of length n arrays with entries that cover an initial interval of positive integers counting chiral pairs as equivalent, i.e., the arrays are reversible.
A326980 (program): Indices of the compositions (ordered partitions) that are not in nonincreasing order in the list of compositions of j in colexicographic order, if 1 <= k <= 2^(j-1), j >= 1.
A326987 (program): Number of nonpowers of 2 dividing n.
A326988 (program): Sum of nonpowers of 2 dividing n.
A326990 (program): Sum of odd divisors of n that are greater than 1.
A326998 (program): a(n) = 1 + binomial(3*n-1, n) + binomial(3*n-1, n-1)*(binomial(2*n-1, n) + 1).
A327006 (program): a(n) = A327005(n, n).
A327007 (program): a(n) = number of iterations of f(x)=floor((x^2+n)/(2x)) starting at x=n to reach the value floor(sqrt(n)) (=A000196(n)).
A327008 (program): a(n) = number of iterations of f(x)=floor((x^2+n^2)/(2x)) starting at x=n^2 to reach the value n.
A327012 (program): Number of factorizations of n into factors > 1 whose dual is a (strict) antichain.
A327019 (program): Number of non-isomorphic set-systems of weight n whose dual is a (strict) antichain.
A327021 (program): a(n) = (2*n-1)! / 2^(n-1) if n > 0 and a(0) = 1.
A327026 (program): a(n) = (1/n) Sum_{k=0..n} Sum_{d|n} phi(d) A241171(n/d, k) for n >= 1, a(0) = 1.
A327030 (program): a(n) = Sum_{d|n} phi(d)*(n/d)! for n > 0, a(0) = 0.
A327032 (program): a(n) = T(n, 4) with T(n, k) = Sum_{d|k} phi(d)*binomial(n - 1 + k/d, k/d).
A327034 (program): Expansion of e.g.f. exp(x) / (2 - cosh(x)).
A327035 (program): An unbounded sequence consisting solely of Fibonacci numbers with the property that for any four consecutive terms the maximum term is the sum of the two minimum terms.
A327091 (program): Number of chiral pairs of length n words with integer entries that cover an initial interval of positive integers.
A327093 (program): Sequence obtained by swapping each (k*(2n))-th element of the positive integers with the (k*(2n-1))-th element, for all k > 0, in ascending order.
A327095 (program): Expansion of Sum_{k>=1} k * x^k * (1 - x^k + x^(2*k)) / (1 - x^(4*k)).
A327096 (program): Expansion of Sum_{k>=1} sigma(k) * x^k / (1 - x^(2*k)), where sigma = A000203.
A327119 (program): Sequence obtained by swapping each (k*(2n))-th element of the nonnegative integers with the (k*(2n+1))-th element, for all k>0 in ascending order, omitting the first term.
A327122 (program): Expansion of Sum_{k>=1} sigma(k) * x^k / (1 + x^(2*k)), where sigma = A000203.
A327123 (program): Expansion of Sum_{k>=1} phi(k) * x^k / (1 + x^(2*k)), where phi = A000010.
A327124 (program): Expansion of Sum_{k>=1} ((1 - (-x)^k)^k - 1).
A327136 (program): Numbers k such that sin(2k) > sin(2k+2) < sin(2k+4).
A327138 (program): Numbers k such that cos(2k) < cos(2k+2).
A327139 (program): Numbers k such that cos(2k) > cos(2k+2) < cos(2k+4).
A327141 (program): a(n) is the number of different sizes of integer-sided rectangles which can be placed inside an n X n square.
A327142 (program): a(n) is the number of different sizes of integer-sided rectangles which can be placed inside an n X n square and with length greater than n.
A327152 (program): r values of Triphosian primes.
A327153 (program): Number of divisors d of n such that sigma(d)*d is equal to n.
A327164 (program): Number of iterations of x -> gcd(usigma(x),x) needed to reach a fixed point, where usigma is the sum of unitary divisors of n (A034448).
A327166 (program): Number of divisors d of n for which A000005(d)*d is equal to n, where A000005(x) gives the number of divisors of x.
A327168 (program): Number of common divisors of n and A276086(n), with a(0) = 1.
A327169 (program): Number of distinct k such that A000005(k)*A000010(k) is equal to n.
A327171 (program): a(n) = phi(n) * core(n), where phi is Euler totient function, and core gives the squarefree part of n.
A327174 (program): a(n) = [(2*n+1)*r] - [(n+1)*r] - [n*r], where [ ] = floor and r = (1+sqrt(5))/2.
A327175 (program): Positions of 0’s in {A327174(n) : n > 0}.
A327176 (program): Positions of 1’s in {A327174(n) : n > 0}.
A327177 (program): a(n) = [(2n+1)r] - [(n+1)r] - [nr], where [ ] = floor and r = sqrt(2).
A327178 (program): Positions of 0’s in {A327177(n) : n > 0}.
A327179 (program): Positions of 1’s in {A327177(n) : n > 0}.
A327180 (program): a(n) = [(2n+1)r] - [(n+1)r] - [nr], where [ ] = floor and r = sqrt(3).
A327189 (program): For any n >= 0: consider the different ways to split the binary representation of n into two (possibly empty) parts, say with value x and y; a(n) is the least possible value of x + y.
A327190 (program): For any n > 0: consider the different ways to split the binary representation of 2*n+1 into two nonempty parts, say with value x and y; a(n) is the least possible value of x * y.
A327192 (program): For any n >= 0: consider the different ways to split the binary representation of n into two (possibly empty) parts, say with value x and y; a(n) is the least possible value of max(x, y).
A327193 (program): For any n >= 0: consider the different ways to split the binary representation of n into two (possibly empty) parts, say with value x and y; a(n) is the greatest possible value of min(x, y).
A327202 (program): a(n) = [(2n+2)r] - [(n+2)r] - [nr], where [ ] = floor and r = (1+sqrt(5))/2.
A327203 (program): Positions of 0’s in {A327202(n) : n > 0}.
A327204 (program): Positions of 1’s in {A327202(n) : n > 0}.
A327205 (program): a(n) = [(2n+2)r] - [(n+2)r] - [nr], where [ ] = floor and r = sqrt(2).
A327206 (program): Positions of 0’s in {A327205(n) : n > 0}.
A327207 (program): Positions of 1’s in {A327205(n) : n > 0}.
A327209 (program): Positions of 0’s in {A327208(n) : n > 0}.
A327210 (program): Positions of 1’s in {A327208(n) : n > 0}.
A327211 (program): a(n) = [(2n+2)e] - [(n+2)e] - [ne], where [ ] = floor.
A327212 (program): Positions of 0’s in {A327211(n) : n > 0}.
A327213 (program): Positions of 1’s in {A327211(n) : n > 0}.
A327217 (program): Positions of 0’s in {A327216(n) : n > 0}.
A327218 (program): Positions of 1’s in {A327216(n) : n > 0}.
A327222 (program): a(n) = [(2n+4)r] - [nr+4r] - [nr], where [ ] = floor and r = sqrt(2).
A327223 (program): Positions of 0’s in {A327222(k) : n > 0}.
A327224 (program): Positions of 1’s in {A327222(k) : n > 0}.
A327238 (program): Expansion of Sum_{k>=1} ((1 + k * x^k)^k - 1).
A327239 (program): For n >= 1, a(n) = b(n+1) - b(n) where b is A013947.
A327242 (program): Expansion of Sum_{k>=1} tau(k) * x^k / (1 + x^k)^2, where tau = A000005.
A327243 (program): a(n) = n! * Sum_{d|n} (-1)^(n - d) / (n/d)!.
A327247 (program): Number of odd prime powers <= n (with exponents > 0).
A327251 (program): Expansion of Sum_{k>=1} psi(k) * x^k / (1 - x^k)^2, where psi = A001615.
A327252 (program): Balanced reversed ternary: Write n as ternary, reverse the order of the digits, then replace all 2’s with (-1)’s.
A327253 (program): a(n) = floor(2*n*r) - 2*floor(n*r), where r = sqrt(6).
A327254 (program): Positions of 0’s in {A327253(n) : n > 0}.
A327255 (program): Positions of 1’s in {A327253(n) : n > 0}.
A327256 (program): a(n) = floor(2*n*r) - 2*floor(n*r), where r = sqrt(8).
A327257 (program): Positions of 0’s in {A327256(n) : n > 0}.
A327258 (program): Positions of 1’s in {A327256(n) : n > 0}.
A327259 (program): Array T(n,k) = 2*n*k - A319929(n,k), n >= 1, k >= 1, read by antidiagonals.
A327260 (program): Odd numbers not of the form 2*n*k - n - k + 1 where n and k are odd numbers > 1.
A327262 (program): a(n) is the sum of all parts of all partitions of n into consecutive parts that differ by 4.
A327268 (program): Dirichlet g.f.: 1 / (zeta(s) * zeta(s-1) * (1 - 2^(2 - s))).
A327274 (program): Dirichlet g.f.: 1 / (zeta(s)^2 * (1 - 2^(1 - s))).
A327276 (program): a(n) = Sum_{d|n, d odd} mu(d) * mu(n/d).
A327277 (program): Irregular triangle read by rows in which row n lists the first prime(n) primes.
A327278 (program): a(n) = Sum_{d|n, d odd} d * mu(d) * mu(n/d).
A327285 (program): Number of partitions of n into colored blocks of equal parts, such that all colors from a set of size two are used and the colors are introduced in increasing order.
A327300 (program): Positions of 1’s in {A327298(n) : n > 0}.
A327302 (program): One of the two successive approximations up to 5^n for the 5-adic integer sqrt(-9). This is the 1 (mod 5) case (except for n = 0).
A327303 (program): One of the two successive approximations up to 5^n for the 5-adic integer sqrt(-9). This is the 4 (mod 5) case (except for n = 0).
A327304 (program): Digits of one of the two 5-adic integers sqrt(-9) that is related to A327302.
A327305 (program): Digits of one of the two 5-adic integers sqrt(-9) that is related to A327303.
A327306 (program): a(n) = floor(3*n*r) - 3*floor(n*r), where r = sqrt(6).
A327307 (program): Positions of 0’s in {A327306(n) : n > 0}.
A327308 (program): Positions of 1’s in {A327306(n) : n > 0}.
A327309 (program): Positions of 2’s in {A327306(n) : n > 0}.
A327310 (program): a(n) = floor(3*n*r) - 3*floor(n*r), where r = sqrt(8).
A327311 (program): Positions of 0’s in {A327310(n) : n > 0}.
A327312 (program): Positions of 1’s in {A327310(n) : n > 0}.
A327313 (program): Positions of 2’s in {A327310(n) : n > 0}.
A327315 (program): Irregular triangular array read by rows: row n shows the coefficients of this polynomial of degree n: (1/n!)*(numerator of n-th derivative of (x-2)/(x^2-x+1)).
A327316 (program): Triangular array read by rows: row n shows the coefficients of this polynomial of degree n: p(x,n) = ((x+r)^n - (x+s)^n)/(r - s), where r = 3 and s = 2.
A327317 (program): Triangular array read by rows: row n shows the coefficients of this polynomial of degree n: p(x,n) = 2^(n-1) ((x+r)^n - (x+s)^n)/(r - s), where r = 2 and s = 1/2.
A327318 (program): Triangular array read by rows: row n shows the coefficients of this polynomial of degree n: p(x,n) = 2^(n-1) ((x+r)^n - (x+s)^n)/(r - s), where r = 1 and s = 1/2.
A327319 (program): a(n) = binomial(n, 2) + 6*binomial(n, 4).
A327326 (program): a(n) = A006218(n) - A005187(n).
A327327 (program): Partial sums of the sum of nonpowers of 2 dividing n.
A327329 (program): Twice the sum of all divisors of all positive integers <= n.
A327340 (program): Numerator of the rationals r(n) = (1/n^2)*Phi_1(n), with Phi_1(n) = Sum{k=1..n} psi(k), with Dedekind’s psi function.
A327341 (program): Denominators of the rationals r(n) = (1/n^2)*Phi_1(n), with Phi_1(n) = Sum{k=1..n} psi(k), with Dedekind’s psi function.
A327367 (program): Number of labeled simple graphs with n vertices, at least one of which is isolated.
A327374 (program): BII-numbers of set-systems with vertex-connectivity 2.
A327376 (program): BII-numbers of set-systems with vertex-connectivity 3.
A327390 (program): Number of connected divisors of n.
A327411 (program): a(n) = multinomial(2*n+3; 3, 2, 2, …, 2) (n times ‘2’).
A327412 (program): a(n) = multinomial(3*n+2; 2, 3, 3, …, 3) (n times ‘3’).
A327419 (program): Numbers, when duplicates removed and sorted, are A327446, the complement of A327093.
A327420 (program): Building sums recursively with the divisibility properties of their partial sums.
A327422 (program): Positive integers k such that tan(k) > 0 (or equivalently, cot(k) > 0).
A327423 (program): Positive integers k such that tan(k) < 0 (or equivalently, cot(k) < 0).
A327440 (program): a(n) = floor(3*n/10).
A327441 (program): a(n) = max_{p <= n} (p’-p), where p and p’ are successive primes.
A327447 (program): a(n) = 4*p(n-1)*p(n+1) - p(n)^2, where p(k) = k-th prime.
A327461 (program): Maximal size of a Binary Decision Diagram (or BDD) of index n.
A327470 (program): Maximum valency of the central line in a certain smooth 2D-polarized K3-surface in P^{n+1}.
A327471 (program): Number of subsets of {1..n} not containing their mean.
A327474 (program): Number of distinct means of subsets of {1..n}, where {} has mean 0.
A327475 (program): Number of subsets of {1..n} whose mean is an integer, where {} has mean 0.
A327477 (program): Number of subsets of {1..n} containing n whose mean is not an element.
A327479 (program): a(n) is the minimum number of squares of unit area that must be removed from an n X n square to obtain a connected figure without holes and of the longest perimeter.
A327486 (program): Product of Omegas of positive integers from 2 to n.
A327488 (program): T(n, k) = 1 + NAND(k - 1, n - k), where NAND is the Sheffer stroke operating bitwise on the inputs, triangle read by rows, T(n, k) for n >= 1, 1 <= k <= n.
A327489 (program): T(n, k) = 1 + NOR(k - 1, n - k), where NOR is the Peirce arrow operating bitwise on the inputs, triangle read by rows, T(n, k) for n >= 1, 1 <= k <= n.
A327490 (program): T(n, k) = 1 + IFF(k - 1, n - k), where IFF is Boolean equality evaluated bitwise on the inputs, triangle read by rows, T(n, k) for n >= 1, 1 <= k <= n.
A327491 (program): a(0) = 0. If 4 divides n then a(n) = valuation(n, 2) else a(n) = (n mod 2) + 1.
A327492 (program): Partial sums of A327491.
A327493 (program): a(n) = 2^A327492(n).
A327496 (program): a(n) = a(n - 1) * 4^r where r = valuation(n, 2) if 4 divides n else r = (n mod 2) + 1; a(0) = 1. The denominators of A327495.
A327497 (program): a(n) = Numerator([x^n] (4*sinh(sqrt(x)/2)^2*cosh(sqrt(x)))/x).
A327500 (program): Number of steps to reach a fixed point starting with n and repeatedly taking the quotient by the maximum divisor whose prime multiplicities are distinct (A327498, A327499).
A327501 (program): Maximum divisor of n that is 1 or not a perfect power.
A327502 (program): a(n) = n/A327501(n), where A327501(n) is the maximum divisor of n that is 1 or not a perfect power.
A327515 (program): Number of steps to reach a fixed point starting with n and repeatedly taking the quotient by the maximum divisor that is 1, 2, or a nonprime number whose prime indices are pairwise coprime (A327512, A327514).
A327517 (program): Number of factorizations of n that are empty or have at least two factors, all of which are > 1 and pairwise coprime.
A327521 (program): Number of factorizations of the n-th squarefree number A005117(n) into squarefree numbers > 1.
A327529 (program): Maximum divisor of n that is 1 or whose prime indices are relatively prime.
A327530 (program): Number of divisors of n that are 1 or whose prime indices are relatively prime.
A327531 (program): a(n) = 1 if the prime indices of n are relatively prime, otherwise a(n) = n.
A327532 (program): Indicator function for numbers whose prime indices are relatively prime (A289509).
A327550 (program): Number of compositions of partitions of 2n with exactly n compositions.
A327555 (program): Decimal expansion of number with continued fraction expansion [1; 2, 1, 4, 1, 6, 1, 8, 1, 10, 1, …].
A327562 (program): a(0) = a(1) = 1; for n > 1, a(n) = (a(n-1) + a(n-2)) / gcd(a(n-1), a(n-2)) if a(n-1) and a(n-2) are not coprime, otherwise a(n) = a(n-1) + a(n-2) + 1.
A327564 (program): If n = Product (p_j^k_j) then a(n) = Product ((p_j + 1)^(k_j - 1)).
A327565 (program): Number of transfers of marbles between two sets until the first repetition.
A327566 (program): Partial sums of the infinitary divisors sum function: a(n) = Sum_{k=1..n} isigma(k), where isigma is A049417.
A327567 (program): Number of r X s rectangles with squarefree side lengths such that r <= s, r + s = 2n and r | s.
A327570 (program): a(n) = n*phi(n)^2, phi = A000010.
A327572 (program): Partial sums of an infinitary analog of Euler’s phi function: a(n) = Sum_{k=1..n} iphi(k), where iphi is A091732.
A327573 (program): Partial sums of the number of infinitary divisors function: a(n) = Sum_{k=1..n} id(k), where id is A037445.
A327582 (program): a(n) = (17 * 7^(2*n+1) + 1)/24. Sequence related to the properties of the partition function A000041 modulo a power of 7.
A327597 (program): a(n) = numerator((a(n-1) + a(n-2) + 1)/a(n-1)), with a(1)=1, a(2)=2.
A327606 (program): Expansion of e.g.f. exp(x)*(1-x)*x/(1-2*x)^2.
A327625 (program): Expansion of Sum_{k>=0} x^(3^k) / (1 - x^(3^k))^2.
A327626 (program): Expansion of Sum_{k>=1} x^(k^3) / (1 - x^(k^3))^2.
A327629 (program): Expansion of Sum_{k>=1} x^(k*(k + 1)/2) / (1 - x^(k*(k + 1)/2))^2.
A327637 (program): a(n) is the number of integers j such that 1 <= j <= n and gcd(n,j) is a triangular number.
A327649 (program): Maximum value of powers of 2 mod n.
A327650 (program): Maximum value of powers of 3 mod n.
A327657 (program): Number of divisors of n that are 1 or whose prime indices have a common divisor > 1.
A327662 (program): Length of shortest word of frequency depth n.
A327666 (program): a(n) = Sum_{k = 1..n} (-1)^(Omega(k) - omega(k)), where Omega(k) counts prime factors of k with multiplicity and omega(k) counts distinct prime factors.
A327667 (program): a(n) is the least base >= 2 where n is the least number with its sum of digits.
A327668 (program): a(n) = n * Sum_{d|n} (-1)^(bigomega(d) - omega(d)) / d.
A327669 (program): Sum of divisors of n that have an odd number of distinct prime factors.
A327670 (program): Sum of divisors of n that have an even number of distinct prime factors.
A327671 (program): Expansion of Product_{k>=1} (1 - (x*(1 - x))^k).
A327672 (program): a(n) = Sum_{k=0..n} ceiling(sqrt(k)).
A327687 (program): Partial sums of Pisano periods (A001175).
A327695 (program): Number of non-constant factorizations of n whose distinct factors are pairwise coprime.
A327704 (program): The minimal size of a partition lambda of n such that every partition of n with at most 4 parts can be obtained by coalescing the parts of lambda.
A327705 (program): The minimal size of a partition lambda of n such that every partition of n with at most 5 parts can be obtained by coalescing the parts of lambda.
A327706 (program): The minimal size of a partition lambda of n such that every partition of n with at most 6 parts can be obtained by coalescing the parts of lambda.
A327707 (program): The minimal size of a partition lambda of n such that every partition of n with at most 7 parts can be obtained by coalescing the parts of lambda.
A327708 (program): The minimal size of a partition lambda of n such that every partition of n with at most 8 parts can be obtained by coalescing the parts of lambda.
A327715 (program): a(0) = 0; for n >= 1, a(n) = 1 + a(n-A009191(n)).
A327721 (program): Dimension of quantum lens space needed for non-uniqueness.
A327724 (program): Product of A003059 and A071797.
A327728 (program): Number of unlabeled multigraphs with loops allowed and n edges covering three vertices.
A327730 (program): a(n) = A060594(2n).
A327736 (program): Expansion of 1 / (1 - Sum_{i>=1, j>=0} x^(i*2^j)).
A327737 (program): a(n) is the sum of the lengths of the base-b expansions of n for all b with 1 <= b <= n.
A327738 (program): Expansion of 1 / (1 - Sum_{i>=1, j>=1} x^(i*j^2)).
A327739 (program): Expansion of 1 / (1 - Sum_{i>=1} Sum_{j=1..i} x^(i*j)).
A327748 (program): Primes p such that the sum of p and the prime before p is not a multiple of 3.
A327752 (program): Primes powers (A246655) congruent to 1 mod 5.
A327753 (program): Primes powers (A246655) congruent to 4 mod 5.
A327755 (program): Odd integers n such that binomial(n-1,(n-1)/2) is coprime to n.
A327760 (program): Primes in Rob Gahan’s arithmetic progression of 27 primes.
A327764 (program): Expansion of 1 / (1 - Sum_{i>=1, j>=1} x^(i*j*(j + 1)/2)).
A327765 (program): a(n) is the trace of the n-th power of the 2 X 2 matrix [1 2; 3 4].
A327767 (program): Period 2: repeat [1, -2].
A327770 (program): a(n) = (23 * 7^(2*n) + 1)/24. Sequence related to the properties of the partition function A000041 modulo a power of 7.
A327782 (program): Numbers n that cannot be written as a sum of two or more distinct parts with the largest part dividing n.
A327794 (program): The number of (n-2)-interval parking functions of size n.
A327798 (program): Expansion of 1 / (1 - Sum_{i>=1, j>=1} x^(i*(j + 1))).
A327799 (program): Expansion of 1 / (1 + Sum_{i>=1} Sum_{j=1..i} x^(i*j)).
A327800 (program): Expansion of 1 / (1 + Sum_{i>=1, j>=1} x^(i*prime(j))).
A327802 (program): Number of primes p such that n < p < (9/8) * n.
A327809 (program): Regular triangle, coefficients of the polynomial P(n)(x) = (-1)^(n+1)*(2*n+1)*binomial(2*n, n)*Sum_{i=0..n} x^i*binomial(n, i)/(n+i+1).
A327813 (program): Number of irreducible factors in the factorization of the n-th cyclotomic polynomial over GF(4) (counted with multiplicity).
A327816 (program): Number of irreducible factors in the factorization of the n-th cyclotomic polynomial over GF(8) (counted with multiplicity).
A327819 (program): Elements of the unique smallest MSTD set of primes.
A327821 (program): Number of legal Go positions on a board which is an n-cycle graph.
A327829 (program): Squarefree numbers with a prime number of prime factors.
A327832 (program): The practical component of n: the largest divisor of n which is a practical number (A005153).
A327836 (program): Least k > 0 such that n^k == 1 (mod (n+1)^(n+1)).
A327853 (program): Triangle read by rows, Sierpinski’s gasket, A047999 * (0,1,2,3,4,…) diagonalized.
A327858 (program): Greatest common divisor of the arithmetic derivative and the primorial base exp-function: a(n) = gcd(A003415(n), A276086(n)).
A327859 (program): a(n) = A276086(A003415(n)), where A003415 is the arithmetic derivative and A276086 converts digits of primorial base representation to exponents in prime factorization.
A327860 (program): Arithmetic derivative of the primorial base exp-function: a(n) = A003415(A276086(n)).
A327862 (program): Numbers whose arithmetic derivative is of the form 4k+2, cf. A003415.
A327863 (program): Numbers whose arithmetic derivative is a multiple of 3, cf. A003415.
A327864 (program): Numbers whose arithmetic derivative is a multiple of 4, cf. A003415.
A327866 (program): a(n) = 1 if arithmetic derivative of n is square, 0 otherwise. Cf. A003415.
A327868 (program): Number of achiral loops (necklaces or bracelets) of length n with integer entries that cover an initial interval of positive integers.
A327871 (program): Number of self-avoiding planar walks starting at (0,0), ending at (n,n), remaining in the first quadrant and using steps (0,1), (-1,1), and (1,-1) with the restriction that (-1,1) and (1,-1) are always immediately followed by (0,1).
A327877 (program): Numbers having an odd number of non-unitary prime factors.
A327882 (program): a(n) = n*(2*(n-1))! for n > 0, a(0) = 1.
A327885 (program): Number of set partitions of [n] such that at least one of the block sizes is 2.
A327896 (program): a(n) is the minimum number of tiles needed for constructing a polyiamond with n holes.
A327904 (program): Number of labeled simple graphs with vertices {1..n} such that every edge has a different sum.
A327916 (program): Triangle T(k, n) read by rows: Array A(k, n) = 2^k*(k + 1+ n), k >= 0, n >= 0, read by antidiagonals upwards.
A327917 (program): Triangle T read by rows: T(k, n) = A(k-n, k) with the array A(k, n) = F(2*k+n) = A000045(2*k+n), for k >= 0 and n >= 0.
A327922 (program): Odd numbers m >= 3 for which phi(2*m)/2 = phi(m)/2 is even, where phi = A000010 (Euler’s totient).
A327926 (program): a(n) = 99^n.
A327927 (program): Expansion of e.g.f. exp(Sum_{i>=1} Sum_{j=1..i} x^(i*j) / (i*j)).
A327929 (program): Numbers for which there is at least one such prime p that p^p divides the arithmetic derivative of n, A003415(n).
A327936 (program): Multiplicative with a(p^e) = p if e >= p, otherwise 1.
A327937 (program): Multiplicative with a(p^e) = p^(p-1) if e >= p, otherwise a(p^e) = p^e.
A327938 (program): Multiplicative with a(p^e) = p^(e mod p).
A327939 (program): Multiplicative with a(p^e) = p^(e-(e mod p)).
A327940 (program): Expansion of e.g.f. exp(Sum_{i>=1} Sum_{j=1..i-1} x^(i*j) / (i*j)).
A327941 (program): Expansion of e.g.f. exp(Sum_{i>=1} Sum_{j>=2} x^(i*j) / (i*j)).
A327952 (program): a(n) is the number of positive integers k such that some multiple of sqrt(k) falls strictly between n and n+1.
A327953 (program): a(n) is the number of positive integers k such that some nontrivial multiple of sqrt(k) falls strictly between n and n+1.
A327954 (program): First differences of A327953.
A327961 (program): Sum of products of n-bit numbers with their n-bit reverse.
A327971 (program): Bitwise XOR of trajectories of rule 30 and its mirror image, rule 86, when both are started from a lone 1 cell: a(n) = A110240(n) XOR A265281(n).
A327974 (program): a(n) = A051023(n) XOR A051023(n-1), where A051023 gives the middle column of rule-30 1-D cellular automaton, when started from a lone 1 cell.
A327982 (program): Partial sums of A051023, the middle column of rule-30 1-D cellular automaton, when started from a lone 1 cell.
A327986 (program): Denominators of the coefficients in the expansion of (4*sinh(sqrt(x)/2)^2*cosh(sqrt(x)))/x.
A327993 (program): a(n) = [x^n] ((x - 1)*(x + 1)*(2*x^2 - 1))/(2*x^4 + 4*x^3 - x^2 - 3*x + 1).
A327998 (program): a(n) = (n!/floor(n/2)!^2)^2.
A327999 (program): a(n) = Sum_{k=0..2n}(k!*(2n - k)!)/(floor(k/2)!*floor((2n - k)/2)!)^2.
A328000 (program): a(n) = Sum_{k=0..n}(k!*(n - k)!)/(floor(k/2)!*floor((n - k)/2)!)^2.
A328002 (program): a(n) = 2^n * Sum_{k=0..n} Product_{j=1..k} (2/j)^((-1)^j).
A328003 (program): a(n) = ppi(2*n) - ppi(n). Number of prime powers (A246655) in the interval (n, 2*n]. See comments.
A328005 (program): Number of distinct coefficients in functional composition of 1 + x + … + x^(n-1) with itself.
A328008 (program): Expansion of e.g.f. 1 / (2 - exp(x) / (1 - x)).
A328010 (program): The 5x + 1 sequence beginning at 17.
A328011 (program): The 5x + 1 sequence beginning at 1.
A328012 (program): Numbers whose binary representations start and end with 1 and contain an even number of zeros between.
A328026 (program): Number of divisible pairs of consecutive divisors of n.
A328034 (program): a(n) = 3n minus the largest power of 2 not exceeding 3n.
A328054 (program): Expansion of e.g.f. log(1 + x / (1 - x)^2).
A328055 (program): Expansion of e.g.f. -log(1 - x / (1 - x)^2).
A328058 (program): Primes p such that 2*p-1 is a semiprime.
A328082 (program): Triangle read by rows: columns are Fibonacci numbers F_{2i+1} shifted downwards.
A328085 (program): Column sums of triangle A328084.
A328099 (program): a(n) = min(A003415(n), A276086(n)).
A328100 (program): Column which is two positions right of the middle column of rule-30 1-D cellular automaton, when started from a lone 1 cell.
A328101 (program): Column immediately right of the middle column of rule-30 1-D cellular automaton, when started from a lone 1 cell.
A328102 (program): Column immediately left of the middle column of rule-30 1-D cellular automaton, when started from a lone 1 cell.
A328104 (program): a(n) = A163617(A110240(n)) = A110240(n) OR 2*A110240(n).
A328105 (program): Binary weight of A328104: a(n) = A000120(A110240(n) OR 2*A110240(n)).
A328106 (program): Binary weight of A327971: a(n) = A000120(A110240(n) XOR A030101(A110240(n))).
A328114 (program): Maximal digit value used when n is written in primorial base (cf. A049345).
A328141 (program): a(n) = a(n-1) - (n-2)*a(n-2), with a(0)=1, a(1)=2.
A328147 (program): a(n) = A025586(n)/4 for n>=3.
A328152 (program): a(n) is the number of squares of side length greater than 1 having vertices at the points of an n X n grid of dots.
A328154 (program): G.f. A(x) satisfies: A(x) = A(x^2) + x / (1 + x)^2.
A328161 (program): Numbers n that are prime or whose proper divisors (greater than 1 and less than n) have no consecutive divisibilities.
A328162 (program): Maximum length of a divisibility chain of consecutive divisors of n.
A328166 (program): Heinz number of the run-lengths of the divisors of n.
A328167 (program): GCD of the prime indices of n, all minus 1.
A328168 (program): Numbers whose prime indices minus 1 are relatively prime.
A328169 (program): GCD of the prime indices of n, all plus 1.
A328181 (program): a(n) = (-1)^(bigomega(n) - omega(n)) * Sum_{d|n} (-1)^(bigomega(d) - omega(d)) * d.
A328182 (program): Expansion of e.g.f. 1 / (2 - exp(3*x)).
A328183 (program): Expansion of e.g.f. 1 / (2 - exp(4*x)).
A328184 (program): Denominator of time taken for a vertex of a rolling regular n-sided polygon to reach the ground.
A328185 (program): Numerators associated with A328184.
A328189 (program): Numbers n with at least one pair of consecutive divisible nontrivial divisors (greater than 1 and less than n).
A328195 (program): Maximum length of a divisibility chain of consecutive divisors of n greater than 1.
A328202 (program): a(n) is the greatest common divisor of all the numbers in row n of Pascal’s triangle excluding 1 and n.
A328203 (program): Expansion of Sum_{k>=1} k * x^k / (1 - x^(2*k))^2.
A328208 (program): Zeckendorf-Niven numbers: numbers divisible by the number of terms in their Zeckendorf representation (A007895).
A328223 (program): Numbers k such that both k and k+4 are sums of two squares.
A328229 (program): Decimal expansion of 2^(7/12).
A328231 (program): a(n) = gcd(n, A048673(n)).
A328232 (program): Numbers whose arithmetic derivative (A003415) is a primorial number, including cases where it is the first primorial, A002110(0) = 1.
A328234 (program): Numbers whose arithmetic derivative (A003415) is a squarefree number (A005117) > 1.
A328239 (program): Numbers whose third arithmetic derivative (A099306) is prime.
A328258 (program): a(n) = Sum_{d|n, gcd(d,n/d) = 1} (-1)^(d + 1) * d.
A328259 (program): a(n) = n * sigma_2(n).
A328260 (program): a(n) = n * omega(n).
A328262 (program): a(n) = a(n-1)*3/2, if noninteger then rounded to the nearest even integer, with a(1) = 1.
A328263 (program): a(n) = number of letters in a(n-1) (in Polish), with a(1) = 1.
A328271 (program): Expansion of Sum_{k>=1} x^(k^2) * (1 + x^(k^2)) / (1 - x^(k^2))^3.
A328283 (program): The maximum number m such that m white, m black and m red queens can coexist on an n X n chessboard without attacking each other.
A328284 (program): An extension of the Jacobsthal numbers: 0, 0, 1, followed by A001045.
A328286 (program): Expansion of e.g.f. -log(1 - x - x^2/2).
A328301 (program): Expansion of Product_{k>0} 1/(1 - x^(k^k)).
A328303 (program): Numbers whose arithmetic derivative is not squarefree.
A328306 (program): a(n) = 1 if k-th arithmetic derivative of A276086(n) is zero for some k, otherwise 0.
A328307 (program): a(n) tells how many numbers m there are in range 0..n such that the k-th arithmetic derivative of A276086(m) is zero for some k >= 0.
A328308 (program): a(n) = 1 if k-th arithmetic derivative of n is zero for some k, otherwise 0.
A328309 (program): a(n) counts the numbers in 0..n whose k-th arithmetic derivative is zero for some k >= 0.
A328316 (program): Iterates of A276086 starting from 0.
A328317 (program): Smallest prime not dividing A328316(n), with a(0) = 1 by convention; Equally, for n > 0, smallest prime dividing A328316(1+n).
A328325 (program): Expansion of Product_{k>=0} 1/(1 - x^(k^k)).
A328332 (program): Expansion of (1 + 4*x - 5*x^2 + 10*x^3) / ((1 - x) * (1 - 10*x^2)).
A328333 (program): Expansion of (1 + 4*x - 6*x^2) / ((1 - x) * (1 - 10*x^2)).
A328334 (program): Forward difference of difference between 2^n and the next smaller power of 3.
A328336 (program): Numbers with no consecutive prime indices relatively prime.
A328337 (program): The number whose binary indices are the nontrivial divisors of n (greater than 1 and less than n).
A328348 (program): Let S be any integer in the range 3 <= S <= 17. Sequence has the property that a(n)*S is the sum of all positive integers whose decimal expansion has <= n digits and contains at most two distinct nonzero digits p and q such that p+q=S.
A328350 (program): Let S be any integer in the range 6 <= S <= 24. Sequence has the property that a(n)*S is the sum of all positive integers whose decimal expansion has <= n digits and contains at most three distinct nonzero digits d1, d2, d3 such that d1+d2+d3 = S.
A328351 (program): Let S be any integer in the range 10 <= S <= 30. Sequence has the property that a(n)*S is the sum of all positive integers whose decimal expansion has <= n digits and contains at most four distinct nonzero digits d1, d2, d3 and d4 such that d1+d2+d3+d4=S.
A328352 (program): Similar to A328350, but for 5 digits rather then 3.
A328353 (program): a(n)*S is the sum of all positive integers whose decimal expansion is up to n digits and uses six distinct nonzero digits d1,d2,d3,d4,d5,d6 such that d1+d2+d3+d4+d5+d6=S.
A328354 (program): a(n)*S is the sum of all positive integers whose decimal expansion is up to n digits and uses seven distinct nonzero digits d1,d2,d3,d4,d5,d6,d7 such that d1+d2+d3+d4+d5+d6+d7=S.
A328355 (program): Let S be any integer in the range 36 <= S <= 44. Sequence has the property that a(n)*S is the sum of all positive integers whose decimal expansion has <= n digits and uses eight distinct nonzero digits d1,d2,d3,d4,d5,d6,d7,d8 such that d1+d2+d3+d4+d5+d6+d7+d8=S.
A328356 (program): a(n) is the sum of all positive integers whose decimal expansion is up to n digits and does not contain the 0 digit.
A328366 (program): a(n) is the surface area of the stepped pyramid with n levels described in A245092.
A328372 (program): Expansion of Sum_{k>=1} x^(k^2) / (1 - x^(2*k^2)).
A328373 (program): Expansion of Sum_{k>=1} x^(k^2) * (1 + x^(2*k^2)) / (1 - x^(2*k^2))^2.
A328380 (program): a(n) = (a(n-1) * a(n-3) - 2 * a(n-2)^2) / a(n-4) with a(0) = a(1) = a(2) = a(3) = 1.
A328382 (program): a(n) = A276086(n) mod A003415(n), where A276086 is the primorial base exp-function and A003415 is the arithmetic derivative.
A328386 (program): a(n) = A276086(n) mod n.
A328387 (program): Numbers k such that A276086(k) is a multiple of k.
A328389 (program): Maximal digit value in primorial base expansion of A276086(n): a(n) = A328114(A276086(n)).
A328393 (program): Numbers whose arithmetic derivative (A003415) is a squarefree number (A005117).
A328394 (program): Maximal digit value in primorial base expansion of A276087(n): a(n) = A328114(A276087(n)).
A328399 (program): Lexicographically earliest infinite sequence such that a(i) = a(j) => A328475(i) = A328475(j) for all i, j.
A328400 (program): Smallest number with the same set of distinct prime exponents as n.
A328403 (program): a(n) = A276086(A276086(A276086(n))), where A276086(n) converts primorial base expansion of n into its prime product form.
A328404 (program): The length of primorial base expansion (number of significant digits) of A276086(n), where A276086(n) converts primorial base expansion of n into its prime product form.
A328405 (program): The length of primorial base expansion (number of significant digits) of A276086(A276086(n)), where A276086(n) converts primorial base expansion of n into its prime product form.
A328406 (program): The length of primorial base expansion (number of significant digits) of A276086(A276086(A276086(n))), where A276086(n) converts primorial base expansion of n into its prime product form.
A328407 (program): G.f. A(x) satisfies: A(x) = A(x^2) + x * (1 + x) / (1 - x)^3.
A328408 (program): G.f. A(x) satisfies: A(x) = A(x^2) + x * (1 + 4*x + x^2) / (1 - x)^4.
A328449 (program): Smallest number in whose divisors the longest run is of length n, and 0 if none exists.
A328460 (program): Number of compositions of n with no part divisible by the next.
A328462 (program): Numbers obtained by reinterpreting base-2 representation of odd numbers in primorial base.
A328465 (program): Row 2 of A328464: a(n) = A276156(4n - 2) / 2.
A328466 (program): Row 3 of A328464: a(n) = A276156(8n - 4) / 6.
A328467 (program): Row 4 of A328464: a(n) = A276156(16n - 8) / 30.
A328468 (program): Row 5 of A328464: a(n) = A276156(32n - 16) / 210.
A328475 (program): Convert the primorial base expansion of n into its prime product form, then divide by the largest primorial which divides that product: a(n) = A111701(A276086(n)).
A328476 (program): Convert the primorial base expansion of n into its prime product form, then subtract the largest primorial which divides that product: a(n) = A276151(A276086(n)).
A328478 (program): Divide n by the largest primorial that divides it and repeat until a fixed point is reached; a(n) is the fixed point.
A328479 (program): a(n) = n/A328478(n), where A328478(n) is obtained by repeatedly dividing n by the largest primorial that divides it until a fixed point is reached.
A328482 (program): Number of distinct terms required when n is expressed as a greedy sum of terms of A129912 (number of nonzero digits when n is expressed in greedy A129912-base).
A328484 (program): Dirichlet g.f.: zeta(s)^2 / (1 - 3^(-s)).
A328485 (program): Dirichlet g.f.: zeta(s)^2 * zeta(s-1) / zeta(2*s-1).
A328486 (program): Dirichlet g.f.: zeta(s)^4 * (1 - 2^(-s))^2.
A328487 (program): Dirichlet g.f.: zeta(s)^2 * zeta(s-1)^2 * (1 - 2^(1 - s))^2.
A328490 (program): Dirichlet g.f.: zeta(s)^2 * zeta(s-2)^2.
A328493 (program): a(n) = (p_n + 1)*q_n - 1; where (p_n, q_n) is the n-th twin prime pair.
A328494 (program): Constant term in the expansion of (1+x+y+1/x+1/y)^n without assuming commutativity.
A328495 (program): Decimal expansion of Sum_{k>=0} (-1)^k*L(k)/k!, where L(k) is the k-th Lucas number (A000032).
A328502 (program): Dirichlet g.f.: zeta(s-1) / (zeta(s) * zeta(s-2)).
A328547 (program): Number of 3-regular bipartitions of n.
A328548 (program): Number of 6-regular bipartitions of n.
A328556 (program): Expansion of Product_{p prime, k>=1} (1 - x^(p^k)).
A328557 (program): Arithmetic numbers (A003601) that are not squares (A000290).
A328558 (program): Squares (A000290) that are not arithmetic numbers (A003601).
A328560 (program): Numbers whose product of digits is a power of 10.
A328563 (program): Nonsquarefree unitary weird numbers that are also weird numbers.
A328564 (program): a(n) is the sum of the elements of the set A_n = {(n-k) AND k, k = 0..n} (where AND denotes the bitwise AND operator).
A328565 (program): a(n) is the sum of the elements of the set X_n = {(n-k) XOR k, k = 0..n} (where XOR denotes the bitwise XOR operator).
A328566 (program): a(n) is the sum of the elements of the set O_n = {(n-k) OR k, k = 0..n} (where OR denotes the bitwise OR operator).
A328567 (program): a(n) is the smallest positive integer divisible by n such that it is possible to strike out a digit from its binary expansion (apart from trailing zeros) so that the resulting number is nonzero and divisible by n.
A328569 (program): Exponent of least prime factor in A276086(A276086(n)), where A276086 converts the primorial base expansion of n into its prime product form.
A328570 (program): Index of the least significant zero digit in the primorial base expansion of n, when the rightmost digit is in the position 1.
A328571 (program): Primorial base expansion of n converted into its prime product form, but with all nonzero digits replaced by 1’s: a(n) = A007947(A276086(n)).
A328572 (program): Primorial base expansion of n converted into its prime product form, but with 1 subtracted from all nonzero digits: a(n) = A003557(A276086(n)).
A328573 (program): a(n) = A328475(n) / A328572(n).
A328574 (program): a(1) = 0, and, for n >= 2, numbers n whose primorial base expansion doesn’t contain any nonleading zeros.
A328575 (program): a(n) = A003557(A032742(A276086(n))).
A328578 (program): Index of the least prime not dividing A276086(A276086(n)): a(n) = A257993(A276087(n)).
A328579 (program): a(n) = A053669(A276086(A276086(n))).
A328580 (program): a(n) is the largest primorial dividing A276086(n), where A276086 converts the primorial base expansion of n into its prime product form.
A328581 (program): Product of nonzero digits in primorial base expansion of n.
A328583 (program): a(n) = A023900(A276086(n)).
A328584 (program): Least common multiple of n and A276086(n).
A328604 (program): G.f.: (1 + 7*x) / (1 - 2*x - 9*x^2).
A328605 (program): Expansion of (1 + 5*x - 2*x^2 - 15*x^3) / (1 - 12*x^2 + 25*x^4).
A328606 (program): Expansion of (1 + 9*x) / (1 - 2*x - 11*x^2).
A328610 (program): Irregular triangular array read by rows: the rows show the coefficients of the first of two factors of even-degree polynomials described in Comments.
A328611 (program): Irregular triangular array read by rows: row n gives the coefficients of the second of two factors of even-degree polynomials described in Comments.
A328614 (program): Number of 1-digits in primorial base expansion of n.
A328615 (program): Number of digits larger than 1 in primorial base expansion of n.
A328616 (program): Number of digits in primorial base expansion of n that are maximal possible in their positions.
A328620 (program): Number of nonleading zeros in primorial base expansion of n, a(0) = 0 by convention.
A328621 (program): Multiplicative with a(p^e) = p^(2e mod p).
A328632 (program): Numbers n >= 0 for which A328578(n) = A257993(A276086(A276086(n))) = 2, where A276086 converts the primorial base expansion of n into its prime product form, and A257993 returns the index of the least prime not present in its argument.
A328633 (program): Numbers n for which A328578(n) = A257993(A276086(A276086(n))) = 3, where A276086 converts the primorial base expansion of n into its prime product form, and A257993 returns the index of the least prime not present in its argument.
A328634 (program): Numbers n for which A328578(n) = A257993(A276086(A276086(n))) = 4.
A328635 (program): Numbers n for which A328578(n) = A257993(A276086(A276086(n))) = 5.
A328636 (program): Numbers n for which A328578(n) = A257993(A276086(A276086(n))) = 6.
A328639 (program): Dirichlet g.f.: zeta(2*s) / (zeta(s) * zeta(s-2)).
A328640 (program): Dirichlet g.f.: zeta(2*s) / (zeta(s) * zeta(s-3)).
A328641 (program): Dirichlet g.f.: zeta(s)^2 / zeta(s-1)^2.
A328645 (program): Triangular array read by rows: row n shows the coefficients of this polynomial of degree n: (1/n!)*(numerator of n-th derivative of 1/(1-3x+x^2)).
A328646 (program): Irregular triangular array read by rows: row n shows the coefficients of this polynomial of degree n: (1/n!)*(numerator of n-th derivative of (1-x)/(x^2-3x+1)).
A328647 (program): Irregular triangular array read by rows: row n shows the coefficients of this polynomial of degree n: (1/n!)*(numerator of n-th derivative of (1+x)/(x^2-3x+1)).
A328649 (program): Irregular triangular array read by rows: row n shows the coefficients of the following polynomial of degree n: (1/n!)*(numerator of n-th derivative of (x-2)/(1-x-x^2).
A328650 (program): Triangular array read by rows: row n shows the coefficients of this polynomial of degree n: (1/n!)*(numerator of n-th derivative of 1)/(1-x-2x^2).
A328652 (program): Number of unlabeled loopless multigraphs with n edges covering four vertices.
A328659 (program): Partial sums of A035100: number of binary digits of the primes.
A328661 (program): If n is the k-th composite number then a(n) = a(k), otherwise a(n) = n.
A328667 (program): a(n) = Sum_{d divides n} (-1)^(n + 1 + d + n/d) * d^2.
A328683 (program): Positive integers that are equal to 99…99 (repdigit with n digits 9) times the sum of their digits.
A328694 (program): a(n) = sum of lead terms of all parking functions of length n.
A328708 (program): Number of non-primitive Pythagorean triples with leg n.
A328712 (program): Number of non-primitive Pythagorean triples with hypotenuse n.
A328713 (program): Constant term in the expansion of (1 + x + y + z + 1/x + 1/y + 1/z)^n.
A328721 (program): Dirichlet g.f.: Product_{p prime, k>=1} (1 + p^(-s*k)) / (1 - p^(-s*k)).
A328722 (program): Dirichlet g.f.: 1 / zeta(s-1)^2.
A328724 (program): a(1)=2, a(2)=3; a(n) is the smallest k > a(n-1) such that k + a(n-1) is a multiple of a(n-2).
A328725 (program): Constant term in the expansion of (1 + x + y + z + 1/x + 1/y + 1/z + x*y + y*z + z*x + 1/(x*y) + 1/(y*z) + 1/(z*x) + x*y*z + 1/(x*y*z))^n.
A328727 (program): Nonnegative numbers whose base-3 expansion has no two consecutive nonzero digits.
A328729 (program): Dirichlet g.f.: zeta(s) / (zeta(s-1) * zeta(2*s)).
A328735 (program): Constant term in the expansion of (x + y + z + 1/x + 1/y + 1/z + x*y + y*z + z*x + 1/(x*y) + 1/(y*z) + 1/(z*x) + x*y*z + 1/(x*y*z))^n.
A328745 (program): Dirichlet g.f.: Product_{p prime} 1 / (1 - p^(-s))^p.
A328749 (program): a(n) = Sum_{k = 0..w and t_k > 0} (-1)^t_k * 2^k, where Sum_{k = 0..w} t_k * 3^k is the ternary representation of n.
A328750 (program): Constant term in the expansion of (-1 + (1 + w) * (1 + x) * (1 + y) * (1 + z) + (1 + 1/w) * (1 + 1/x) * (1 + 1/y) * (1 + 1/z))^n.
A328751 (program): Constant term in the expansion of (-2 + (1 + w) * (1 + x) * (1 + y) * (1 + z) + (1 + 1/w) * (1 + 1/x) * (1 + 1/y) * (1 + 1/z))^n.
A328752 (program): Lexicographically earliest sequence of distinct positive numbers such that for any n > 0, the first nonzero digit of a(n+1)/a(n) is “1”.
A328766 (program): Number of nonleading zeros in primorial base expansion of A276086(n).
A328769 (program): The second primorial based variant of arithmetic derivative: a(p) = A034386(p) for p prime, a(u*v) = a(u)*v + u*a(v), with a(0) = a(1) = 0.
A328770 (program): Numbers in whose primorial base expansion any digit is at most half of the maximal allowed digit for that position.
A328778 (program): Number of indecomposable closed walks of length 2n along the edges of a cube based at a vertex.
A328791 (program): Triangular numbers of the form k^2 + 3.
A328792 (program): Numbers that are not the difference between any triangular number and the largest square that does not exceed it.
A328806 (program): Row lengths of A276427: largest k such that a partition of n has k-1 distinct parts i of multiplicity i.
A328808 (program): Constant term in the expansion of (3 + x + y + z + 1/x + 1/y + 1/z + x*y + y*z + z*x + 1/(x*y) + 1/(y*z) + 1/(z*x) + x*y*z + 1/(x*y*z))^n.
A328809 (program): Constant term in the expansion of (1 + (1 + w) * (1 + x) * (1 + y) * (1 + z) + (1 + 1/w) * (1 + 1/x) * (1 + 1/y) * (1 + 1/z))^n.
A328812 (program): Constant term in the expansion of (Product_{k=1..n} (1 + x_k) + Product_{k=1..n} (1 + 1/x_k))^n.
A328819 (program): Third digit after decimal point of square root of n.
A328820 (program): Fourth digit after decimal point of square root of n.
A328821 (program): Triangular array read by rows. Let P be the poset of all even sized subsets of [2n] ordered by inclusion. T(n,k) is the number of intervals in P with length k, 0<=k<=n, n>=0.
A328823 (program): a(n) is the least prime factor of A000096(n) = n*(n+3)/2.
A328824 (program): Numerators of A113405(-n) (see the comment for details).
A328826 (program): Triangle read by rows: binomial(n,k)*(2*n-k)!, n>=0, 0<=k<=n.
A328827 (program): a(n) is the largest prime factor of n + n*(n+1)/2 = n*(n+3)/2.
A328830 (program): The second prime shadow of n: a(1) = 1; for n > 1, a(n) = a(A003557(n)) * prime(A056169(n)) when A056169(n) > 0, otherwise a(n) = a(A003557(n)).
A328834 (program): Square root of the prime factor form (A276086) of the primorial base expansion, computed for such numbers for which it is a square.
A328835 (program): Prime shadow of primorial base exp-function: a(n) = A181819(A276086(n)).
A328840 (program): Numbers with no digit 1 in their primorial base expansion (A049345).
A328841 (program): Substitute ones for all nonzero digits in primorial base expansion of n, then convert back to decimal.
A328842 (program): Decrement each nonzero digit by one in primorial base representation of n, then convert back to decimal.
A328849 (program): Numbers in whose primorial base expansion only even digits appear.
A328854 (program): Dirichlet g.f.: Product_{p prime} 1 / (1 - 2 * p^(-s))^2.
A328864 (program): For any three-digit number k = hdu, f(k) = (h+d+u) + (h*d+d*u+u*h) + (h*d*u). This sequence consists of the numbers k for which the ratio k/f(k) is an integer.
A328865 (program): The first repeating term in the trajectory of n under iterations of A329623, or -1 if no such terms exists.
A328875 (program): Constant term in the expansion of (-1 + (1 + w + 1/w) * (1 + x + 1/x) * (1 + y + 1/y) * (1 + z + 1/z))^n.
A328878 (program): If n = Product (p_j^k_j) then a(n) = Product (prime(p_j)).
A328879 (program): If n = Product (p_j^k_j) then a(n) = Product (pi(p_j) + 1), where pi = A000720.
A328881 (program): a(n+3) = 2^n - a(n), a(0)=a(2)=1, a(1)=0 for n >= 0.
A328882 (program): a(n) = n - 2^(sum of digits of n).
A328886 (program): Squares that end in 444.
A328890 (program): Number of acyclic edge covers of the complete bipartite graph K_{n,2}.
A328892 (program): If n = Product (p_j^k_j) then a(n) = Sum (2^(k_j - 1)).
A328893 (program): Partial sums of A095112: sum of the Dirichlet convolution of the characteristic function of the prime powers (A069513) with the positive integers (A000027) from 1 to n.
A328898 (program): Sum of p-ary comparisons units required to rank a sequence in parallel when the sequence is partitioned into heaps equal to the prime factors p of the initial sequence length n.
A328915 (program): If n = Product (p_j^k_j) then a(n) = Product (nextprime(p_j)), where nextprime = A151800.
A328943 (program): a(n) = 2 + (n mod 4).
A328944 (program): Arithmetic numbers (A003601) that are not harmonic (A001599).
A328946 (program): Product of primorials of consecutive integers (second definition A034386).
A328950 (program): Numerators for the “Minimum-Redundancy Code” card problem.
A328956 (program): Numbers k such that sigma_0(k) = omega(k) * Omega(k), where sigma_0 = A000005, omega = A001221, Omega = A001222.
A328957 (program): Numbers k such that sigma_0(k) != omega(k) * Omega(k), where sigma_0 = A000005, omega = A001221, Omega = A001222.
A328958 (program): a(n) = sigma_0(n) - omega(n) * nu(n), where sigma_0 = A000005, nu = A001221, omega = A001222.
A328959 (program): a(n) = sigma_0(n) - 2 - (omega(n) - 1) * nu(n), where sigma_0 = A000005, nu = A001221, omega = A001222.
A328961 (program): Positive integers n such that sigma_0(n) - 3 = (omega(n) - 1) * nu(n), where sigma_0 = A000005, nu = A001221, omega = A001222.
A328967 (program): a(n+1) = 1 - Sum_{k=1..n} a(floor(n/k)).
A328973 (program): Numbers k such that A053392(k) > k.
A328978 (program): Row sums of A329059.
A328979 (program): Trajectory of 0 under repeated application of the morphism 0 -> 0010, 1 -> 1010.
A328981 (program): Indicator function of numbers whose binary representation ends in an even positive number of 0’s.
A328982 (program): Sorted list of the numbers of the form 5m+2 (m>=0) together with numbers of the form 5m-2+eps (m>=1), where eps = 1 if the binary expansion of m ends in an odd number of 0’s and is otherwise 0.
A328983 (program): Complement of A328982.
A328984 (program): If n is even, a(n) = floor((5t+1)/2) where t=n/2; if n == 1 (mod 4) then a(n) = 10t+1 where t = (n-1)/4; and if n == 3 (mod 4) then a(n) = 10t+7 where t = (n-3)/4.
A328985 (program): First differences of A328984.
A328986 (program): The sequence C(n) defined in the comments (A and B smallest missing numbers, offset 1).
A328987 (program): The sequence C(n) defined in the comments (A and B smallest missing numbers, offset 0).
A328990 (program): a(n) = (3*b(n) + b(n-1) + 1)/2, where b = A005409.
A328994 (program): a(n) = n^2*(1+n)*(1+n^2)/4.
A328995 (program): Dirichlet g.f. = Product_{primes p == 1 mod 3} (1+p^(-s))/(1-p^(-s)).
A329004 (program): a(n) is the largest index in [n] that maximizes tau.
A329005 (program): a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(2) as in A327320.
A329007 (program): a(n) = p(2,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(2) as in A327320.
A329008 (program): a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3) as in A327321.
A329009 (program): a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3) as in A327321.
A329010 (program): a(n) = p(2,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3) as in A327321.
A329011 (program): a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(5) as in A327322.
A329014 (program): a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(6) as in A327323.
A329015 (program): a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(6) as in A327323.
A329017 (program): a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3/2) as in A328644.
A329018 (program): a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3/2) as in A328644.
A329019 (program): a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3/2) as in A328644.
A329028 (program): The least missing nonzero digit in the primorial base expansion of n.
A329029 (program): a(n) = A069359(A276086(n)), where A276086 converts the primorial base expansion of n into its prime product form and A069359(n) = n * Sum_{p|n} 1/p where p are primes dividing n.
A329031 (program): a(n) = A327860(A328841(n)).
A329032 (program): a(n) = A327860(A328842(n)).
A329033 (program): a(n) = A003415(A122111(n)).
A329036 (program): Number of common divisors of n and A122111(n).
A329038 (program): a(n) = A246277(A276086(n)).
A329039 (program): If n = Product p_i^e_i, a(n) = n * Sum ((e_i - 1)/p_i).
A329040 (program): Number of distinct primorials in the greedy sum of primorials adding to A108951(n).
A329044 (program): a(n) = A064989(A324886(n)).
A329046 (program): a(n) = A000005(A324886(n)).
A329047 (program): a(n) = A003415(A324886(n)).
A329049 (program): Transpose of square array A329050.
A329050 (program): Square array A(n,k) = prime(n+1)^(2^k), read by descending antidiagonals (0,0), (0,1), (1,0), (0,2), (1,1), (2,0), …; Fermi-Dirac primes (A050376) in matrix form, sorted into rows by their prime divisor.
A329057 (program): 1-parking triangle T(r, i, 1) read by rows: T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i) with k = 1 and 0 <= i <= r.
A329058 (program): 2-parking triangle T(r, i, 2) read by rows: T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i) with k = 2 and 0 <= i <= r.
A329059 (program): 3-parking triangle T(r, i, 3) read by rows: T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i) with k = 3 and 0 <= i <= r.
A329060 (program): 4-parking triangle T(r, i, 4) read by rows: T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i) with k = 4 and 0 <= i <= r.
A329069 (program): Expansion of Product_{k>=1} 1 / (1 + mu(k)^2 * x^k).
A329071 (program): a(n) = phi(A275314(n)) - mu(A275314(n)), where A275314(n) is Euler’s gradus function.
A329095 (program): Odd numbers k such that x^2 == 2 (mod k) has no solution.
A329096 (program): Row sums of A329057.
A329098 (program): Expansion of 1 / (1 + Sum_{p prime, k>=1} x^(p^k)).
A329099 (program): Expansion of 1 / (1 + Sum_{k>=1} mu(k)^2 * x^k).
A329110 (program): Number of integer sequences 1 <= b_1 < b_2 < … < b_t <= n such that b_i divides b_(i+1) for all 0 < i < t.
A329113 (program): Row sums of A329058.
A329114 (program): a(n) = floor(A026532(n)/5).
A329115 (program): a(n) = floor(A026549(n)/5).
A329116 (program): Successively count to (-1)^(n+1)*n (n = 0, 1, 2, … ).
A329119 (program): Orders of the finite groups SL_2(K) when K is a finite field with q = A246655(n) elements.
A329123 (program): Row sums of A329060.
A329130 (program): a(0)=0; for any n >= 0, if a(n) > n then a(n+1) = a(n) - n, otherwise a(n+1) = a(n) + k, where k is the total number of terms a(m) <= m with m <= n.
A329138 (program): Numbers whose prime signature is a necklace.
A329139 (program): Numbers whose prime signature is an aperiodic word.
A329140 (program): Numbers whose prime signature is a periodic word.
A329145 (program): Number of non-necklace compositions of n.
A329146 (program): Triangle read by rows: T(n,k) is the number of subsets of {1,…,n} such that the difference between any two elements is k or greater, 1 <= k <= n.
A329152 (program): a(n) = Sum_{i=1..n-1} Sum_{j=1..i-1} [1 == i*j (mod n)], where [] is the Iverson bracket.
A329153 (program): Sum of the iterated unitary totient function (A047994).
A329154 (program): Coefficients of polynomials related to the sum of Gaussian binomial coefficients for q = 2. Triangle read by row, T(n,k) for 0 <= k <= n.
A329162 (program): a(n) = Sum_{k<n} ((2^n-1) mod (2^k-1)).
A329170 (program): Numbers of the form k^2 + 2 that are the sums of two squares.
A329178 (program): Sum of the products of pairs of Padovan numbers which are two apart, starting from A000931(5).
A329185 (program): Number of ways to tile a 2 X n grid with dominoes and L-trominoes such that no four tiles meet at a corner.
A329191 (program): The prime divisors of the orders of the sporadic finite simple groups.
A329193 (program): a(n) = floor(log_2(n^3)) = floor(3 log_2(n))
A329194 (program): a(n) = floor(log_3(n^2)) = floor(2 log_3(n))
A329195 (program): a(n) = floor(log_5(n^2)) = floor(2 log_5(n))
A329199 (program): a(n) = round(log_3(n)).
A329202 (program): a(n) = floor(2*log_2(n)) = floor(log_2(n^2)).
A329207 (program): Decimal expansion of the fundamental frequency of the note C4 (middle C) in Hertz.
A329208 (program): Decimal expansion of the fundamental frequency of the note C#4/Db4 in hertz.
A329210 (program): Decimal expansion of the fundamental frequency of the note D#4/Eb4 in hertz.
A329212 (program): Decimal expansion of the fundamental frequency of the note F4 in hertz.
A329213 (program): Decimal expansion of the fundamental frequency of the note F#4/Gb4 in hertz.
A329216 (program): Decimal expansion of 2^(5/12).
A329219 (program): Decimal expansion of 2^(10/12) = 2^(5/6).
A329220 (program): Decimal expansion of 2^(11/12).
A329221 (program): a(0)=0. If a(n)=k is the first occurrence of k then a(n+1)=a(k), otherwise a(n+1)=n-m where m is the index of the greatest prior term.
A329227 (program): Products of consecutive terms of the Padovan sequence A000931.
A329244 (program): Sum of every third term of the Padovan sequence A000931.
A329249 (program): Starting from n: as long as the decimal representation starts with an odd number, multiply the largest such prefix by 2; a(n) corresponds to the final value.
A329269 (program): Integers k such that 8*k + 1 is a prime or a square.
A329273 (program): a(1)=1. If n is prime, a(n)=0; if not, a(n) = (the smallest prime number greater than n) minus (the largest prime number smaller than n) minus 1.
A329274 (program): Expansion of 1 / (1 + Sum_{k>=1} phi(k) * log(1 - 2 * x^k) / k), where phi = A000010.
A329275 (program): Expansion of 1 / (1 + Sum_{k>=1} mu(k) * log(1 - 2 * x^k) / k), where mu = A008683.
A329277 (program): a(n) is the fixed point reached by iterating Euler’s gradus function A275314 starting at n.
A329278 (program): Irregular table read by rows. The n-th row is the permutation of {0, 1, 2, …, 2^n-1} given by T(n,k) = k(k+1)/2 (mod 2^n).
A329279 (program): Number of distinct tilings of a 2n X 2n square with 1 x n polyominoes.
A329289 (program): G.f.: (1 + x) * (1 + x^2) * Product_{k>=1} (1 + x^k).
A329290 (program): Number of ordered triples (i, j, k) of integers such that n = i^2 + 4*j^2 + 4*k^2.
A329293 (program): Number of positive integers k such that A002805(k) is not divisible by n, or a(n) = 0 if there are infinitely many such numbers.
A329301 (program): a(0) = a(1) = a(2) = 1; thereafter a(n) = a(n-1) - (-1)^n*a(n-2) + 2*a(n-3).
A329304 (program): Numerators of convergents to A309930, the constant whose continued fraction representation consists of the cubes, [0; 1, 8, 27, 64, …].
A329305 (program): Denominators of convergents to A309930, the constant whose continued fraction representation consists of the cubes, [0; 1, 8, 27, 64, …].
A329320 (program): a(n) = Sum_{k=0..floor(log_2(n))} 1 - A035263(1 + floor(n/2^k)).
A329321 (program): a(n) is the total number of odd parts in all partitions of n into consecutive parts.
A329322 (program): a(n) is the total number of even parts in all partitions of n into consecutive parts.
A329323 (program): Triangle read by rows: T(n,k) is the sum of the parts congruent to 0 mod k in the partitions of n into equal parts, 1 <= k <= n.
A329332 (program): Table of powers of squarefree numbers, powers of A019565(n) in increasing order in row n. Square array A(n,k) n >= 0, k >= 0 read by descending antidiagonals.
A329344 (program): Number of times most frequent primorial is present in the greedy sum of primorials adding to A108951(n).
A329347 (program): Dirichlet convolution of the identity function with bigomega.
A329348 (program): The least significant nonzero digit in the primorial base expansion of primorial inflation of n, A108951(n).
A329349 (program): Number of occurrences of the largest primorial present in the greedy sum of primorials adding to A108951(n).
A329354 (program): a(n) = Sum_{d|n} d*omega(d).
A329355 (program): The binary expansion of a(n) is the second through n-th terms of A000002 - 1.
A329356 (program): The binary expansion of a(n) is the first n terms of 2 - A000002.
A329360 (program): The decimal expansion of a(n) is the first n terms of A000002.
A329361 (program): a(n) = Sum_{i = 1..n} 2^(n - i) * A000002(i).
A329375 (program): a(n) = Sum_{d|n, d<n} d*omega(d).
A329376 (program): Multiplicative with a(p^e) = p when e == 2, otherwise a(p^e) = 1.
A329377 (program): Number of iterations done when n is divided by its divisors starting from the smallest one in increasing order until one no longer gets an integer, or until divisors are exhausted.
A329379 (program): a(n) = n/A093411(n), where A093411(n) is obtained by repeatedly dividing n by the largest factorial that divides it until an odd number is reached.
A329382 (program): Product of exponents of prime factors of A108951(n), where A108951 is fully multiplicative with a(prime(i)) = prime(i)# = Product_{i=1..i} A000040(i).
A329384 (program): G.f.: (1 + x) * (1 + x^2) * (1 + x^3) * Product_{k>=1} (1 + x^k).
A329393 (program): Number of odd divisors minus number of even divisors of the n-th composite.
A329398 (program): Number of compositions of n with uniform Lyndon factorization and uniform co-Lyndon factorization.
A329402 (program): Number of rectangles (w X h, w <= h) with integer side lengths w and h having area = n * perimeter.
A329404 (program): Interleave 2*n*(3*n-1), (2*n+1)*(6*n+1) for n >= 0.
A329422 (program): Maximum length of a binary n-similar word.
A329434 (program): Expansion of Sum_{k>=1} (-1 + Product_{j>=1} (1 + x^(k*(2*j - 1)))).
A329435 (program): Expansion of Sum_{k>=1} (-1 + Product_{j>=2} 1 / (1 - x^(k*j))).
A329436 (program): Expansion of Sum_{k>=1} (-1 + Product_{j>=2} (1 + x^(k*j))).
A329437 (program): Expansion of Sum_{k>=1} (-1 + Product_{j>=1} 1 / (1 - x^(k*prime(j)))).
A329438 (program): Expansion of Sum_{k>=1} (-1 + Product_{j>=1} (1 + x^(k*prime(j)))).
A329439 (program): Expansion of Sum_{k>=1} (-1 + Product_{j>=1} 1 / (1 - x^(k*j^2))).
A329444 (program): The sixth moments of the squared binomial coefficients; a(n) = Sum_{m=0..n} m^6*binomial(n, m)^2.
A329445 (program): Dirichlet inverse of A328745.
A329451 (program): Maximum number of pieces that can be captured during one move on an n X n board according to the international draughts capture rules.
A329465 (program): Expansion of Sum_{k>=1} (-1 + Product_{j>=1} 1 / (1 - x^(k*j*(j + 1)/2))).
A329469 (program): Perfectly cyclic numbers: numbers k such that the iterations of the mapping x -> f(x) = x^2 + c (mod k), starting at x = f(c), is purely periodic for all 0 <= c <= k.
A329470 (program): a(n) = 2 a(n-1)^2 + 1 for n >=2 , where a(0) = 1, a(1) = 1.
A329472 (program): Partial sums of numbers that are not squarefree.
A329474 (program): a(n) = log_2(A110428(n)). Also, a(n) = a(n-1) + a(m) for n >= 3, where m = 2^(p+1) + 2 - n and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 0 and a(2) = 1.
A329480 (program): a(n) = (1 - A075677(n))/6 if 6|(A075677(n)-1) or a(n) = (A075677(n) + 1)/6 if 6|(A075677(n)+1).
A329482 (program): Interleave 1 - n + 3*n^2, 1 + 3*n*(1+n) for n >= 0.
A329484 (program): Dirichlet convolution of the Louiville function with itself.
A329486 (program): a(n) = 3*A006519(n)/2 + n/2 where A006519(n) is the highest power of 2 dividing n.
A329488 (program): a(n) = A001350(n)^4.
A329491 (program): Dirichlet g.f.: Sum_{n>=0} a(n+1)/(1+10n)^s = Product ((1+p^(-s))/(1-p^(-s))) (p==1 mod 5).
A329494 (program): Numerator of 2*(2*n+1)/(n+2).
A329500 (program): Coordination sequence for 1-skeleton of truncated icosahedron or “Buckyball”.
A329502 (program): G.f. = (1+x)*(1+2*x)/(1-x).
A329503 (program): G.f. = (1+x)*(1+2*x+2*x^2)/(1-x).
A329505 (program): Expansion of (1 + x)*(1 + 2*x - x^2) / (1 - x).
A329506 (program): Expansion of (1 + x)*(1 + 2*x + 2*x^2 - 2*x^3) / (1 - x).
A329507 (program): Expansion of (1 + x)*(1 + 2*x + 2*x^2 + 2*x^3 - 3*x^4) / (1 - x).
A329509 (program): Expansion of (1 + x)*(1 + x + x^2 - x^3) / (1 - x).
A329510 (program): Expansion of (1 + x)*(1 + x + x^2)*(1 + x^2 - x^3) / (1 - x).
A329511 (program): Expansion of (1 + x)*(1 + x^2)^2*(1 + x - x^3) / (1 - x).
A329513 (program): G.f. = (1+x)^2*(1+2*x^2-x^3)/(1-x).
A329514 (program): Expansion of g.f.: (2*x^5-3*x^4+x^3-2*x^2-1)*(1+x)^2/(x-1).
A329516 (program): Expansion of (x^4 - x^3 - 3*x^2 - 2*x - 1)/(x - 1).
A329517 (program): Expansion of (2*x^6 - 3*x^4 - 3*x^3 - 3*x^2 - 2*x - 1)/(x - 1).
A329521 (program): The sixth moments of the alternated squared binomial coefficients; a(n) = Sum_{m=0..n} (-1)^m*m^6*binomial(n, m)^2.
A329523 (program): a(n) = n * (binomial(n + 1, 3) + 1).
A329530 (program): a(n) = n * (7*binomial(n, 2) + 1).
A329531 (program): Number of primes between squares of successive even numbers.
A329533 (program): First differences of A051924, or second differences of Central binomial coefficients A000984.
A329547 (program): Number of natural numbers k <= n such that k^k is a square.
A329549 (program): Numbers 4*k such that 1 is the last integer obtained when 4*k is successively divided by its divisors in increasing order.
A329550 (program): Total number of consecutive triples of the form (odd, even, odd) or (even, odd, even) in all permutations of [n].
A329558 (program): Product of primes indexed by the first n squarefree numbers.
A329562 (program): a(n) = 2^(sum of digits of n).
A329570 (program): a(n) is the least prime P such that log(P)/log(p) >= valuation(n,p) for all primes p.
A329571 (program): a(n) = Product_{prime p} p^floor(log_p P) with P = A329570(n) the least prime with log_p P >= valuation(n,p) for all primes p.
A329575 (program): Numbers whose smallest Fermi-Dirac factor is 3.
A329583 (program): Numerators of 1 + n^2/4 + period 3: repeat [-1, 1, 1].
A329584 (program): phi(A327922(n))/4, for n >= 1, with phi = A000010 (Euler’s totient).
A329586 (program): Row lengths of A329585: number of solutions of the congruences x^2 == +1 (mod n) or (inclusive) x^2 == -1 (mod n), for n >= 1.
A329591 (program): Decimal expansion of sqrt(34 + 2*sqrt(17))/4 = sqrt(8 + A222132)/2.
A329593 (program): a(n) = (2^(A003558(n)) - A332433(n))/(2*n+1), for n >= 0.
A329598 (program): Partial sums of the nontriangular numbers (A014132).
A329600 (program): Smallest number with the same set of distinct prime exponents as A108951(n).
A329601 (program): The squarefree kernel of Product prime(e(i)), when n = Product prime(i)^e(i).
A329605 (program): Number of divisors of A108951(n), where A108951 is fully multiplicative with a(prime(i)) = prime(i)# = Product_{i=1..i} A000040(i).
A329607 (program): a(n) = A007947(A122111(n)).
A329612 (program): a(n) = gcd(d(n), d(A108951(n))), where d(n) gives the number of divisors of n, A000005(n), and A108951 is fully multiplicative with a(prime(i)) = prime(i)# = prime(1) * … * prime(i).
A329614 (program): Smallest prime factor of the number of divisors of A108951(n).
A329617 (program): Product of distinct exponents of prime factors of A108951(n), where A108951 is fully multiplicative with a(prime(i)) = prime(i)# = Product_{i=1..i} A000040(i).
A329618 (program): a(n) = gcd(A001222(n), A324888(n)), where A324888(n) is the minimal number of primorials (A002110) that add to A108951(n).
A329619 (program): Difference between the maximal digit value used when A108951(n) is written in primorial base and its 2-adic valuation.
A329621 (program): a(n) = gcd(A056239(n), A324888(n)) = gcd(A001222(A108951(n)), A001222(A324886(n))).
A329622 (program): a(n) = A056239(n) - A324888(n) = A001222(A108951(n)) - A001222(A324886(n)).
A329624 (program): Number of iterations of A329623 for starting value n before a repeated value appears, or -1 if this never happens.
A329625 (program): Smallest BII-number of a connected set-system with n edges.
A329655 (program): Square array read by antidiagonals: T(n,k) is the number of relations between set A with n elements and set B with k elements that are both right unique and left unique.
A329664 (program): Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UD, HH and DU.
A329670 (program): Number of excursions of length n with Motzkin-steps allowing only consecutive steps UH and HD.
A329671 (program): Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UU, HH and DD.
A329672 (program): Number of meanders of length n with Motzkin-steps avoiding the consecutive steps UU.
A329673 (program): Number of meanders of length n with Motzkin-steps avoiding the consecutive steps HH.
A329674 (program): Number of meanders of length n with Motzkin-steps avoiding the consecutive steps DD.
A329677 (program): Number of excursions of length n with Motzkin-steps consisting only of consecutive steps UH, HD, and DH.
A329678 (program): Number of excursions of length n with Motzkin-steps consisting only of consecutive steps UD and DH.
A329679 (program): Number of excursions of length n with Motzkin-steps consisting only of consecutive steps UH, UD, HD and DH.
A329680 (program): Number of excursions of length n with Motzkin-steps consisting only of consecutive steps UH, HD and DU.
A329682 (program): Number of excursions of length n with Motzkin-steps forbidding all consecutive steps of length 2 except UH, UD, HU and DD.
A329683 (program): Number of excursions of length n with Motzkin-steps forbidding all consecutive steps of length 2 except UH, HH and HD.
A329684 (program): Number of excursions of length n with Motzkin-steps forbidding all consecutive steps of length 2 except UD and HH.
A329686 (program): Number of excursions of length n with Motzkin-steps forbidding all consecutive steps of length 2 except UH, HU, HD and DH.
A329687 (program): Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UU, UD, HH and DH.
A329688 (program): Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UU, HH, HD and DU.
A329689 (program): Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UU, UD, HH and DU.
A329690 (program): Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UU, HH, DU and DD.
A329691 (program): Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UD, HU, HH and DH.
A329694 (program): Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UU, HH and DU.
A329696 (program): Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UH, HU, HD and DH.
A329697 (program): a(n) is the number of iterations needed to reach a power of 2 starting at n and using the map k -> k-(k/p), where p is the largest prime factor of k.
A329699 (program): Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UH, HU and HH.
A329700 (program): Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UH, HH and HD.
A329707 (program): Number of placements of zero or more dominoes on a 2 X n grid where no two empty squares are horizontally adjacent.
A329717 (program): a(n) is n (plus or minus) the number of distinct primes dividing n according to parity (even or odd).
A329723 (program): Coefficients of expansion of (1-2x^3)/(1-x-x^2) in powers of x.
A329725 (program): a(1)=0, a(n) = n - (product of nonzero digits of n) - a(n-1).
A329728 (program): Partial sums of A092261.
A329752 (program): a(0) = 0, a(n) = a(floor(n/2)) + (n mod 2) * floor(log_2(2n))^2 for n > 0.
A329753 (program): Doubly square pyramidal numbers.
A329754 (program): Doubly pentagonal pyramidal numbers.
A329755 (program): Doubly hexagonal pyramidal numbers.
A329756 (program): Doubly heptagonal pyramidal numbers.
A329757 (program): Doubly octagonal pyramidal numbers.
A329761 (program): Primes whose product of decimal digits is a power of 3.
A329771 (program): G.f. = (3*x^8 + x^7 - 3*x^6 - 3*x^5 - 3*x^4 - 3*x^3 - 3*x^2 - 2*x - 1)/(x - 1).
A329774 (program): a(n) = n+1 for n <= 2; otherwise a(n) = 3*a(n-3)+1.
A329783 (program): Numbers that are either +-2 (mod 5) or +-11 (mod 55).
A329784 (program): Numbers that are either +-1 (mod 5) or +-22 (mod 55).
A329791 (program): a(n) = floor(sqrt(2)*n) + floor(sqrt(3)*n).
A329801 (program): Expansion of Sum_{k>=1} x^(k*(k + 1)/2) / (1 + x^(k*(k + 1)/2)).
A329822 (program): The minimum weight of a Boolean function of algebraic degree at most n-3 whose support contains n linearly independent elements.
A329825 (program): Beatty sequence for (3+sqrt(17))/4.
A329826 (program): Beatty sequence for (5+sqrt(17))/4.
A329827 (program): Beatty sequence for (5+sqrt(37))/6.
A329828 (program): Beatty sequence for (7+sqrt(37))/6.
A329829 (program): Beatty sequence for (2+sqrt(10))/3.
A329830 (program): Beatty sequence for (4+sqrt(10))/3.
A329831 (program): Beatty sequence for (7+sqrt(65))/8.
A329832 (program): Beatty sequence for (9+sqrt(65))/8.
A329833 (program): Beatty sequence for (5+sqrt(73))/8.
A329834 (program): Beatty sequence for (11+sqrt(73))/8.
A329835 (program): Beatty sequence for (9+sqrt(101))/10.
A329836 (program): Beatty sequence for (11+sqrt(101))/10.
A329837 (program): Beatty sequence for (4+sqrt(26))/5.
A329838 (program): Beatty sequence for (6+sqrt(26))/5.
A329839 (program): Beatty sequence for (-1+sqrt(41))/4.
A329840 (program): Beatty sequence for (9+sqrt(41))/4.
A329841 (program): Beatty sequence for (7+sqrt(109))/10.
A329842 (program): Beatty sequence for (13+sqrt(109))/10.
A329843 (program): Beatty sequence for (1+sqrt(61))/6.
A329844 (program): Beatty sequence for (11+sqrt(61))/6.
A329845 (program): Beatty sequence for (3+sqrt(29))/5.
A329846 (program): Beatty sequence for (7+sqrt(29))/5.
A329847 (program): Beatty sequence for (3+sqrt(89))/8.
A329848 (program): Beatty sequence for (13+sqrt(89))/8.
A329854 (program): Triangle read by rows: T(n,k) = ((n - k)*(n + k - 1) + 2)/2, 0 <= k <= n.
A329886 (program): Primorial inflation of Doudna-tree: a(0) = 1, a(1) = 2; for n > 1, if n is even, a(n) = A283980(a(n/2)), and if n is odd, then a(n) = 2*a((n-1)/2).
A329887 (program): a(0) = 1, a(1) = 2; for n > 1, if n is even, then a(n) = 2*a(n/2), and if n is odd, a(n) = A283980(a((n-1)/2)).
A329888 (program): a(n) = A329900(A329602(n)); Heinz number of the even bisection (even-indexed parts) of the integer partition with Heinz number n.
A329893 (program): Product_{k=0..floor(log_2(n))} (1 + A004718(floor(n/(2^k)))), where A004718 is Per Nørgård’s “infinity sequence”.
A329900 (program): Primorial deflation of n: starting from x = n, repeatedly divide x by the largest primorial A002110(k) that divides it, until x is an odd number. Then a(n) = Product prime(k_i), for primorial indices k_1 >= k_2 >= …, encountered in the process.
A329903 (program): a(n) = A156552(n) mod 3.
A329908 (program): Number of oriented rational links with crossing number n.
A329913 (program): The fifth moments of the squared binomial coefficients; a(n) = Sum_{m=0..n} m^5*binomial(n, m)^2.
A329914 (program): Numbers k such that there exist numbers M_k which, when 1 is placed at both ends of M_k, the number M_k is multiplied by k.
A329918 (program): Coefficients of orthogonal polynomials related to the Jacobsthal numbers A152046, triangle read by rows, T(n, k) for 0 <= k <= n.
A329923 (program): Beatty sequence for (2+sqrt(34))/5.
A329924 (program): Beatty sequence for (8+sqrt(34))/5.
A329925 (program): Beatty sequence for (1+sqrt(41))/5.
A329926 (program): Beatty sequence for (9+sqrt(41))/5.
A329928 (program): a(n) = (Pi/2)*(2*n+1)!*binomial(2*n+1, (2*n+1)/2).
A329930 (program): a(n) = n!^2*(Sum_{k=1..n} 1/k).
A329938 (program): Beatty sequence for sinh x, where csch x + sech x = 1 .
A329939 (program): Beatty sequence for cosh x, where csch x + sech x = 1 .
A329940 (program): Square array read by antidiagonals upwards: T(n,k) is the number of right unique relations between set A with n elements and set B with k elements.
A329943 (program): Square array read by antidiagonals: T(n,k) is the number of right total relations between set A with n elements and set B with k elements.
A329944 (program): Number of permutations of [n] whose cycle lengths avoid primes.
A329945 (program): Number of permutations of [n] whose cycle lengths avoid squares.
A329949 (program): Lexicographically earliest sequence of positive numbers such that following proposition is true: a(n) is the number of occurrences of a(n+1) in the sequence so far, up to and including a(n+1).
A329952 (program): Numbers k such that binomial(k,3) is divisible by 8.
A329958 (program): Expansion of q^(-13/24) * eta(q^2)^3 * eta(q^3) * eta(q^6) / eta(q)^2 in powers of q.
A329961 (program): Beatty sequence for 2 + sin x, where x = least positive solution of 1/(2 + sin x) + 1/(2 + cos x) = 1.
A329962 (program): Beatty sequence for 2 + cos x, where x = least positive solution of 1/(2 + sin x) + 1/(2 + cos x) = 1.
A329963 (program): Numbers k such that sigma(k) is not divisible by 3.
A329964 (program): a(n) = (n!/floor(1+n/2)!)^2.
A329965 (program): a(n) = ((1+n)*floor(1+n/2))*(n!/floor(1+n/2)!)^2.
A329966 (program): a(n) = n! * Sum_{d|n} binomial(n-1,d-1) / d!.
A329970 (program): a(n) = (-1)^(n + 1) * n * ceiling(n/2) + Sum_{k=1..n} (-1)^k * k^2 * floor(n/k).
A329971 (program): Expansion of 1 / (1 - 2 * Sum_{k>=1} x^(k^2)).
A329974 (program): Beatty sequence for the real solution x of 1/x + 1/(1+x+x^2) = 1.
A329975 (program): Beatty sequence for 1 + x + x^2, where x is the real solution of 1/x + 1/(1+x+x^2) = 1.
A329977 (program): Beatty sequence for the number x satisfying 1/x + 1/(log x) = 1.
A329978 (program): Beatty sequence for log x, where 1/x + 1/(log x) = 1.
A329987 (program): Beatty sequence for the number x satisfying 1/x + 1/2^x = 1.
A329988 (program): Beatty sequence for 2^x, where 1/x + 1/2^x = 1.
A329990 (program): Beatty sequence for the number x satisfying 1/x + 1/3^x = 1.
A329991 (program): Beatty sequence for 3^x, where 1/x + 1/3^x = 1.
A329993 (program): Beatty sequence for x^2, where 1/x^2 + 1/2^x = 1.
A329994 (program): Beatty sequence for 2^x, where 1/x^2 + 1/2^x = 1.
A329996 (program): Beatty sequence for x^3, where 1/x^3 + 1/3^x = 1.
A329997 (program): Beatty sequence for 3^x, where 1/x^3 + 1/3^x = 1.
A329998 (program): Decimal expansion of the solution of 1/sqrt(x-1) + 1/sqrt(x+1) = 1.
A329999 (program): Beatty sequence for sqrt(x-1), where 1/sqrt(x-1) + 1/sqrt(x+1) = 1.
A330000 (program): Beatty sequence for sqrt(x+1), where 1/sqrt(x-1) + 1/sqrt(x+1) = 1.
A330002 (program): Beatty sequence for x, where 1/x + 1/(x+1)^2 = 1.
A330003 (program): Beatty sequence for (x+1)^2, where 1/x + 1/(x+1)^2 = 1.
A330010 (program): Number of length-n ternary strings x with the property that if w is a subword of x and |w| >= 3, then w reversed is not a subword of x.
A330016 (program): a(n) = Sum_{k=1..n} (-1)^(n - k) * H(k) * k!, where H(k) is the k-th harmonic number.
A330018 (program): a(n) = Sum_{d|n} (bigomega(d) - omega(d)).
A330020 (program): Expansion of e.g.f. Sum_{k>=1} x^k / (k! * (1 - x^k)^k).
A330023 (program): a(n) counts the cube-words immediately before a(n), with a(1) = 0.
A330025 (program): a(n) = (-1)^floor(n/5) * sign(mod(n, 5)).
A330030 (program): Least k such that Sum_{i=0..n} k^n / i! is a positive integer.
A330033 (program): a(n) = Kronecker(n, 5) * (-1)^floor(n/5).
A330034 (program): a(n) = sign(cos(n)).
A330035 (program): a(n) = sign(tan(n)).
A330037 (program): The sum of digits function modulo 2 of the natural numbers in base phi.
A330038 (program): a(1) = 1, a(n) = [n/2] + a([n/2]) + a([(n+1)/2]) for n > 1, where [x] = floor(x).
A330043 (program): Product of largest prime power factors of numbers <= n.
A330044 (program): Expansion of e.g.f. exp(x) / (1 - x^3).
A330045 (program): Expansion of e.g.f. exp(x) / (1 - x^4).
A330046 (program): Expansion of e.g.f. exp(x) / (1 - sinh(x)).
A330047 (program): Expansion of e.g.f. exp(-x) / (1 - sinh(x)).
A330050 (program): a(n) = 2*((-1)^n - 1)*(F(n) - 1) - (3*(-1)^n + 7)/2 * F(n+1) + 5*F(n+1)^2.
A330051 (program): a(n) = 1 + F(2*n+1) - (F(n+4) - (-1)^n*F(n-2))/2 where F=A000045.
A330055 (program): Number of non-isomorphic set-systems of weight n with no singletons or endpoints.
A330063 (program): Beatty sequence for x, where 1/x + sech(x) = 1.
A330064 (program): Beatty sequence for cosh(x), where 1/x + sech(x) = 1.
A330066 (program): Beatty sequence for x, where 1/x + csch(x) = 1.
A330067 (program): Beatty sequence for sinh(x), where 1/x + 1/sinh(x) = 1.
A330072 (program): a(n) is the sum of all integers whose binary representation is contained in the binary representation of n (with multiplicity).
A330081 (program): If the binary expansion of n is (b(1), …, b(w)), then the binary expansion of a(n) is (b(1), b(3), b(5), …, b(6), b(4), b(2)).
A330082 (program): a(n) = 5*A064038(n).
A330085 (program): Length of longest binary word with the property that all distinct occurrences of identical-length blocks agree on at most n positions.
A330087 (program): Permanent of a square matrix M(n) whose general element M_{i,j} is defined by i*prime(j).
A330094 (program): Beatty sequence for 2^x, where 1/2^x + 1/3^(x-1) = 1.
A330095 (program): Beatty sequence for 3^(x-1), where 1/2^x + 1/3^(x-1) = 1.
A330112 (program): Beatty sequence for e^x, where 1/e^x + sech(x) = 1.
A330113 (program): Beatty sequence for cosh(x), where 1/e^x + sech(x) = 1.
A330115 (program): Beatty sequence for e^x, where 1/e^x + csch(x) = 1.
A330116 (program): Beatty sequence for sinh(x), where 1/e^x + csch(x) = 1.
A330117 (program): Beatty sequence for 1+x, where 1/(1+x) + 1/(1+x+x^2) = 1.
A330118 (program): Beatty sequence for 1+x+x^2, where 1/(1+x) + 1/(1+x+x^2) = 1.
A330133 (program): a(n) = (1/16)*(5 + (-1)^(1+n) - 4*cos(n*Pi/2) + 10*n^2).
A330136 (program): Numbers m such that 1 < gcd(m, 6) < m and m does not divide 6^e for e >= 0.
A330137 (program): Numbers m such that 1 < gcd(m, 30) < m and m does not divide 30^e for e >= 0.
A330139 (program): a(1)=1 and a(2)=1; if a(n-1)+a(n-2) == 0 mod n then a(n) = (a(n-1)+a(n-2))/n else a(n) = a(n-1)+a(n-2).
A330143 (program): Beatty sequence for (3/2)^x, where (3/2)^x + (5/2)^x = 1.
A330144 (program): Beatty sequence for (5/2)^x, where (3/2)^x + (5/2)^x = 1.
A330149 (program): Expansion of e.g.f. exp(-x) / (1 + log(1 - x)).
A330150 (program): Expansion of e.g.f. exp(-x) / (1 - log(1 + x)).
A330151 (program): Partial sums of 4th powers of the even numbers.
A330156 (program): Decimal expansion of the continued fraction expansion [1; 1/2, 1/3, 1/4, 1/5, 1/6, …].
A330167 (program): Length of the longest run of 1’s in the ternary expression of n.
A330168 (program): Length of the longest run of 2’s in the ternary expression of n.
A330169 (program): a(n) is the total area of all closed Deutsch paths of length n.
A330170 (program): a(n) = 2^n + 3^n + 6^n - 1.
A330171 (program): a(n) = n + floor(ns/r) + floor(nt/r), where r = sqrt(2) - 1, s = sqrt(2), t = sqrt(2) + 1.
A330172 (program): a(n) = n + floor(nr/t) + floor(ns/t), where r = sqrt(2) - 1, s = sqrt(2), t = sqrt(2) + 1.
A330173 (program): a(n) = n + floor(ns/r) + floor(nt/r), where r = sqrt(2), s = sqrt(2) + 1, t = sqrt(2) + 2.
A330174 (program): Number of primitive Pythagorean triangles with sum of legs n.
A330175 (program): a(n) = n + floor(ns/r) + floor(nt/r), where r = sqrt(5) - 2, s = sqrt(5) - 1, t = sqrt(5).
A330176 (program): a(n) = n + floor(nr/t) + floor(ns/t), where r = sqrt(5) - 2, s = sqrt(5) - 1, t = sqrt(5).
A330177 (program): a(n) = n + floor(ns/r) + floor(nt/r), where r = e - 2, s = e - 1, t = e.
A330178 (program): a(n) = n + floor(nr/t) + floor(ns/t), where r = e - 2, s = e - 1, t = e.
A330179 (program): a(n) = n + floor(ns/r) + floor(nt/r), where r = e - 1, s = e, t = e + 1.
A330180 (program): a(n) = n + floor(nr/t) + floor(ns/t), where r = e - 1, s = e, t = e + 1.
A330181 (program): a(n) = n + floor(ns/r) + floor(nt/r), where r = Pi - 1, s = Pi, t = Pi + 1.
A330182 (program): a(n) = n + floor(nr/t) + floor(ns/t), where r = Pi - 1, s = Pi, t = Pi + 1.
A330183 (program): a(n) = n + floor(ns/r) + floor(nt/r), where r = sqrt(2) - 1/2, s = sqrt(2), t = sqrt(2) + 1/2.
A330184 (program): a(n) = n + floor(nr/t) + floor(ns/t), where r = sqrt(2) - 1/2, s = sqrt(2), t = sqrt(2) + 1/2.
A330185 (program): a(n) = n + floor(ns/r) + floor(nt/r), where r = tau - 1/2, s = tau, t = tau + 1/2, tau = golden ratio = (1+sqrt(5))/2.
A330186 (program): a(n) = n + floor(nr/t) + floor(ns/t), where r = tau - 1/2, s = tau, t = tau + 1/2, tau = golden ratio = (1+sqrt(5))/2.
A330197 (program): Number of scalene triangles whose vertices are the vertices of a regular n-gon.
A330200 (program): Expansion of e.g.f. Product_{k>=1} exp(x^k) / (1 - x^k).
A330201 (program): Expansion of e.g.f. Product_{k>=1} exp(-x^k) / (1 - x^k).
A330210 (program): Numbers that can be expressed as the sum of 2 prime numbers in a prime number of different ways.
A330225 (program): Position of first appearance of n in A290103 = LCM of prime indices.
A330239 (program): Minimum circular (strong) similarity of a length-n binary word.
A330241 (program): a(n) is the greatest k such that there is an increasing sequence of positive integers j(0),j(1),…,j(k) such that n == i (mod j(i)) for each i.
A330242 (program): Sum of largest emergent parts of the partitions of n.
A330243 (program): Numbers k such that the first digit of the decimal expansion of 2^k is 7.
A330246 (program): a(n) = 4^(n+1) + (4^n-1)/3.
A330248 (program): a(1) = 1; for n > 1, a(n) is the least nonnegative number such that a(n) + a(n-1) + n is a prime number.
A330254 (program): Expansion of e.g.f. Sum_{k>=1} sinh(x^k).
A330255 (program): Expansion of e.g.f. Sum_{k>=1} (cosh(x^k) - 1) (even powers only).
A330260 (program): a(n) = n! * Sum_{k=0..n} binomial(n,k) * n^(n - k) / k!.
A330279 (program): Numbers k such that x^k == k (mod k + 1) has multiple solutions for 0 <= x < k.
A330285 (program): The maximum number of arithmetic progressions in a sequence of length n.
A330298 (program): a(n) is the number of subsets of {1..n} that contain exactly 1 odd and 2 even numbers.
A330299 (program): a(n) is the number of subsets of {1..n} that contain exactly 1 odd and 3 even numbers.
A330300 (program): a(n) is the number of subsets of {1..n} that contain exactly 2 odd and 3 even numbers.
A330302 (program): Number of chains of 2-element subsets of {0,1, 2, …, n} that contain no consecutive integers.
A330312 (program): Gaps between palindromes in base 3: first differences of A014190.
A330315 (program): a(n) = r(n)*r(n+1), where r(n) = A004018(n) is the number of ways of writing n as a sum of two squares.
A330316 (program): a(n) = r(n)*r(n+1)/4, where r(n) = A004018(n) is the number of ways of writing n as a sum of two squares.
A330317 (program): a(n) = Sum_{i=0..n} r(i)*r(i+1), where r(n) = A004018(n) is the number of ways of writing n as a sum of two squares.
A330318 (program): a(n) = Sum_{i=0..n} r(i)*r(i+1)/4, where r(n) = A004018(n) is the number of ways of writing n as a sum of two squares.
A330319 (program): a(n) = Sum_{i=1..n} phi(i)*phi(i+1), where phi(n) = A000010(n) is Euler’s totient function.
A330320 (program): a(n) = Sum_{i=1..n} tau(i)*tau(i+1), where tau(n) = A000005(n) is the number of divisors of n.
A330321 (program): a(n) = Sum_{i=1..n} tau(i)*tau(i+1)/2, where tau(n) = A000005(n) is the number of divisors of n.
A330322 (program): a(n) = Sum_{i=1..n} sigma(i)*sigma(i+1), where sigma(n) = A000203(n) is the sum of the divisors of n.
A330323 (program): a(n) = Moebius(n)*Moebius(n+1).
A330324 (program): a(n) = Sum_{i=1..n} Moebius(i)*Moebius(i+1), where Moebius(n) = A008683(n).
A330349 (program): a(n) = A070826(n+1) - 2^(n-1).
A330357 (program): a(n) = (2*n^2 + 9 - (-1)^n)/4.
A330358 (program): a(n) = n mod 5 + n mod 25 + … + n mod 5^k, where 5^k <= n < 5^(k+1).
A330373 (program): Sum of all parts of all self-conjugate partitions of n.
A330381 (program): Triangle read by rows: T(n,k) is the number of ternary strings of length n with k indispensable digits, with 0 <= k <= n.
A330390 (program): G.f.: (1 + 15*x) / (1 - 2*x - 17*x^2).
A330393 (program): A 2-regular sequence whose reciprocal is not 2-regular.
A330395 (program): Number of nontrivial equivalence classes of S_n under the {1234,3412} pattern-replacement equivalence.
A330396 (program): Permutation of the nonnegative integers partitioned into triples [3*k+2, 3*k+1, 3*k] for k >= 0.
A330405 (program): a(1) = 0; thereafter a(n) = (a(n-1)^2+1) mod n.
A330407 (program): Number of ordered integer pairs (b,c) with -n <= b <= n and -n <= c <= n such that both roots of x^2 + b*x + c = 0 are distinct integers.
A330408 (program): Table of A(n,k) read by antidiagonals, where A(1,k)=k; A(n,k) is the least multiple of n >= A(n-1,k).
A330409 (program): Semiprimes of the form p(6p - 1).
A330410 (program): a(n) = 6*prime(n) - 1.
A330411 (program): a(n) is the index of the first 0 term in the rumor sequence with initial 0th term 1 and parameters b = 3 and n.
A330432 (program): Number of permutations sigma of [n] such that k * sigma(k) >= n for 1 <= k <= n.
A330436 (program): a(n) = n * n!! - Sum_{k=1..n-1} k!! * a(n-k).
A330451 (program): a(n) = a(n-3) + 20*n - 30 for n > 2, with a(0)=0, a(1)=3, a(2)=13.
A330476 (program): a(n) = Sum_{m=2..n} floor(n/m)^2.
A330479 (program): Decimal expansion of 2*e^2-2 (or 2*(e^2-1)).
A330492 (program): a(n) = sum of second differences of the sorted divisors of n.
A330497 (program): a(n) = n! * Sum_{k=0..n} (-1)^k * binomial(n,k) * n^(n - k) / k!.
A330500 (program): a(n) = a(n-1) + a(floor(n/3)), a(1) = a(2) = 1.
A330503 (program): Number of Sós permutations of {0,1,…,n}.
A330505 (program): Expansion of e.g.f. Sum_{k>=1} arctanh(x^k).
A330510 (program): Triangle read by rows: T(n,k) is the number of ternary strings of length n+1 with k+1 indispensable digits and a nonzero leading digit, with 0 <= k <= n.
A330511 (program): Expansion of e.g.f. Sum_{k>=1} arctan(x^k).
A330520 (program): Sum of even integers <= n times the sum of odd integers <= n.
A330527 (program): Expansion of e.g.f. Sum_{k>=1} (sec(x^k) + tan(x^k) - 1).
A330545 (program): a(1) = 2; thereafter a(n) = a(n-1) + (-1)^(n + 1)*(prime(n) - prime(n - 1) - 1) (where prime(k) denotes the k-th prime).
A330547 (program): a(1)=2; thereafter a(n) = a(n-1) + (-1)^(n+1)*(prime(n)-prime(n-1)) (where prime(k) denotes the k-th prime).
A330557 (program): a(n) = number of primes p <= 2*n+1 with Delta(p) == 2 mod 4, where Delta(p) = nextprime(p) - p.
A330559 (program): a(n) = (number of primes p <= prime(n) with Delta(p) == 2 mod 4) - (number of primes p <= prime(n) with Delta(p) == 0 mod 4), where Delta(p) = nextprime(p) - p.
A330560 (program): a(n) = number of primes p <= prime(n) with Delta(p) == 2 mod 4, where Delta(p) = nextprime(p) - p.
A330561 (program): a(n) = number of primes p <= prime(n) with Delta(p) == 0 mod 4, where Delta(p) = nextprime(p) - p.
A330565 (program): The thirteen entries from A005848 for which the integers of the cyclotomic field form a Euclidean ring with respect to the norm.
A330569 (program): a(n) = 1 if n is odd, otherwise a(n) = 2^(v-1)+1 where v is the 2-adic valuation of n (A007814(n)).
A330570 (program): Partial sums of A097988 (d_3(n)^2).
A330571 (program): Square of number of unordered factorizations of n as n = i*j.
A330573 (program): Sum_{k = 1 to floor(n/2)} [u_2(k)*u_2(n+1-k)], where u_2(k) is number of unordered factorization k = i*j (A038548).
A330574 (program): a(n) = r_2(n)^2*d(n+1), where r_2 = A004018, d = A000005.
A330575 (program): a(n) = n + Sum_{d|n and d<n} a(d) for n>1; a(1) = 1.
A330578 (program): a(n) is the remainder when the sum of the first n composite numbers is divided by the n-th composite number.
A330591 (program): Number of Collatz steps to reach 1 starting from 6^n + 1.
A330592 (program): a(n) is the number of subsets of {1,2,…,n} that contain exactly two odd numbers.
A330602 (program): a(n) = a(n-1) XOR (n+1), with a(0) = 0.
A330603 (program): a(n) = Sum_{k>=0} (k - n)^n / 2^(k + 1).
A330604 (program): a(n) = Sum_{k>=0} (n*k - 1)^n / 2^(k + 1).
A330609 (program): T(n, k) = binomial(n-k-1, k-1)*(n-k)!/k! for n >= 0 and 0 <= k <= floor(n/2). Irregular triangle read by rows.
A330613 (program): Triangle read by rows: T(n, k) = 1 + k - 2*n - 2*k*n + 2*n^2, with 0 <= k < n.
A330617 (program): Triangle read by rows: T(n,k) is the number of paths from node 0 to k in a directed graph with n+1 vertices labeled 0, 1, …, n and edges leading from i to i+1 for all i, and from i to i+2 for even i and from i to i-2 for odd i.
A330620 (program): Number of length n necklaces with entries covering an initial interval of positive integers and no adjacent entries equal.
A330638 (program): a(n) = P(n)*a(n-1) + a(n-2), with a(0) = 0, a(1) = 1 where P(n) is the n-th Pell number.
A330640 (program): a(n) is the number of partitions of n with Durfee square of size <= 2.
A330644 (program): Number of non-self-conjugate partitions of n.
A330651 (program): a(n) = n^4 + 3*n^3 + 2*n^2 - 2*n.
A330657 (program): Number of ways the n-th pentagonal number A000326(n) can be written as the difference of two positive pentagonal numbers.
A330669 (program): The prime indices of the prime powers (A000961).
A330700 (program): a(n) = (n - 1)*n*(2*n^2 + 4*n - 1)/6.
A330707 (program): a(n) = ( 3*n^2 + n - 1 + (-1)^floor(n/2) )/4.
A330709 (program): Two-column table read by rows: pairs (i,j) in order sorted from the left.
A330714 (program): For any n >= 0 with binary expansion Sum_{k=0..w} b_k * 2^k, let h(n) = Sum_{k=0..w} b_k * i^k (where i denotes the imaginary unit); a(n) is the square of the modulus of h(n).
A330715 (program): a(1), a(2), a(3) = 1; a(n) = (a(n-1) mod a(n-3)) + a(n-2) + 1.
A330717 (program): a(n) is the greatest binary palindrome of the form floor(n/2^k) with k >= 0.
A330718 (program): a(n) = numerator(Sum_{k=1..n} (2^k-2)/k).
A330719 (program): a(n) = denominator(Sum_{k=1..n} (2^(k-1) - 1)/k).
A330724 (program): Sum of prime factors (with multiplicity) of the n-th composite number coprime to 6.
A330740 (program): a(n) = min(n, A004488(n)), where A004488(n) is base-3 sum n+n without carries.
A330749 (program): a(n) = gcd(n, A064989(n)), where A064989 is fully multiplicative with a(2) = 1 and a(prime(k)) = prime(k-1) for odd primes.
A330761 (program): Array read by antidiagonals: T(n,k) is the number of faces on a ring formed by connecting the ends of a prismatic rod whose cross-section is an n-sided regular polygon after applying a twist of k/n turns.
A330767 (program): a(n) = 25*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 25.
A330769 (program): a(n) = Product_{k=n..2*n} prime(k).
A330770 (program): a(n) = 19 * 8^n + 17 for n >= 0.
A330786 (program): Number of steps to reach 1 by iterating the absolute alternating sum-of-divisors function (A206369).
A330793 (program): a(n) = A193737(2*n, n).
A330795 (program): Evaluation of the polynomials given by the Riordan square of the Fibonacci sequence with a(0) = 1 (A193737) at 1/2 and normalized with 2^n.
A330796 (program): a(n) = Sum_{k=0..n} binomial(n, k)*(2^k - binomial(k, floor(k/2)).
A330797 (program): Evaluation of the Stirling cycle polynomials at -1/2 and normalized with (-2)^n.
A330798 (program): Triangle read by rows, interpolating between the central binomial coefficients and the central coefficients of the Catalan triangle. T(n, k) for 0 <= k <= n.
A330799 (program): Evaluation of the Motzkin polynomials at 1/2 and normalized with 2^n.
A330800 (program): Evaluation of the Motzkin polynomials at -1/2 and normalized with (-2)^n.
A330801 (program): a(n) = A080247(2*n, n), the central values of the Big-Schröder triangle.
A330802 (program): Evaluation of the Big-Schröder polynomials at 1/2 and normalized with 2^n.
A330803 (program): Evaluation of the Big-Schröder polynomials at -1/2 and normalized with (-2)^n.
A330805 (program): Number of squares and rectangles in the interior of the square with vertices (n,0), (0,n), (-n,0) and (0,-n) in a square (x,y)-grid.
A330806 (program): a(1) = 1; a(2) = 1; for n >= 3, a(n) = a(n-1) / gcd(a(n-1), n-1) + a(n-2) / gcd(a(n-2), n-2).
A330809 (program): Triangular numbers having exactly 8 divisors.
A330843 (program): Square array T(n,k) = [x^n] ((1+x)^(k+1) / (1-x)^(k-1))^n, n>=0, k>=0, read by descending antidiagonals.
A330856 (program): Total sum of divisors of all the parts in the partitions of n into 2 parts.
A330859 (program): The additive version of the ‘Decade transform’ : to obtain a(n) write n as a sum of its power-of-ten parts and then continue to calculate the sum of the adjacent parts until a single number remains.
A330861 (program): Number of ways to represent n as a sum of 2 triangular numbers and a perfect square.
A330866 (program): a(n) = Sum_{d|n, d<n} (n/d) * (n-d).
A330868 (program): Number of proper divisors d of n such that n-d is squarefree.
A330881 (program): Length of longest LB factorization over all binary strings of length n.
A330885 (program): Square array T(n,k) read by antidiagonals upwards: T(n,0)=1; T(n,1) = n+1; T(n,2) = 2n+1, T(n,k>2) = T(n,k-1) - T(n,k-2) - T(n,k-3).
A330889 (program): a(n) is the total number of parts in all partitions of n into consecutive parts that differ by 3.
A330892 (program): Square array of polygonal numbers read by descending antidiagonals (the transpose of A317302).
A330908 (program): a(n+1) = a(n) + (number of divisors of a(n) that are not divisors of other divisors of a(n)) for n>1; a(1)=1.
A330910 (program): a(n-5) is the number of nonempty subsets of {1,2,…,n} such that the difference of successive elements is at least 5.
A330926 (program): a(n) = Sum_{k=1..n} (ceiling(n/k) mod 2).
A330938 (program): Numbers that cannot be written as the sum of four proper powers. A proper power is an integer of the form a^b where a,b are integers greater than or equal to 2.
A330944 (program): Number of nonprime prime indices of n.
A330945 (program): Numbers whose prime indices are not all prime numbers.
A330946 (program): Odd numbers whose prime indices are not all prime numbers.
A330950 (program): Number of integer partitions of n whose Heinz number (product of primes of parts) is divisible by n.
A330965 (program): Array read by descending antidiagonals: A(n,k) = (1 + k*n)*C(n) where C(n) = Catalan numbers (A000108).
A330968 (program): Prime numbers p such that 2*p - last digit of p is prime.
A330983 (program): Alternatively add and multiply pairs of the nonnegative integers.
A330987 (program): Alternatively add and half-multiply pairs of the nonnegative integers.
A330994 (program): Numerator of P(n)/Q(n) = A000041(n)/A000009(n).
A330995 (program): Denominator P(n)/Q(n) = A000041(n)/A000009(n).
A331007 (program): Number of derangements of a set of n elements where 2 specific elements cannot appear in each other’s positions.
A331022 (program): Numbers k such that the number of strict integer partitions of k is a power of 2.
A331044 (program): a(n) is the greatest prime number of the form floor(n/10^k) for some k >= 0, or 0 if no such prime number exists.
A331046 (program): Numbers k such that floor(k/10^m) is a prime number for some m >= 0.
A331071 (program): a(n) = Sum_{k <= n} r_2(k)^2*d(k+1), where r_2 = A004018, d = A000005.
A331072 (program): a(n) = Sum_{k <= n} u_3(k), where u_3 = A034836.
A331077 (program): Sum_{k = 1 to n} [d(k)*d_3(k)], where d = A000005, d_3 = A007425.
A331080 (program): a(n) = Sum_{i=1..n} d_3(i)*d_3(i+1), where d_3(n) = A007425(n).
A331081 (program): a(n) = Sum_{i=1..n} d_3(i)*d_3(i+1)/3, where d_3(n) = A007425(n).
A331101 (program): Denominators of the best approximations for sqrt(2).
A331105 (program): T(n,k) = -k*(k+1)/2 mod 2^n; triangle T(n,k), n>=0, 0<=k<=2^n-1, read by rows.
A331112 (program): Sum of the digits of the n-th prime number in balanced ternary.
A331115 (program): Numerators of the best approximations for sqrt(2).
A331124 (program): Number of function evaluations in a recursive calculation of Fibonacci(n).
A331125 (program): Numbers k such that there is no prime p between k and (9/8)k, exclusive.
A331132 (program): a(n) = Sum_{i=1..n} d(i)^2*d(i+1), where d(n) = A000005(n).
A331133 (program): a(n) = Sum_{i=1..n} d(i)^2*d(i+1)/2, where d(n) = A000005(n).
A331134 (program): a(n) = Sum_{primes p <= n} r_2(p)/4, where r_2(n) = A004018(n).
A331136 (program): a(n) = Sum_{primes p < n} r_2(n-p)/4, where r_2(n) = A004018(n).
A331137 (program): a(n) = Sum_{primes p <= n} b(p-1), where b = A108548.
A331145 (program): Triangle read by rows: T(n,k) (n>=k>=1) = ceiling((n/k)*ceiling(n/k)).
A331146 (program): Triangle read by rows: T(n,k) (n>=k>=1) = f(n,n-k+1) where f(n,k) = ceiling((n/k)*ceiling(n/k)).
A331147 (program): Triangle read by rows: T(n,k) (n>=k>=1) = floor((n/k)*floor(n/k)).
A331148 (program): Triangle read by rows: T(n,k) (n>=k>=1) = f(n,n-k+1) where f(n,k) = floor((n/k)*floor(n/k)).
A331149 (program): Triangle read by rows: T(n,k) (n>=k>=1) = floor((n/k)*ceiling(n/k)).
A331150 (program): Triangle read by rows: T(n,k) (n>=k>=1) = f(n,n-k+1) where f(n,k) = floor((n/k)*ceiling(n/k)).
A331151 (program): Triangle read by rows: T(n,k) (n>=k>=1) = ceiling((n/k)*floor(n/k)).
A331152 (program): Triangle read by rows: T(n,k) (n>=k>=1) = f(n,n-k+1) where f(n,k) = ceiling((n/k)*floor(n/k)).
A331162 (program): a(n) is the number of digits in the concatenation of a(0) to a(n-1) that are equal to the corresponding digit in the concatenation of all integers >= 0, with a(0) = 0.
A331166 (program): a(n) = min(n, A057889(n)), where A057889 is bijective base-2 reverse.
A331167 (program): a(n) = min(n, A193231(n)), where A193231(n) is blue code of n.
A331168 (program): If A122111(n) <= n, then a(n) = 1, otherwise a(n) = 0.
A331169 (program): If A122111(n) < n, then a(n) = 1, otherwise a(n) = 0.
A331170 (program): a(n) = min(n, A122111(n)), where A122111 conjugates the prime factorization of n.
A331171 (program): a(n) = min(n, A225901(n)), where A225901 is factorial base flip.
A331173 (program): a(n) = min(n, A263273(n)), where A263273 is bijective base-3 reverse.
A331176 (program): a(n) = n - n/gcd(n, phi(n)), where phi is Euler totient function.
A331188 (program): Primorial inflation of A052126(n), where A052126(n) = n/(largest prime dividing n).
A331190 (program): Expansion of (-5*(9 - 6*x + 2*x^2))/(-1 + x)^3.
A331192 (program): Numbers whose Zeckendorf representation (A014417) and dual Zeckendorf representation (A104326) are both palindromic.
A331201 (program): Numbers k such that the number of factorizations of k into distinct factors > 1 is a prime number.
A331206 (program): Numbers k such that A053985(k) divides k.
A331211 (program): Number of green nodes in n-th power graph W exponentiation of a cycle graph with 7 blue nodes and one green node.
A331213 (program): a(n) = 1 + Sum_{i=1..n} (-1)^i * Product_{j=1..i} floor(n/j).
A331230 (program): Numbers k such that the number of factorizations of k into distinct factors > 1 is odd.
A331231 (program): Numbers k such that the number of factorizations of k into distinct factors > 1 is even.
A331260 (program): Denominator of harmonic mean of 3 consecutive primes. Numerators are A331259.
A331261 (program): List of pairs of numbers having certain properties (see Comments).
A331279 (program): a(n) = A122111(A006047(n)).
A331281 (program): If A061395(n) <= A001222(n), then a(n) = 1, otherwise a(n) = 0.
A331282 (program): If A061395(n) < A001222(n), then a(n) = 1, otherwise a(n) = 0.
A331283 (program): a(n) = gcd(n, A329605(n)), where A329605(n) gives the number of divisors of primorial inflation of n, A108951(n).
A331286 (program): Odd part of number of divisors of primorial inflation of n: a(n) = A000265(A329605(n)).
A331289 (program): a(n) = A329348(n) - A001222(n).
A331290 (program): a(n) = gcd(A001222(n), A329348(n)).
A331291 (program): a(n) = A001222(n) * A329348(n).
A331299 (program): a(n) = min(n, A241909(n)).
A331319 (program): a(n) = x^n/(1 - 2*x*(x + 1))^2.
A331320 (program): a(n) = [x^n] ((x + 1)*(2*x - 1)*(2*x^2 - 1))/(2*x^2 + 2*x - 1)^2.
A331321 (program): a(n) = [x^n] ((x^2 - 1)*(x^2 + x - 1))/(x^2 + 2*x - 1)^2.
A331322 (program): a(n) = (3*n + 1)!/(n!)^3.
A331323 (program): a(n) = [x^n] (1 - 2*x)/(1 - 8*x + 4*x^2)^(3/2).
A331325 (program): a(n) = n!*[x^n] cosh(x/(1-x))/(1-x).
A331326 (program): a(n) = n!*[x^n] sinh(x/(1 - x))/(1 - x).
A331328 (program): Evaluation of the Little-Schröder polynomials at 1/2 and normalized with 2^n.
A331329 (program): a(n) = binomial(5*n, n)*hypergeom([-4*n, -n], [-5*n], -1).
A331331 (program): T(n, k) = (-m)^(n-k)*[x^k] KummerU(-n, 1/m, x) for m = 3. Triangle read by rows, T(n, k) for 0 <= k <= n.
A331333 (program): Interpolating the factorial and the powers of 2. Triangle read by rows, T(n, k) for 0 <= k <= n.
A331334 (program): a(n) = n! * [x^n] exp(1 - 1/(2*x + 1))/(2*x + 1).
A331335 (program): L.g.f.: log(Sum_{k>=0} k! * x^k / Product_{j=1..k} (1 - j*x)).
A331343 (program): a(n) = lcm(1,2,…,n) * Sum_{k=1..n} (2^(k-1) - 1) / k.
A331345 (program): a(n) = (1/n^2) * Sum_{k>=1} k^n * (1 - 1/n)^(k - 1).
A331347 (program): Number of permutations w in S_n that form Boolean intervals [s, w] in the Bruhat order for every simple reflection s in the support of w.
A331353 (program): Number of achiral colorings of the edges (or triangular faces) of a regular 4-dimensional simplex with n available colors.
A331386 (program): Numbers with at least one prime prime index.
A331388 (program): a(n) = Sum_{k=1..n} mu(gcd(n, k)) * k / gcd(n, k).
A331390 (program): Number of binary matrices with 3 distinct columns and any number of nonzero rows with n ones in every column and rows in nonincreasing lexicographic order.
A331394 (program): Number of ways of 4-coloring the Fibonacci square spiral tiling of n squares with colors introduced in order.
A331396 (program): Number of nonnegative integer matrices with 2 distinct columns and any number of nonzero rows with column sums n and columns in decreasing lexicographic order.
A331397 (program): Number of nonnegative integer matrices with 2 distinct columns and any number of nonzero rows with column sums n and columns in decreasing lexicographic order.
A331403 (program): E.g.f.: 1 / ((1 + x) * sqrt(1 - 2*x)).
A331408 (program): Number of subsets of {1..n} that contain exactly three odd numbers.
A331409 (program): a(1)=1; for n>1, a(n) = a(n-1)+n, divided by its largest prime factor.
A331410 (program): a(n) is the number of iterations needed to reach a power of 2 starting at n and using the map k -> k + k/p, where p is the largest prime factor of k.
A331413 (program): a(n) = 2*a(n-1) + a(n-2) + a(n-3) + a(n-4), a(0)=4, a(1)=2, a(2)=6, a(3)=17.
A331415 (program): Sum of prime factors minus sum of prime indices of n.
A331417 (program): Maximum sum of primes of the parts of an integer partition of n.
A331418 (program): If A331417(n) is the maximum sum of primes of the parts of an integer partition of n, then a(n) = A331417(n) - n + 1.
A331419 (program): a(n) is the number of subsets of {1..n} that contain exactly 4 odd numbers.
A331420 (program): a(n) is the number of subsets of {1..n} that contain exactly 5 odd numbers.
A331429 (program): Expansion of x^2*(10-5*x+x^2)/((1-x)^4*(1-x^2)).
A331430 (program): Triangle read by rows: T(n, k) = (-1)^(k+1)*binomial(n,k)*binomial(n+k,k) (n >= k >= 0).
A331431 (program): Triangle read by rows: T(n,k) = (-1)^(n+k)*(n+k+1)*binomial(n,k)*binomial(n+k,k) for n >= k >= 0.
A331433 (program): Column 1 of triangle in A331431.
A331434 (program): Column 2 of triangle in A331431.
A331436 (program): Array read by antidiagonals: A(n,k) is the number of n element multisets of n element multisets of a k-set.
A331443 (program): Number of 1-complete partitions of n with largest part 4.
A331444 (program): Number of 2-complete partitions of n with largest part 4.
A331473 (program): Alternating sum of (n+1)*A000108(n+1).
A331476 (program): The (10^n)-th even-digit number.
A331477 (program): Number of n element multisets of n element multisets of an n-set.
A331484 (program): Expansion of 1/(1 + x*Product_{k>=1} (1 - x^k)).
A331501 (program): Decimal expansion of exp(3/4).
A331502 (program): Decimal expansion of exp(4/9).
A331504 (program): Number of labeled graphs with n nodes and floor(n*(n-1)/4) edges.
A331505 (program): Number of labeled graphs with n nodes and floor(n/2) edges.
A331512 (program): a(n) = Sum_{k=0..n} n^(n-k) * (n+k+1) * binomial(n,k) * binomial(n+k,k).
A331513 (program): a(n) = Sum_{k=0..n} (-n)^(n-k) * (n+k+1) * binomial(n,k) * binomial(n+k,k).
A331514 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of 1/(1 - 2*k*x + ((k-2)*x)^2)^(3/2).
A331515 (program): Expansion of 1/(1 - 8*x + 4*x^2)^(3/2).
A331516 (program): Expansion of 1/(1 - 10*x + 9*x^2)^(3/2).
A331520 (program): a(0) = a(1) = 1; a(n+2) = Sum_{k=0..n} (binomial(n,k) mod 2) * a(k).
A331528 (program): a(n) = n^2 * (n+1)^2 * (n^2+n+1) / 12.
A331548 (program): 15-adic integer x = …2AA66B44A40E43797853AD13 satisfying x^5 = x; also x^3 = -x; (x^2)^3 = x^2 = A331550; (x^4)^2 = x^4 = A331549.
A331549 (program): 15-adic integer x = …8978C2E9CE8570624D4BDA86 satisfying x^2 = x.
A331550 (program): 15-adic integer x = …65762C0520697E8CA1A31469 satisfying x^3 = x.
A331551 (program): Expansion of (1 + 3*x)/(1 + 2*x + 9*x^2)^(3/2).
A331552 (program): Expansion of (1 + 2*x)/(1 + 4*x^2)^(3/2).
A331558 (program): E.g.f.: log(1 - x - log(1 - x)).
A331559 (program): E.g.f.: -log(1 + x + log(1 - x)).
A331573 (program): The bottom entry in the forward difference table of the Euler totient function phi for 1..n.
A331574 (program): a(n) is the number of subsets of {1..n} that contain 3 even and 3 odd numbers.
A331575 (program): a(n) is the number of subsets of {1..n} that contain 4 even and 4 odd numbers.
A331580 (program): Smallest number whose unsorted prime signature is the reversed unsorted prime signature of n.
A331581 (program): Maximum part of the n-th integer partition in graded reverse-lexicographic order (A080577); a(1) = 0.
A331601 (program): a(n) = A002487(A241909(n)).
A331602 (program): a(1) = 0; for n > 1, a(n) = A007947(A156552(n)).
A331605 (program): Positive integers k such that k = (a^2 + b^2 + c^2)/(a*b + b*c + c*a) for some integers a, b and c.
A331622 (program): a(n) is the number of k such that k and n-k are both composite.
A331656 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+k,k) * n^k.
A331657 (program): a(n) = Sum_{k=0..n} (-1)^(n - k) * binomial(n,k) * binomial(n+k,k) * n^k.
A331658 (program): E.g.f.: exp(x/(1 - 2*x)) / (1 - x).
A331660 (program): E.g.f. A(x) satisfies: d/dx A(x) = 1 + (1/(1 - x)) * A(x/(1 - x)).
A331661 (program): E.g.f. A(x) satisfies: d/dx A(x) = 1 + (1/(1 + x)) * A(x/(1 + x)).
A331671 (program): Number of Pythagorean triangles with sum of legs n.
A331677 (program): a(n) is the difference between the number of primes smaller than prime(n) (i.e., n-1) and greater than prime(n) but less than 2*prime(n).
A331688 (program): E.g.f.: exp(-x/(1 - x)) / (1 - 2*x).
A331689 (program): E.g.f.: exp(x/(1 - x)) / (1 - 2*x).
A331690 (program): a(n) = Sum_{k=0..n} Stirling2(n,k) * k! * n^(n - k).
A331694 (program): For any n > 0, let d_1, …, d_k be the divisors of n, in ascending order; set e_0 = 0 and for i = 1..k, if e_{i-1} >= d_i then set e_i = e_{i-1} - d_i else set e_i = e_{i-1} + d_i; a(n) = e_k.
A331714 (program): Number of non-isomorphic set-systems with 3 sets each with n elements.
A331725 (program): E.g.f.: exp(x/(1 - x)) / (1 + x).
A331726 (program): E.g.f.: -LambertW(-x/(1 - x)) / (1 - x).
A331727 (program): E.g.f.: -LambertW(-x/(1 + x)) / (1 + x).
A331728 (program): Negabinary-Niven numbers: numbers divisible by the sum of digits in their negabinary representation (A027615).
A331732 (program): Odd part of A241909(n).
A331737 (program): Multiplicative with a(p^e) = p^A000265(e), where A000265(x) gives the odd part of x.
A331739 (program): a(n) is n minus its largest odd divisor.
A331743 (program): Lexicographically earliest infinite sequence such that a(i) = a(j) => A002487(i) = A002487(j) and A323901(i) = A323901(j) for all i, j.
A331750 (program): a(n) = A048675(sigma(n)).
A331764 (program): a(n) = ((p-1)^3 - (p-1)^2)/4 where p is the n-th prime.
A331781 (program): Triangle read by rows: T(m,n) = Sum_{0<i<m, 0<j<n, gcd{i,j}=1} 1, where m >= n >= 1.
A331791 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of 2/(1 - 2*k*x + ((k-2)*x)^2 + (1 - k*x) * sqrt(1 - 2*k*x + ((k-2)*x)^2)).
A331792 (program): Expansion of ((1 - 4*x)/sqrt(1 - 8*x + 4*x^2) - 1)/(6*x^2).
A331793 (program): Expansion of ((1 - 5*x)/sqrt(1 - 10*x + 9*x^2) - 1)/(8*x^2).
A331794 (program): a(n) = Sum_{k=0..n} n^k * binomial(n+1,k) * binomial(n+1,k+1).
A331795 (program): a(n) = Sum_{k=0..n} (-n)^k * binomial(n+1,k) * binomial(n+1,k+1).
A331798 (program): E.g.f.: -log(1 - x) / ((1 - x) * (1 + log(1 - x))).
A331799 (program): Normalized volume of the Caracol flow polytope. Also equal to the number of “unified diagrams” of the Caracol graph (see Section 4.3 and Section 5 in Benedetti et al. reference).
A331801 (program): Integers that are sum of two nonsquarefree numbers.
A331802 (program): Integers having no representation as sum of two nonsquarefree numbers.
A331817 (program): a(n) = (n!)^2 * Sum_{k=0..n} (2*k)! / (2^k * (k!)^3 * (n - k)!).
A331819 (program): Positive numbers k such that -k is a negative negabinary-Niven number, i.e., divisible by the sum of digits of its negabinary representation (A027615).
A331830 (program): Numbers k such that k and k + 1 are both negabinary evil numbers.
A331831 (program): Numbers k such that k and k + 1 are both negabinary odious numbers.
A331836 (program): Number of noncrossing anti-commutator friendly partitions on {1,2,…,2n}.
A331839 (program): a(n) = (4^(n + 1) - 2)*(2*n)!.
A331840 (program): Numbers k such that 30*k-13, 30*k-11 are twin primes.
A331848 (program): Number of partitions of n into odd parts with some part repeated.
A331890 (program): a(n) = -a(n-1) - a(n-2) + 2*a(n-3) with a(0)=3, a(1)=-1, a(2)=-1.
A331891 (program): Negabinary palindromes: nonnegative numbers whose negabinary expansion (A039724) is palindromic.
A331892 (program): Positive numbers k such that the negabinary expansion (A039724) of -k is palindromic.
A331914 (program): Numbers with at most one prime prime index, counted with multiplicity.
A331915 (program): Numbers with exactly one prime prime index, counted with multiplicity.
A331916 (program): Numbers with exactly one distinct prime prime index.
A331933 (program): Number of semi-lone-child-avoiding rooted trees with at most one distinct non-leaf branch directly under any vertex.
A331943 (program): a(n) = n^2 + 1 - ceiling((n + 2)/3).
A331952 (program): a(n) = (-7 + (-1)^(1+n) + 6*n^2) / 8.
A331954 (program): a(n) is the least positive k such that floor(n/k) is a prime number.
A331959 (program): a(n) is the greatest prime number of the form floor(n/k) where k > 0.
A331969 (program): T(n, k) = [x^(n-k)] 1/(((1 - 2*x)^k)*(1 - x)^(k + 1)). Triangle read by rows, for 0 <= k <= n.
A331978 (program): E.g.f.: -log(2 - cosh(x)) (even powers only).
A331987 (program): a(n) = ((n + 1) - 9*(n + 1)^2 + 8*(n + 1)^3)/6.
A331991 (program): Number of semi-lone-child-avoiding achiral rooted trees with n vertices.
A331999 (program): a(n) is the product of n, the n-th prime and the n-th composite number.
A332017 (program): a(n) is the sum of the squares of the lengths of the runs of consecutive equal digits in the binary representation of n.
A332019 (program): The number of cells added in the n-th generation of the following procedure: start by coloring any triangle on the snub square tiling, then repeatedly color every cell that shares a vertex with a colored cell.
A332023 (program): T(n, k) = binomial(n+2, 3) + binomial(k+1, 2) + binomial(k, 1). Triangle read by rows, T(n, k) for 0 <= k <= n.
A332026 (program): Savannah problem: number of new possibilities after n weeks.
A332027 (program): Savannah problem: number of distinct possible populations after n weeks, allowing populations after the empty set.
A332028 (program): Savannah problem: number of distinct possible populations after n weeks, not allowing new populations after the empty set.
A332031 (program): G.f.: Sum_{k>=1} k! * x^(k^2) / (1 - x^k).
A332032 (program): G.f.: Sum_{k>=1} k! * x^(k^2) / (1 - x^(2*k)).
A332042 (program): Number of integers whose Dedekind psi function (A001615) values are n.
A332044 (program): a(n) is the length of the shortest circuit that visits every edge of an undirected n X n grid graph.
A332048 (program): a(n) = n! * [x^n] 1 / (1 - LambertW(x))^n.
A332049 (program): a(n) = (1/2) * Sum_{d|n, d > 1} d * phi(d).
A332051 (program): Number of compositions of 2n where the multiplicity of the first part equals n.
A332052 (program): Number of binary words of length n with an even number of occurrences of the subword 0101.
A332056 (program): a(1) = 1, then a(n+1) = a(n) - (-1)^a(n) Sum_{k=1..n} a(k): if a(n) is odd, add the partial sum, else subtract.
A332057 (program): Partial sums (and absolute value of first differences) of A332056: if odd (resp. even) add (resp. subtract) the partial sum to get the next term.
A332060 (program): a(n) = 3*a(n-1) + a(n-2) after initial values a(0..5) = (0, 1, 2, 3, 5, 13).
A332063 (program): a(1) = 1, a(n + 1) = a(n) + Sum_{k = 1..n} floor(log_2(a(k)) + 1): add total number of bits of the terms so far.
A332082 (program): a(n) = Sum_{1 <= m <= n} Sum_{1 <= k <= n+1-m} m*R(k,n+1), where R(k,b) = (b^k - 1)/(b - 1) is the base-b repunit of length k.
A332086 (program): a(n) = pi(prime(n) + n) - n, where pi is the prime counting function.
A332097 (program): Maximum of s^n - Sum_{0 < x < s} x^n.
A332101 (program): Least m such that m^n <= Sum_{k<m} k^n.
A332102 (program): Least m > 0 such that 2*m^n <= Sum_{k < m} k^n.
A332103 (program): Numbers not of the form floor(p/4) + 1, where p is a prime.
A332104 (program): Triangle read by rows in which row n >= 0 lists numbers from 0 to n starting at floor(n/2) and using alternatively larger respectively smaller numbers than the values used so far.
A332112 (program): a(n) = (10^(2n+1)-1)/9 + 10^n.
A332113 (program): a(n) = (10^(2n+1)-1)/9 + 2*10^n.
A332114 (program): a(n) = (10^(2n+1)-1)/9 + 3*10^n.
A332115 (program): a(n) = (10^(2n+1)-1)/9 + 4*10^n.
A332116 (program): a(n) = (10^(2n+1)-1)/9 + 5*10^n.
A332117 (program): a(n) = (10^(2n+1)-1)/9 + 6*10^n.
A332118 (program): a(n) = (10^(2n+1)-1)/9 + 7*10^n.
A332119 (program): a(n) = (10^(2n+1)-1)/9 + 8*10^n.
A332120 (program): a(n) = 2*(10^(2n+1)-1)/9 - 2*10^n.
A332121 (program): a(n) = 2*(10^(2n+1)-1)/9 - 10^n.
A332122 (program): Decimal expansion of unique real root of the polynomial X^3 - X^2 - X/2 - 1/6.
A332123 (program): a(n) = 2*(10^(2n+1)-1)/9 + 10^n.
A332124 (program): a(n) = 2*(10^(2n+1)-1)/9 + 2*10^n.
A332125 (program): a(n) = 2*(10^(2n+1)-1)/9 + 3*10^n.
A332126 (program): a(n) = 2*(10^(2n+1)-1)/9 + 4*10^n.
A332127 (program): a(n) = 2*(10^(2n+1)-1)/9 + 5*10^n.
A332128 (program): a(n) = 2*(10^(2n+1)-1)/9 + 6*10^n.
A332129 (program): a(n) = 2*(10^(2n+1)-1)/9 + 7*10^n.
A332130 (program): a(n) = (10^(2n+1)-1)/3 - 3*10^n.
A332131 (program): a(n) = (10^(2n+1)-1)/3 - 2*10^n.
A332132 (program): a(n) = (10^(2n+1)-1)/3 - 10^n.
A332133 (program): Decimal expansion of (1 + sqrt(3))/2, unique positive root of x^2 - x - 1/2.
A332134 (program): a(n) = (10^(2n+1)-1)/3 + 10^n.
A332135 (program): a(n) = (10^(2n+1)-1)/3 + 2*10^n.
A332136 (program): a(n) = 3*(10^(2n+1)-1)/9 + 3*10^n.
A332137 (program): a(n) = (10^(2n+1)-1)/3 + 4*10^n.
A332138 (program): a(n) = (10^(2*n+1)-1)/3 + 5*10^n.
A332139 (program): a(n) = (10^(2*n+1)-1)/3 + 6*10^n.
A332140 (program): a(n) = 4*(10^(2n+1)-1)/9 - 4*10^n.
A332141 (program): a(n) = 4*(10^(2*n+1)-1)/9 - 3*10^n.
A332142 (program): a(n) = 4*(10^(2*n+1)-1)/9 - 2*10^n.
A332143 (program): a(n) = 4*(10^(2*n+1)-1)/9 - 10^n.
A332145 (program): a(n) = 4*(10^(2*n+1)-1)/9 + 10^n.
A332146 (program): a(n) = 4*(10^(2*n+1)-1)/9 + 2*10^n.
A332147 (program): a(n) = 4*(10^(2*n+1)-1)/9 + 3*10^n.
A332148 (program): a(n) = 4*(10^(2*n+1)-1)/9 + 4*10^n.
A332149 (program): a(n) = 4*(10^(2*n+1)-1)/9 + 5*10^n.
A332150 (program): a(n) = 5*(10^(2n+1)-1)/9 - 5*10^n.
A332151 (program): a(n) = 5*(10^(2*n+1)-1)/9 - 4*10^n.
A332152 (program): a(n) = 5*(10^(2*n+1)-1)/9 - 3*10^n.
A332153 (program): a(n) = 5*(10^(2*n+1)-1)/9 - 2*10^n.
A332154 (program): a(n) = 5*(10^(2*n+1)-1)/9 - 10^n.
A332156 (program): a(n) = 5*(10^(2*n+1)-1)/9 + 10^n.
A332157 (program): a(n) = 5*(10^(2*n+1)-1)/9 + 2*10^n.
A332158 (program): a(n) = 5*(10^(2*n+1)-1)/9 + 3*10^n.
A332159 (program): a(n) = 5*(10^(2*n+1)-1)/9 + 4*10^n.
A332160 (program): a(n) = 6*(10^(2n+1)-1)/9 - 6*10^n.
A332161 (program): a(n) = 6*(10^(2*n+1)-1)/9 - 5*10^n.
A332162 (program): a(n) = 6*(10^(2*n+1)-1)/9 - 4*10^n.
A332163 (program): a(n) = 6*(10^(2*n+1)-1)/9 - 3*10^n.
A332164 (program): a(n) = 6*(10^(2*n+1)-1)/9 - 2*10^n.
A332165 (program): a(n) = 6*(10^(2*n+1)-1)/9 - 10^n.
A332167 (program): a(n) = 6*(10^(2*n+1)-1)/9 + 10^n.
A332168 (program): a(n) = 6*(10^(2*n+1)-1)/9 + 2*10^n.
A332169 (program): a(n) = 6*(10^(2*n+1)-1)/9 + 3*10^n.
A332170 (program): a(n) = 7*(10^(2n+1)-1)/9 - 7*10^n.
A332171 (program): a(n) = 7*(10^(2n+1)-1)/9 - 6*10^n.
A332172 (program): a(n) = 7*(10^(2n+1)-1)/9 - 5*10^n.
A332173 (program): a(n) = 7*(10^(2n+1)-1)/9 - 4*10^n.
A332174 (program): a(n) = 7*(10^(2n+1)-1)/9 - 3*10^n.
A332175 (program): a(n) = 7*(10^(2n+1)-1)/9 - 2*10^n.
A332176 (program): a(n) = 7*(10^(2n+1)-1)/9 - 10^n.
A332178 (program): a(n) = 7*(10^(2n+1)-1)/9 + 10^n.
A332179 (program): a(n) = 7*(10^(2n+1)-1)/9 + 2*10^n.
A332180 (program): a(n) = 8*(10^(2n+1)-1)/9 - 8*10^n.
A332181 (program): a(n) = 8*(10^(2n+1)-1)/9 - 7*10^n.
A332182 (program): a(n) = 8*(10^(2n+1)-1)/9 - 6*10^n.
A332183 (program): a(n) = 8*(10^(2n+1)-1)/9 - 5*10^n.
A332184 (program): a(n) = 8*(10^(2n+1)-1)/9 - 4*10^n.
A332185 (program): a(n) = 8*(10^(2n+1)-1)/9 - 3*10^n.
A332186 (program): a(n) = 8*(10^(2n+1)-1)/9 - 2*10^n.
A332187 (program): a(n) = 8*(10^(2n+1)-1)/9 - 10^n.
A332188 (program): a(n) = (1/e^n) * Sum_{j>=2} j^n * n^j / (j-2)!.
A332189 (program): a(n) = 8*(10^(2n+1)-1)/9 + 10^n.
A332190 (program): a(n) = 10^(2n+1) - 1 - 9*10^n.
A332191 (program): a(n) = 10^(2n+1) - 1 - 8*10^n.
A332192 (program): a(n) = 10^(2n+1) - 1 - 7*10^n.
A332193 (program): a(n) = 10^(2n+1) - 1 - 6*10^n.
A332194 (program): a(n) = 10^(2n+1) - 1 - 5*10^n.
A332195 (program): a(n) = 10^(2n+1) - 4*10^n - 1.
A332196 (program): a(n) = 10^(2n+1) - 1 - 3*10^n.
A332197 (program): a(n) = 10^(2n+1) - 1 - 2*10^n.
A332202 (program): Largest k >= 0 such that 3^k divides 2^(2^n-1) + 1.
A332206 (program): Numbers k such that A332205(k) = 0.
A332209 (program): Starting from sigma(n), number of halving and tripling steps to reach 1 in ‘3x+1’ problem, or -1 if 1 is never reached.
A332221 (program): a(n) = A156552(sigma(n)).
A332222 (program): a(n) = A156552(sigma(A005940(1+n))).
A332223 (program): a(1) = 1, and for n > 1, a(n) = A005940(1+sigma(A156552(n))).
A332224 (program): a(n) = A087808(sigma(n)).
A332226 (program): Numbers k such that sigma(k) is congruent to 2 modulo 8.
A332227 (program): Odd numbers k such that sigma(k) is congruent to 2 modulo 8.
A332231 (program): a(n) = 1/n! * ((n+1)*n)!/Gamma(1 + (n+1)*n/2) * Gamma(1 + (n-1)*n/2)/((n-1)*n)!.
A332233 (program): Number of integer partitions lambda (of any k) satisfying n = max_{p:lambda} p*m(p,lambda), where m(p,lambda) is the multiplicity of part p in lambda.
A332236 (program): E.g.f.: -log(2 - 1 / (1 + LambertW(-x))).
A332238 (program): a(n) = n^(n-1) - Sum_{k=1..n-1} k^(k-1) * a(n-k).
A332239 (program): a(n) = n^(n-2) - Sum_{k=1..n-1} k^(k-2) * a(n-k).
A332243 (program): Starhex honeycomb numbers: a(n) = 13 + 60*n + 60*n^2.
A332251 (program): a(n) is the real part of f(n) defined by f(0) = 0 and f(n+1) = f(n) + i^A000120(n) (where i denotes the imaginary unit). Sequence A332252 gives imaginary parts.
A332252 (program): a(n) is the imaginary part of f(n) defined by f(0) = 0 and f(n+1) = f(n) + i^A000120(n) (where i denotes the imaginary unit). Sequence A332251 gives real parts.
A332255 (program): E.g.f.: 1 / (2 - 1 / (2 + x - exp(x))).
A332257 (program): E.g.f.: (1 - sinh(x)) / (1 - 2*sinh(x)).
A332264 (program): Partial sums of A334136.
A332269 (program): Numbers m with only one divisor d such that sqrt(m) < d < m.
A332273 (program): Sizes of maximal weakly decreasing subsequences of A000002.
A332288 (program): Number of unimodal permutations of the multiset of prime indices of n.
A332294 (program): Number of unimodal permutations of a multiset whose multiplicities are the prime indices of n.
A332324 (program): Decimal expansion of the minimum value of the 4th Maclaurin polynomial of e^x.
A332326 (program): Decimal expansion of the least positive zero of the 4th Maclaurin polynomial of cos x.
A332382 (program): If n = Sum (2^e_k) then a(n) = Product (prime(e_k + 2)).
A332383 (program): a(n) is the X-coordinate of the n-th point of the dragon curve. Sequence A332384 gives Y-coordinates.
A332384 (program): a(n) is the Y-coordinate of the n-th point of the dragon curve. Sequence A332383 gives X-coordinates.
A332385 (program): Sum of squares of indices of distinct prime factors of n.
A332408 (program): a(n) = Sum_{k=0..n} binomial(n,k) * k! * k^n.
A332409 (program): a(n) = n!! mod Fibonacci(n).
A332410 (program): a(n) = 2*a(n-1) - a(n-2) + a(n-5) - 2*a(n-6) + a(n-7) with a(0)=0, a(1)=1, a(2)=3, a(3)=6, a(4)=11, a(5)=17, a(6)=24.
A332420 (program): Number of Maclaurin polynomials of sin x having exactly n positive zeros.
A332423 (program): If n = Product (p_j^k_j) then a(n) = Sum ((-1)^(k_j + 1) * k_j).
A332426 (program): Number of unordered pairs of non-selfintersecting paths with nodes that cover all vertices of a convex n-gon.
A332433 (program): Signs appearing in the definition of A329593.
A332435 (program): Row sums of the irregular triangle A332434. a(n) equals the number of odd numbers <= n, of the smallest nonnegative reduced residue system modulo (2*n + 1), for n >= 1.
A332436 (program): The number of even numbers <= n of the smallest nonnegative reduced residue system modulo 2*n + 1, for n >= 0.
A332437 (program): Decimal expansion of 2*cos(Pi/9).
A332438 (program): Decimal expansion of (2*cos(Pi/9))^2 = A332437^2.
A332439 (program): Primitive period of the partial sums of the periodic unsigned Schick sequence for N = 7 (A130794), taken modulo 14, and the related Euler tour using all regular 14-gon vertices.
A332442 (program): Triangle read by rows, T(n,k) is the number of regular triangles of length k (in some length unit), for k from {1, 2, … , n}, in a matchstick arrangement with enclosing triangle of length n, but only triangles with orientation opposite to the enclosing triangle are counted.
A332447 (program): a(n) = A007814(A087808(n)).
A332448 (program): a(n) = A007814(A087808(sigma(n))).
A332452 (program): Starting from sigma(n), number of halving steps to reach 1 in ‘3x+1’ problem, or -1 if this never happens.
A332453 (program): Starting from sigma(n), number of tripling steps to reach 1 in ‘3x+1’ problem, or -1 if 1 is never reached.
A332454 (program): Starting from sigma(n)+1, number of halving steps to reach 1 in ‘3x+1’ problem, or -1 if this never happens.
A332455 (program): Starting from sigma(n)+1, number of tripling steps to reach 1 in ‘3x+1’ problem, or -1 if 1 is never reached.
A332459 (program): Odd part of 1+sigma(n).
A332464 (program): Rule 124 one-dimensional cellular automaton applied for one step to the configuration read from the base-2 expansion of sigma(n), then converted back to decimal.
A332469 (program): a(n) = Sum_{k=1..n} floor(n/k)^n.
A332476 (program): The number of unitary divisors of n in Gaussian integers.
A332480 (program): Numbers k such that sin(k) > 0 and cos(k) > 0.
A332481 (program): Numbers k such that sin(k) > 0 and cos(k) < 0.
A332482 (program): Numbers k such that sin(k) < 0 and cos(k) > 0.
A332483 (program): Numbers k such that sin(k) < 0 and cos(k) < 0.
A332484 (program): Numbers k such that sin(k) > 0 or cos(k) > 0.
A332485 (program): Numbers k such that sin(k) > 0 or cos(k) < 0.
A332486 (program): Numbers k such that sin(k) < 0 or cos(k) > 0.
A332487 (program): Numbers k such that sin(k) < 0 or cos(k) < 0.
A332490 (program): a(n) = Sum_{k=1..n} k * ceiling(n/k).
A332491 (program): a(n) = 2*a(n-1) + a(n-3), where a(0) = 3, a(1) = 1, a(2) = 2.
A332495 (program): a(n-2) = a(n-6) + 5*(1+2*n) with a(0)=0, a(1)=2, a(2)=7, a(3)=15 for n>=4.
A332496 (program): Triangular array T(n,k): the number of not necessarily proper colorings of the complete graph on n unlabeled vertices minus an edge using exactly k colors.
A332497 (program): a(n) = x(w+1) where x(0) = 0 and x(k+1) = 2^(k+1)-1-x(k) (resp. x(k)) when d_k = 1 (resp. d_k <> 1) and Sum_{k=0..w} d_k*3^k is the ternary representation of n. Sequence A332498 gives corresponding y’s.
A332498 (program): a(n) = y(w+1) where y(0) = 0 and y(k+1) = 2^(k+1)-1-y(k) (resp. y(k)) when d_k = 2 (resp. d_k <> 2) and Sum_{k=0..w} d_k*3^k is the ternary representation of n. Sequence A332497 gives corresponding x’s.
A332502 (program): Rectangular array read by antidiagonals: T(n,k) = floor(n + k*r), where r = golden ratio = (1+sqrt(5))/2.
A332508 (program): a(n) = Sum_{d|n} binomial(n+d-2, n-1).
A332509 (program): a(n) = Sum_{k=1..n} mu(floor(n/k)), where mu = A008683.
A332510 (program): a(n) = Sum_{k=1..n} lambda(floor(n/k)), where lambda = A008836.
A332512 (program): Numbers k such that phi(k) == 0 (mod 12), where phi is the Euler totient function (A000010).
A332513 (program): Numbers k such that phi(k) == 4 (mod 12), where phi is the Euler totient function (A000010).
A332514 (program): Numbers k such that phi(k) == 6 (mod 12), where phi is the Euler totient function (A000010).
A332515 (program): Numbers k such that phi(k) == 8 (mod 12), where phi is the Euler totient function (A000010).
A332516 (program): Numbers k such that phi(k) == 10 (mod 12), where phi is the Euler totient function (A000010).
A332517 (program): a(n) = Sum_{k=1..n} gcd(n,k)^n.
A332519 (program): a(n) = 4*(n^2 + n - 2).
A332529 (program): Rectangular array by antidiagonals: T(n,k) = floor(n + k*r), where r = golden ratio = (1+sqrt(5))/2.
A332533 (program): a(n) = (1/n) * Sum_{k=1..n} floor(n/k) * n^k.
A332542 (program): a(n) is the smallest k such that n+(n+1)+(n+2)+…+(n+k) is divisible by n+k+1.
A332543 (program): a(n) = n + A332542(n) + 1.
A332544 (program): a(n) = (k+1)*n + k*(k+1)/2, where k = A332542(n).
A332547 (program): a(n) = largest odd divisor d < n of n*(n+1)/2.
A332548 (program): (A332547(n)-1)/2.
A332552 (program): a(n) = A082184(n) - A082183(n).
A332553 (program): a(n) = n + A082183(n) - A082184(n).
A332554 (program): a(n) = (n*(n+1)/2)/Q(n) - (Q(n)+1)/2, where Q(n) = A332547(n).
A332557 (program): Number of inequivalent Z_{2^s}-linear Hadamard codes of length 2^n.
A332558 (program): a(n) is the smallest k such that n*(n+1)*(n+2)*…*(n+k) is divisible by n+k+1.
A332559 (program): a(n) = n + A332558(n) + 1.
A332560 (program): a(n) = (n + A332558(n))!/(n-1)!.
A332561 (program): a(n) = A332560(n)/A332559(n).
A332562 (program): a(n) = number formed by concatenating the decimal digits of 44, 45, 46, …, 44+n.
A332569 (program): a(n) = Sum_{k=1..n} floor(n/k) * ceiling(n/k).
A332587 (program): a(n) = least m such that there is a component of a certain pawn game based on a word of length m that is equivalent to a Nim-heap of size n.
A332602 (program): Tridiagonal matrix M read by antidiagonals: main diagonal is 1,2,2,2,2,…, two adjacent diagonals are 1,1,1,1,1,…
A332613 (program): Covering radius of the dihedral group code D_n.
A332618 (program): a(n) = Sum_{d|n} lcm(d, n/d) / gcd(d, n/d).
A332619 (program): a(n) = Sum_{d|n} lcm(d, n/d) / d.
A332620 (program): a(n) = Sum_{k=1..n} n^(n/gcd(n, k)).
A332621 (program): a(n) = (1/n) * Sum_{k=1..n} n^(n/gcd(n, k)).
A332623 (program): a(n) = Sum_{k=1..n} ceiling(n/k)^2.
A332624 (program): a(n) = Sum_{k=1..n} ceiling(n/k)^n.
A332627 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * k! * k^n.
A332635 (program): a(n) = n!! mod prime(n).
A332644 (program): Largest of the least integers of prime signatures over all partitions of n into distinct parts.
A332646 (program): Numbers m with a divisor d such that d^tau(d) = m.
A332647 (program): a(n) = 2*a(n-1) + a(n-3) with a(0) = 3, a(1) = 2, a(2) = 4.
A332652 (program): a(n) = Sum_{k=1..n} n^(k/gcd(n, k)).
A332653 (program): a(n) = (1/n) * Sum_{k=1..n} n^(k/gcd(n, k)).
A332654 (program): a(n) = Sum_{k=1..n} (k/gcd(n, k))^2.
A332655 (program): a(n) = Sum_{k=1..n} (k/gcd(n, k))^n.
A332658 (program): a(n) = Sum_{k=1..n} mu(gcd(n, k)) * lcm(n, k) / gcd(n, k).
A332660 (program): Alternate adding and multiplying Fibonacci numbers: a(0) = F(0) + F(1), for n >= 0, a(2n+1) = a(2n) * F(2n+2), a(2n+2) = a(2n+1) + F(2n+3).
A332663 (program): Even bisection of A332662: the x-coordinates of an enumeration of N X N.
A332679 (program): a(n) = (-1)^n * n! * Laguerre(n, 4*n).
A332682 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * ceiling(n/k).
A332683 (program): a(n) = Sum_{k=1..n, gcd(n, k) = 1} ceiling(n/k).
A332685 (program): a(n) = Sum_{k=1..n} mu(k/gcd(n, k)).
A332686 (program): a(n) = Sum_{k=1..n} phi(k/gcd(n, k)).
A332687 (program): a(n) = Sum_{k=1..n} ceiling(n/prime(k)).
A332692 (program): a(n) = n! * Laguerre(n, 2*n).
A332693 (program): a(n) = n! * Laguerre(n, 3*n).
A332694 (program): a(n) = (-1)^n * n! * Laguerre(n, 5*n).
A332695 (program): a(n) = (-1)^n * n! * Laguerre(n, 6*n).
A332697 (program): a(n) = (n^4 + 5*n^3 + 11*n^2 + 7*n)/6.
A332698 (program): a(n) = (8*n^3 + 15*n^2 + 13*n)/6.
A332699 (program): First row of A332662, also main diagonal of A332667.
A332705 (program): Number of unit square faces (or surface area) of a stage-n Menger sponge.
A332706 (program): Index position of {2}^n within the list of partitions of 2n in canonical ordering.
A332710 (program): Maximum value in n-th row of A332709.
A332711 (program): Sum of all numbers in bijective base-n numeration with digit sum n.
A332712 (program): a(n) = Sum_{d|n} mu(d/gcd(d, n/d)).
A332724 (program): Number of length n - 1 ordered set partitions of {1..n} where no element of any block is greater than any element of a non-adjacent consecutive block.
A332730 (program): a(n) = Sum_{d|n} tau(d/gcd(d, n/d)), where tau = A000005.
A332732 (program): Dirichlet g.f.: zeta(6*s) / (zeta(s) * zeta(2*s) * zeta(3*s)).
A332741 (program): Number of unimodal negated permutations of a multiset whose multiplicities are the prime indices of n.
A332750 (program): The number of flips to go from Hamiltonian cycle alpha_n to beta_n in the Cameron graph of size n using Thomason’s algorithm.
A332754 (program): a(n) = Sum_{k=1..n-1} ((-1)^(k+n+1)*binomial(k,floor(k/2))).
A332756 (program): A loop sequence within Pi. Let a(1) = 19. For n > 1, a(n+1) is the position of the first occurrence of a(n) after the decimal point in the decimal expansion of Pi.
A332757 (program): Number of involutions (plus identity) in the n-fold iterated wreath product of C_2.
A332758 (program): Number of fixed-point free involutions in the n-fold iterated wreath product of C_2.
A332761 (program): Exponents m such that the number of nonnegative k <= n, possessing the property that n + n*k - k is a square, is equal to 2^m.
A332769 (program): Permutation of the positive integers: a(n) = A258996(A054429(n)) = A054429(A258996(n)).
A332774 (program): Given n line segments, the k-th of which is drawn from (k,0) to (x_k,1) where {x_1,x_2,…,x_n} is a permutation of {1,2,…,n}, a(n) is the maximum number of distinct points at which line segments intersect.
A332775 (program): a(n) = n + sopf(n) - omega(n).
A332777 (program): a(n) = k^2 mod p where p is the n-th prime and of the form 6k-1 or 6k+1.
A332785 (program): Nonsquarefree numbers that are not squareful.
A332786 (program): a(n) = numerator(-1/n + Sum_{k=1..n} 2^(k-1)/k).
A332789 (program): First differences of the iterated Beatty sequence A007069.
A332790 (program): Triangle read by rows: T(n,k) = 1 + 2*n + k + 5*k(n-k) for n >= 0, 0 <= k <= n.
A332793 (program): a(1) = 1; a(n) = n * Sum_{d|n, d < n} (-1)^(n/d) * a(d) / d.
A332794 (program): a(n) = Sum_{d|n} (-1)^(d + 1) * d * phi(n/d).
A332796 (program): Number of compositions of n^2 into parts >= n.
A332797 (program): Numbers whose smallest prime factor is 23.
A332798 (program): Numbers whose smallest prime factor is 19.
A332799 (program): Numbers whose smallest prime factor is 17.
A332801 (program): a(n) is the number of even results of n mod k, for 1 < k < n.
A332807 (program): a(n) = A000720(A108546(n)).
A332813 (program): a(n) = A048675(n) mod 3.
A332814 (program): a(n) is -1, 0, or +1 such that a(n) == A156552(n) (mod 3).
A332820 (program): Integers in the multiplicative subgroup of positive rationals generated by the products of two consecutive primes and the cubes of primes. Numbers k for which A048675(k) is a multiple of three.
A332821 (program): One part of a 3-way classification of the positive integers. Numbers n for which A048675(n) == 1 (mod 3).
A332822 (program): One part of a 3-way classification of the positive integers. Numbers n for which A048675(n) == 2 (mod 3).
A332823 (program): A 3-way classification indicator generated by the products of two consecutive primes and the cubes of primes. a(n) is -1, 0, or 1 such that a(n) == A048675(n) (mod 3).
A332824 (program): a(n) = Product_{d|n} A019565(phi(d)), where phi is Euler totient function A000010.
A332825 (program): a(n) = A019565(phi(n)).
A332828 (program): Expansion of (x + x^2 + x^6 - x^7)/(1 - x^2 + x^4 - x^6 + x^8) in powers of x.
A332834 (program): Number of compositions of n that are neither weakly increasing nor weakly decreasing.
A332844 (program): Dirichlet g.f.: zeta(s) * zeta(s-1) * zeta(2*s).
A332845 (program): a(n) = (-1)^omega(n) * Sum_{k=1..n} (-1)^omega(n/gcd(n, k)), where omega = A001221.
A332846 (program): a(1) = 1; a(n+1) = Sum_{k=1..n} a(k) * ceiling(n/k).
A332849 (program): a(n) = prime(n)^prime(n+1) + prime(n) + prime(n+1).
A332872 (program): Number of ordered set partitions of {1..n} where no element of any block is greater than any element of a non-adjacent consecutive block.
A332875 (program): Sizes of maximal weakly increasing subsequences of A000002.
A332880 (program): If n = Product (p_j^k_j) then a(n) = numerator of Product (1 + 1/p_j).
A332881 (program): If n = Product (p_j^k_j) then a(n) = denominator of Product (1 + 1/p_j).
A332882 (program): If n = Product (p_j^k_j) then a(n) = numerator of Product (1 + 1/p_j^k_j).
A332883 (program): If n = Product (p_j^k_j) then a(n) = denominator of Product (1 + 1/p_j^k_j).
A332884 (program): a(n) = -n^2 + 21*n - 1.
A332885 (program): a(0) = a(1) = 1; a(n) = a(n-2) + Sum_{k=0..n-2} binomial(n-2,k) * a(k).
A332890 (program): Decimal expansion of Sum_{k>=0} 1/(4*k)!.
A332891 (program): Sum of the widths of all r X s rectangles such that r < s, r + s = 2n and (s - r) | (s * r).
A332892 (program): Decimal expansion of Sum_{k>=0} 1/(6*k)!.
A332917 (program): A332916(n)/2^a(n) is the average number of binary strings of length n with Levenshtein distance <= 3 from a uniform randomly sampled binary string of this length.
A332919 (program): a(n) is the sum of the sums of squared digits of all n-digit numbers.
A332921 (program): Number of symmetric non-isomorphic free unrooted snake-shaped polyominoes of maximum length on a quadratic board of n X n squares.
A332931 (program): Sum of round(sqrt(d)) where d runs through the divisors of n.
A332932 (program): Sum of ceiling(sqrt(d)) where d runs through the divisors of n.
A332933 (program): Sum of floor(d^(3/2)) where d runs through the divisors of n.
A332934 (program): Sum of round(d^(3/2)) where d runs through the divisors of n.
A332935 (program): Sum of ceiling(n^(3/2)) where d runs through the divisors of n.
A332936 (program): Number of blue nodes in n-th power graph W exponentiation of a cycle graph with 7 blue nodes and 1 green node.
A332937 (program): a(n) is the greatest common divisor of the first two terms of row n of the Wythoff array (A035513).
A332938 (program): Indices of the primitive rows of the Wythoff array (A035513); see Comments.
A332958 (program): Number of labeled forests with 2n nodes consisting of n-1 isolated nodes and a labeled tree with n+1 nodes.
A332966 (program): a(n) is the largest value in the sequence s defined by s(1) = 0 and for any k > 0, s(k+1) = (s(k)^2+1) mod n.
A332979 (program): Largest integer m satisfying Omega(m) + pi(gpf(m)) - [m<>1] = n.
A332987 (program): Sums of two nonzero pentagonal numbers.
A332993 (program): a(1) = 1, for n > 1, a(n) = n + a(A032742(n)).
A332994 (program): a(1) = 1, for n > 1, a(n) = n + a(A052126(n)).
A333041 (program): Odd numbers m such that sigma(m) > sigma(m-1).
A333042 (program): G.f.: exp(Sum_{k>=1} (4*k)!/k!^4 * x^k/k).
A333043 (program): G.f.: exp(Sum_{k>=1} (5*k)!/k!^5 * x^k/k).
A333046 (program): a(1) = 1; a(n) = n * Sum_{d|n, d < n, gcd(d, n/d) = 1} a(d) / d.
A333048 (program): Number of compositions of n^2 into powers of n.
A333068 (program): a(1) = 1; for n > 1, a(n) = n*(n-1)/2 + ((a(n-1)-1) mod n) + 1, the a(n-1)-th term of the n-th row of the triangle of positive integers, indexed in cyclic manner.
A333093 (program): a(n) is the n-th order Taylor polynomial (centered at 0) of c(x)^n evaluated at x = 1, where c(x) = (1 - sqrt(1 - 4*x))/(2*x) is the o.g.f. of the Catalan numbers A000108.
A333094 (program): a(n) is the n-th order Taylor polynomial (centered at 0) of c(x)^(2*n) evaluated at x = 1, where c(x) = (1 - sqrt(1 - 4*x))/(2*x) is the o.g.f. of the Catalan numbers A000108.
A333095 (program): a(n) = the n-th order Taylor polynomial (centered at 0) of c(x)^(3*n) evaluated at x = 1, where c(x) = (1 - sqrt(1 - 4*x))/(2*x) is the o.g.f. of the sequence of Catalan numbers A000108.
A333096 (program): a(n) = the n-th order Taylor polynomial (centered at 0) of c(x)^(4*n) evaluated at x = 1, where c(x) = (1 - sqrt(1 - 4*x))/(2*x) is the o.g.f. of the sequence of Catalan numbers A000108.
A333097 (program): a(n) = the n-th order Taylor polynomial (centered at 0) of c(x)^(5*n) evaluated at x = 1, where c(x) = (1 - sqrt(1 - 4*x))/(2*x) is the o.g.f. of the sequence of Catalan numbers A000108.
A333119 (program): Triangle T read by rows: T(n, k) = (n - k)*(1 - (-1)^k + 2*k)/4, with 0 <= k < n.
A333125 (program): a(n) = binomial(Fibonacci(n),n).
A333145 (program): Number of unimodal negated permutations of the multiset of prime indices of n.
A333147 (program): Number of compositions of n that are either strictly increasing or strictly decreasing.
A333167 (program): a(n) = r_2(n^2 + 1), where r_2(k) is the number of ways of writing k as a sum of 2 squares (A004018).
A333168 (program): a(n) = Sum_{k=0..n} r_2(k^2 + 1), where r_2(k) is the number of ways of writing k as a sum of 2 squares (A004018).
A333169 (program): a(n) = phi(n^2 + 1), where phi is the Euler totient function (A000010).
A333170 (program): a(n) = Sum_{k=0..n} phi(k^2 + 1), where phi is the Euler totient function (A000010).
A333171 (program): a(n) = Sum_{k=0..n} d(k^2 + 1), where d(k) is the number of divisors of k (A000005).
A333172 (program): a(n) = Sum_{k=0..n} sigma(k^2 + 1), where sigma(k) is the sum of divisors of k (A000203).
A333173 (program): a(n) = r_4(n^2 + 1), where r_4(k) is the number of ways of writing k as a sum of 4 squares (A000118).
A333174 (program): a(n) = Sum_{k=0..n} r_4(k^2 + 1), where r_4(k) is the number of ways of writing k as a sum of 4 squares (A000118).
A333175 (program): If n = Product (p_j^k_j) then a(n) = Sum (a(n/p_j^k_j)), with a(1) = 1.
A333183 (program): Number of digits in concatenation of first n positive even integers.
A333194 (program): a(n) = Sum_{k=1..n} (ceiling(n/k) mod 2) * k.
A333196 (program): Least k such that Sum_{i=1..n} k^n / i is a positive integer.
A333206 (program): a(n) is the least decimal digit of n^3.
A333212 (program): Lengths of maximal weakly decreasing subsequences in the sequence of prime gaps (A001223).
A333214 (program): Positions of adjacent unequal terms in the sequence of differences between primes.
A333215 (program): Lengths of maximal weakly increasing subsequences in the sequence of prime gaps (A001223).
A333219 (program): Heinz number of the n-th composition in standard order.
A333220 (program): The number k such that the k-th composition in standard order consists of the prime indices of n in weakly increasing order.
A333229 (program): First sums of the Kolakoski sequence A000002.
A333230 (program): Positions of weak ascents in the sequence of differences between primes.
A333231 (program): Positions of weak descents in the sequence of differences between primes.
A333236 (program): Largest digit in the decimal expansion of 1/n.
A333237 (program): Numbers k such that 1/k contains at least one ‘9’ in its decimal expansion.
A333242 (program): Prime numbers with an odd number of steps in their prime index chain.
A333243 (program): Prime numbers with prime indices in A262275.
A333251 (program): Tropical version of Somos-5 sequence A006721.
A333252 (program): Lengths of maximal strictly decreasing subsequences in the sequence of prime gaps (A001223).
A333254 (program): Lengths of maximal runs in the sequence of prime gaps (A001223).
A333255 (program): Numbers k such that the k-th composition in standard order is strictly increasing.
A333256 (program): Numbers k such that the k-th composition in standard order is strictly decreasing.
A333262 (program): Number of steps to reach 1 by iterating the alternating sum of divisors function A071324 starting from n.
A333291 (program): a(n) = Sum_{i=1..n, gcd(i,n)=1} i*phi(i) where phi is Euler’s totient function A000010.
A333293 (program): a(n) = Sum_{k=1..n-1} k^2*phi(k) + n^2*phi(n)/2, where phi = A000010.
A333295 (program): Triangle read by rows: T(m,n) = Sum_{1 <= i <= m, 1 <= j <= n, gcd{i,j}=1} 1, where m >= n >= 1.
A333296 (program): Largest number of non-congruent integer-sided bricks that can be assembled into an n X n X n cube.
A333297 (program): a(n) = Sum_{i=1..n, j=1..n, gcd(i,j)=1} i.
A333298 (program): Number of canonical sequences of moves of length n for the Rubik cube puzzle using the half-turn metric.
A333299 (program): Number of canonical sequences of moves of length n for the Rubik cube puzzle using the quarter-turn metric.
A333302 (program): Numbers produced by iteratively sorting the digits of the last number from largest to smallest in base 10 and then doubling, starting with the number 1.
A333306 (program): a(n) = sqrt(Pi/4)*2^A048881(2*n)*L(2*n) where L(s) = lim_{t->s} (t/2)!/((1-t)/2)!.
A333308 (program): Numbers that are the sum of two distinct terms of A003622 (1st column of the Wythoff array, A035513).
A333315 (program): a(n) = Sum_{k=1..n} phi(prime(k)-1), where phi is the Euler totient function (A000005).
A333317 (program): Partial sums of A248577.
A333319 (program): a(n) is the number of subsets of {1..n} that contain exactly 3 odd and 1 even numbers.
A333320 (program): a(n) is the number of subsets of {1..n} that contain exactly 4 odd and 1 even numbers.
A333321 (program): a(n) is the number of subsets of {1..n} that contain exactly 1 odd and 4 even numbers.
A333322 (program): Decimal expansion of (3/8) * sqrt(3).
A333326 (program): Odd numbers k such that k is the product of 2 numbers greater than one, in two or more ways.
A333329 (program): Number of winnable configurations in Lights Out game (played on a digraph) summed over every labeled digraph on n nodes.
A333334 (program): a(n) is the smallest positive number k such that n divides 3^k + k.
A333335 (program): a(n) is the smallest positive number k such that n divides 4^k + k.
A333336 (program): a(n) is the smallest positive number k such that n divides 5^k + k.
A333339 (program): a(n) is the smallest positive number k such that n divides 3^k - k.
A333340 (program): a(n) is the smallest positive number k such that n divides 4^k - k.
A333341 (program): a(n) is the smallest positive number k such that n divides 5^k - k.
A333344 (program): a(n) = 11*a(n-1) - 9*a(n-2) starting a(0)=1, a(1)=10.
A333345 (program): Decimal expansion of (11 + sqrt(85))/2.
A333353 (program): Primes p whose order of primeness A078442(p) is prime.
A333355 (program): Number of bits in binary expansion of n minus the number of digits of n when written in base 3.
A333363 (program): Horizontal visibility sequence at the onset of chaos in the 3-period cascade.
A333364 (program): Indices of primes p whose order of primeness A078442(p) is prime.
A333378 (program): a(n) = F(n) * (-1)^(n*(n-1)/2) where F(n) = A000045(n) Fibonacci numbers.
A333381 (program): Number of maximal anti-runs of the n-th composition in standard order.
A333382 (program): Number of adjacent unequal parts in the n-th composition in standard-order.
A333385 (program): a(n) = 3^n + 2 * 17^n for n >= 0.
A333392 (program): a(0) = 1; thereafter a(n) = 2^(prime(n)-1) + Sum_{k=1..n} 2^(prime(n)-prime(k)).
A333415 (program): Odd positive integers in base 2 read backwards.
A333426 (program): Primorial base Niven numbers: numbers divisible by their sum of digits in primorial base (A276150).
A333449 (program): a(n) = Sum_{k=1..n} prime(floor(n/k)).
A333451 (program): Expansion of golden ratio (1 + sqrt(5))/2 in base 3.
A333452 (program): Expansion of golden ratio (1 + sqrt(5))/2 in base 4.
A333454 (program): Expansion of golden ratio (1 + sqrt(5))/2 in base 6.
A333461 (program): a(n) = gcd(2*n, binomial(2*n,n))/2.
A333462 (program): a(n) is the number of Gaussian integers z such that (n-1)/2 < |z| <= n/2, divided by 4.
A333463 (program): a(n) = Sum_{k=1..n} floor(n/k) * gcd(n,k).
A333465 (program): a(n) = Sum_{k=1..n} ceiling(n/k) * gcd(n,k).
A333470 (program): Lexicographically earliest sequence of distinct positive terms such that a(n) is the number of commas that a(n) has to step over (to the right) to be met by an odd term. This odd term might not be the closest odd term to a(n).
A333472 (program): a(n) = [x^n] ( c (x/(1 + x)) )^n, where c(x) = (1 - sqrt(1 - 4*x))/(2*x) is the o.g.f. of the Catalan numbers A000108.
A333473 (program): a(n) = [x^n] ( S(x/(1 + x) )^n, where S(x) = (1 - x - sqrt(1 - 6*x + x^2))/(2*x) is the o.g.f. of the large Schröder numbers A006318.
A333481 (program): a(n) = [x^n] S(x)^(2*n), where S(x) = (1 - x - sqrt(1 - 6*x + x^2))/(2*x) is the o.g.f. of the large Schröder numbers A006318.
A333482 (program): a(n) = [x^(2*n)] S(x)^n, where S(x) = (1 - x - sqrt(1 - 6*x + x^2))/(2*x) is the o.g.f. of the large Schröder numbers A006318.
A333485 (program): Heinz numbers of all integer partitions sorted first by sum, then by decreasing length, and finally lexicographically. A code for the Fenner-Loizou tree A228100.
A333489 (program): Numbers k such that the k-th composition in standard order is an anti-run (no adjacent equal parts).
A333493 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * lcm(n,k) / gcd(n,k).
A333494 (program): a(1) = 1; a(n) = Sum_{k=1..n-1} ceiling(n/k) * a(k).
A333505 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * k * ceiling(n/k).
A333510 (program): Number of self-avoiding walks in the n X 2 grid graph which start at any of the n vertices on left side of the graph and terminate at any of the n vertices on the right side.
A333516 (program): Irregular triangle read by rows in which row n lists the first A000217(n) terms of A002260, n >= 1.
A333525 (program): Degree of polytope representing the number n.
A333535 (program): Card{ k<=n, k such that all prime divisors of k are < sqrt(k) }.
A333536 (program): Number of sqrt(n-1)-smooth numbers <= n.
A333537 (program): Greatest prime factor of A332559.
A333557 (program): a(n) = Sum_{d|n, gcd(d, n/d) = 1} uphi(d) * uphi(n/d), where uphi = unitary totient function (A047994).
A333558 (program): a(n) = Sum_{d|n} phi(d) * prime(d).
A333560 (program): Square array read by antidiagonals: T(n,k) = Sum_{j = 0..n*k} binomial(n+j-1,j)*2^j; n,k >= 0.
A333561 (program): a(n) = Sum_{j = 0..2*n} binomial(n+j-1,j)*2^j.
A333562 (program): a(n) = Sum_{j = 0..3*n} binomial(n+j-1,j)*2^j.
A333563 (program): a(n) = [x^n] G(x)^n, where G(x) is the o.g.f. of A079489.
A333564 (program): a(n) = [x^n] ( c(x)/c(-x) )^n, where c(x) = (1 - sqrt( 1 - 4*x))/(2*x) is the o.g.f. of the Catalan numbers A000108.
A333565 (program): O.g.f.: (1 + 4*x)/((1 + x)*sqrt(1 - 8*x)).
A333566 (program): Decimal expansion of the integral_{x=0..Pi} sin(sin(x)) dx.
A333569 (program): a(n) = Sum_{d|n} (-1)^(bigomega(d) - omega(d)) * phi(n/d).
A333570 (program): Number of nonnegative values c such that c^n == -c (mod n).
A333572 (program): a(n) is the number of Gaussian integers z with 0 < |z| <= n/2.
A333573 (program): a(n) = A333572(n)/4.
A333574 (program): Number of Hamiltonian paths in the n X 2 grid graph which start at any of the n vertices on left side of the graph and terminate at any of the n vertices on the right side.
A333576 (program): a(1) = 1; thereafter a(n) = n * uphi(n) / 2.
A333588 (program): a(n) = floor(-(3/2)*a(n-1)), a(1)=-2.
A333591 (program): Alternate multiplying and adding Fibonacci numbers: a(0) = F(0) * F(1), for n >= 0, a(2n+1) = a(2n) + F(2n+2), a(2n+2) = a(2n+1) * F(2n+3).
A333592 (program): a(n) = Sum_{k = 0..n} binomial(n + k - 1, k)^2.
A333593 (program): a(n) = Sum_{k = 0..n} (-1)^(n + k)*binomial(n + k - 1, k)^2.
A333596 (program): a(0) = 0; for n > 0, a(n) = a(n-1) + (number of 1’s and 3’s in base-4 representation of n) - (number of 0’s and 2’s in base-4 representation of n).
A333597 (program): The number of unit cells intersected by the circumference of a circle centered on the origin with radius squared equal to the norm of the Gaussian integers A001481(n).
A333599 (program): a(n) = Fibonacci(n) * Fibonacci(n+1) mod Fibonacci(n+2).
A333609 (program): The number of iterations of the infinitary totient function iphi (A091732) required to reach from n to 1.
A333611 (program): Sum of the iterated infinitary totient function iphi (A091732).
A333616 (program): Expansion of x*(1 + 2*x + x^2 - 4*x^3 - x^4 + 2*x^5)/((1 - x)^3*(1 + x)^2).
A333618 (program): a(n) is the total number of terms (1-digits) in the dual Zeckendorf representation of all divisors of n.
A333634 (program): Numbers with an even number of non-unitary prime divisors.
A333635 (program): Numbers m such that m^2 + 1 has at most 2 prime factors.
A333637 (program): The number of cells which contain multiple squares of a Genealodron formed from 2^n - 1 equal-sized squares (when viewed from above).
A333638 (program): Numbers m such that (m * sigma(m)) / tau(m) is an integer k.
A333644 (program): a(n) = Sum_{k=1..n} floor(n/k) * prime(k).
A333645 (program): a(n) = Sum_{d|n} uphi(d).
A333656 (program): Numbers having at least one 5 in their representation in base 6.
A333675 (program): Partial sums of non-Lucas numbers A057854.
A333694 (program): Expansion of Sum_{k>=1} k * x^k / (1 - x^(k^2)).
A333695 (program): Numerators of coefficients in expansion of Sum_{k>=1} phi(k) * log(1/(1 - x^k)).
A333696 (program): Denominators of coefficients in expansion of Sum_{k>=1} phi(k) * log(1/(1 - x^k)).
A333699 (program): a(n) = Sum_{d|n} phi(n/d) * pi(d).
A333700 (program): a(n) = Sum_{k=1..n} pi(k) * pi(n-k).
A333714 (program): Squares visited by a chess king moving on a square-spiral numbered board where the king moves to the adjacent unvisited square containing the spiral number with the most divisors. In case of a tie it chooses the square with the highest spiral number.
A333715 (program): a(n) = [x^(3*n)] ( (1 + x)/(1 - x) )^n.
A333718 (program): a(n) = L(8*n+4)/7, where L=A000032 (the Lucas sequence).
A333747 (program): Numbers that are either the product of two consecutive primes or two primes with a prime in between.
A333750 (program): Number of prime power divisors of n that are <= sqrt(n).
A333753 (program): Sum of prime power divisors of n that are <= sqrt(n).
A333754 (program): Sum of the areas of all r X s rectangles such that r < s, r + s = 2n and (s - r) | (s * r).
A333760 (program): Number of self-avoiding closed paths in the 4 X n grid graph which pass through all vertices on four (left, right, upper, lower) sides of the graph.
A333763 (program): a(n) = A161604(n) / A030101(A161604(n)).
A333766 (program): Maximum part of the n-th composition in standard order. a(0) = 0.
A333767 (program): Length of shortest run of zeros after a one in the binary expansion of n. a(0) = 0.
A333768 (program): Minimum part of the n-th composition in standard order. a(0) = 0.
A333771 (program): Triangular numbers that are the product of four distinct primes.
A333772 (program): a(n) = n * 2^n * (n!)^2.
A333780 (program): a(n) = g(-n) - g(n), where g corresponds to the inverse of A333773.
A333781 (program): G.f.: Sum_{k>=1} (-1)^(k + 1) * x^(k^2) / (1 - x^k).
A333782 (program): G.f.: Sum_{k>=1} (-1)^(k + 1) * k * x^(k^2) / (1 - x^k).
A333783 (program): a(n) = sigma(n) - A332993(n).
A333784 (program): a(n) = sigma(n) - A332994(n).
A333787 (program): Fully multiplicative with a(2) = 2 and a(p) = p-1 for odd primes p.
A333790 (program): Smallest path sum when iterating from n to 1 with nondeterministic map k -> k - k/p, where p is any prime factor of k.
A333791 (program): Difference of sums of two subsets of divisors of n, those obtained by repeatedly dividing with the smallest remaining prime factor (A332993) and those obtained by repeatedly dividing with the largest remaining prime factor (A332994).
A333794 (program): a(1) = 1, for n > 1, a(n) = n + a(n-A052126(n)).
A333805 (program): Number of odd divisors of n that are < sqrt(n).
A333807 (program): Sum of odd divisors of n that are < sqrt(n).
A333809 (program): G.f.: Sum_{k>=1} (-1)^(k + 1) * x^(k*(k + 1)) / (1 - x^k).
A333810 (program): G.f.: Sum_{k>=1} (-1)^(k + 1) * k * x^(k*(k + 1)) / (1 - x^k).
A333813 (program): a(n) = 2^(1 + floor(n*log_2(3))) - (3^n + 1).
A333814 (program): Multiples of 12 whose sum of digits is 12.
A333815 (program): G.f.: Sum_{k>=1} x^(k*(3*k - 1)/2) / (1 - x^(3*k)).
A333816 (program): Number of ways to write n as the difference of two hexagonal numbers.
A333817 (program): G.f.: Sum_{k>=1} x^(k*(5*k - 3)/2) / (1 - x^(5*k)).
A333818 (program): G.f.: Sum_{k>=1} x^(k*(3*k - 2)) / (1 - x^(6*k)).
A333823 (program): a(n) = Sum_{d|n, d odd} (n/d)^d.
A333824 (program): a(n) = Sum_{d|n, n/d odd} (n/d)^d.
A333828 (program): The 20-adic integer x = …70D9AE7F1DI8 satisfying x^5 = x.
A333834 (program): Multiples of 10 whose sum of digits is 10.
A333841 (program): Integers n such that n! = x^2 + y^3 + z^4 where x, y and z are nonnegative integers, is soluble.
A333842 (program): G.f.: Sum_{k>=1} k * x^(prime(k)^2) / (1 - x^(prime(k)^2)).
A333843 (program): G.f.: Sum_{k>=1} k * x^(k^3) / (1 - x^(k^3)).
A333848 (program): a(n) gives the sum of the odd numbers of the smallest nonnegative reduced residue system modulo 2*n + 1, for n >= 0.
A333870 (program): The number of iterations of the absolute Möbius divisor function (A173557) required to reach from n to 1.
A333871 (program): Sum of the iterated absolute Möbius divisor function (A173557).
A333881 (program): E.g.f.: exp(Sum_{k>=0} x^(3*k + 1) / (3*k + 1)!).
A333883 (program): E.g.f.: exp(Sum_{k>=0} x^(6*k + 1) / (6*k + 1)!).
A333884 (program): Difference between smallest cube > n and n.
A333885 (program): Number of triples (i,j,k) with 1 <= i < j < k <= n such that i divides j divides k.
A333905 (program): Lexicographically earliest sequence of distinct positive integers such that a(n) divides the concatenation of a(n+1) to a(n+2).
A333906 (program): For n >= 2, a(n) = Sum_{k=2..n} prevpower2(k) + nextpower2(k) - 2*k, where prevpower2(k) is the largest power of 2 < k, nextpower2(k) is the smallest power of 2 > k.
A333907 (program): For n >= 1, a(n) = Sum_{k=1..n} prevfib(k) + nextfib(k) - 2*k, where prevfib(k) is the largest Fibonacci number < k, nextfib(k) is the smallest Fibonacci number > k.
A333909 (program): Numbers k such that phi(k) is the sum of 2 squares, where phi is the Euler totient function (A000010).
A333937 (program): Triangle read by rows: T(n, k) = (k-1)*n - binomial(n, 2) + floor((n-k)/2) + 1, transposed.
A333972 (program): Decimal expansion of Pi^6/540 = zeta(2) * zeta(4).
A333975 (program): a(1) = 1, a(2) = 2 and for n > 2, a(n) is the smallest number not of the form OR(a(i),a(j)) for 1 <= i < j < n.
A333976 (program): Number of pairs of divisors of n, (d1,d2), such that d1 <= d2 and gcd(d1,d2) > 1.
A333988 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of (1-(k+1)*x) / (1-2*(k+1)*x+((k-1)*x)^2).
A333989 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of (1+(k-1)*x) / (1+2*(k-1)*x+((k+1)*x)^2).
A333990 (program): a(n) = Sum_{k=0..n} n^k * binomial(2*n,2*k).
A333991 (program): a(n) = Sum_{k=0..n} (-n)^k * binomial(2*n,2*k).
A333996 (program): Number of composite numbers in the triangular n X n multiplication table.
A333998 (program): Positive even integers 2k such that for all Goldbach partitions (p,q) of 2k, there exists a prime r_0 in p < r_0 < q.
A334000 (program): a(n) = (2*n+1)!! * Sum_{k=0..n} k/(2*k+1).
A334009 (program): Triangle read by rows: T(n, k) = binomial(n + k - 1, 2*k - 1) * 4^(k - 1) * n/k, 1 <= k <= n.
A334014 (program): Array read by antidiagonals: T(n,k) is the number of functions f: X->Y, where X is a subset of Y, |X| = n, |Y| = n+k, such that for every x in X, f(f(x)) != x.
A334025 (program): a(0)=0, a(1)=1; and a(n) = {2*a(n-2), 2*a(n-1)}, where {x,y} is the concatenation of x and y.
A334028 (program): Number of distinct parts in the n-th composition in standard order.
A334031 (program): The smallest number whose unsorted prime signature is the reversed n-th composition in standard order.
A334032 (program): The a(n)-th composition in standard order (graded reverse-lexicographic) is the unsorted prime signature of n.
A334033 (program): The a(n)-th composition in standard order (graded reverse-lexicographic) is the reversed unsorted prime signature of n.
A334039 (program): For any n > 0: start with x = n; for k = 1..n, if k divides x then divide x by k; a(n) corresponds to the final value of x.
A334041 (program): (a(n-2) XOR a(n-1)) OR (highest bit of a(n-2))*2 OR 1; a(0)=2, a(1)=3.
A334042 (program): Write n^2 in binary, interchange 0’s and 1’s, convert back to decimal.
A334045 (program): Bitwise NOR of binary representation of n and n-1.
A334047 (program): a(n) is the number of tilings of a bracelet of length 2n with 1 color of 5-minoes and 6-minoes, 2 colors of 7-minoes and 8-minoes, 3 colors of 9-minoes and 10-minoes, and so on.
A334051 (program): The difference between the number of prime numbers in the ranges (1, p_n] and (p_n, 2*p_n], where p_n is the n-th prime.
A334065 (program): Total area of all triangles such that p + q = 2*n, p < q (p, q prime), with base (q + p) and height (q - p).
A334066 (program): a(n) = (2n-1)!!*(Sum_{k=1..n}k/(2*k-1)).
A334070 (program): Number of even-order elements in the multiplicative group of integers modulo n.
A334074 (program): a(n) is the numerator of the sum of reciprocals of primes not exceeding n and not dividing binomial(2*n, n).
A334075 (program): a(n) is the denominator of the sum of reciprocals of primes not exceeding n and not dividing binomial(2*n, n).
A334076 (program): a(n) = bitwise NOR of n and 2n.
A334084 (program): Integers m such that only 2 binomial coefficients C(m,k), with 0<=k<=m, are practical numbers.
A334085 (program): GCD of n and the product of all primes < n.
A334087 (program): Draw the lines with equations y=kx (k=1..n) on the R^2/Z^2 square flat torus. a(n) is the number of intersection points.
A334090 (program): a(1) = 0, and then after the first differences of A064097.
A334091 (program): a(1) = 0, then after the first differences of A329697.
A334097 (program): a(n) is the exponent of the eventual power of 2 reached when starting from n and using the map k -> k + k/p, where p can be any odd prime factor of k, for example, the largest.
A334098 (program): a(n) = A334097(n) - A331410(n), where former is the exponent of the eventual power of 2 reached, and the latter is the number of iterations needed to get there, when starting from n and using the map k -> k + k/p, where p can be any odd prime factor of k, for example, the largest.
A334102 (program): Numbers n for which A329697(n) == 2.
A334103 (program): Numbers n for which A329697(n) == 3.
A334104 (program): Numbers m for which A329697(m) = 4.
A334105 (program): Numbers m for which A329697(m) = 5.
A334106 (program): Numbers n for which A329697(n) == 6.
A334110 (program): The squares of squarefree numbers (A062503), ordered lexicographically according to their prime factors. a(n) = Product_{k in I} prime(k+1)^2, where I are the indices of nonzero binary digits in n = Sum_{k in I} 2^k.
A334117 (program): Odd numbers with abundancy >= 3/2; that is, numbers m such that sigma(m) >= 3m/2.
A334122 (program): a(n) is the sum of all primes <= n, mod n.
A334135 (program): Number of dimer tilings of a 2*n x 4 Moebius strip.
A334136 (program): a(n) = (n-1)*sigma(n) where sigma is the sum of divisors A000203.
A334142 (program): Indices of twin primes.
A334143 (program): a(n) = bitwise NOR of prime(n) and prime(n+1).
A334146 (program): Numbers with at least two prime factors greater than 3 counted with multiplicity.
A334155 (program): a(n) is the number of length n decorated permutations avoiding the pattern 001.
A334156 (program): Triangle read by rows: T(n,m) is the number of length n decorated permutations avoiding the word 0^m = 0…0 of m 0’s, where 1 <= m <= n.
A334157 (program): Row sums of array A158777.
A334158 (program): Number of Goldbach partitions (p,q) of 2n such that primes p and q can be written as the sum of two primes.
A334160 (program): Even numbers with a Goldbach partition (p,q), p < q, such that p and q can be written as the sum of two primes.
A334163 (program): Primes p whose continued fraction expansion of sqrt(p) has a 1 in the second position.
A334168 (program): Numbers m whose leading digit and the other decimal digits appear respectively before and directly after the decimal point of its m-th root.
A334169 (program): a(n) is the number of ON-cells in the n-th full level of ON-cells of a triangular wedge in the hexagonal grid of A151723 (after 2^k >= n generations have been computed).
A334172 (program): Bitwise XNOR of prime(n) and prime(n + 1).
A334190 (program): a(n) = exp(1/2) * Sum_{k>=0} (2*k + 1)^n / ((-2)^k * k!).
A334191 (program): a(n) = exp(1/3) * Sum_{k>=0} (3*k + 1)^n / ((-3)^k * k!).
A334195 (program): a(1) = 0, then after the first differences of A064415.
A334196 (program): a(1) = 0, then after the first differences of A003434.
A334201 (program): a(n) = A056239(n) - A061395(n).
A334202 (program): a(n) = A064097(n) - A323077(n).
A334203 (program): a(n) = A064097(A032742(n)).
A334204 (program): a(n) = A329697(A163511(n)).
A334207 (program): Number of ways to write 2n as the sum of two nonprime positive integers.
A334208 (program): Number of partitions of 2n into two composite parts, (r,s), such that r and s have the same number of primes less than or equal to them.
A334209 (program): Number of solutions to n = i+j, 0 <= i,j <= n for which A010060(i)=A010060(j)=0, i != j.
A334210 (program): a(n) = sigma(prime(n) + 1) - sigma(prime(n)).
A334216 (program): a(n) is the number of distinct terms in the n-th row of A334215.
A334224 (program): Consider a graph as defined in A306302 formed from a row of n adjacent congruent squares with the diagonals of all possible rectangles; a(n) is the minimum edge length of the squares such that the vertices formed by all intersections have integer x and y coordinates.
A334227 (program): Length of the shortest prefix of the Thue-Morse sequence (A010060) containing, as subwords, all length-n blocks appearing in A010060.
A334229 (program): Sum of the areas of all r X s rectangles such that r + s = 2n, with r, s composite.
A334237 (program): a(n) = 2*Sum_{k=0..n-1} binomial(n,k)^2*binomial(n,k+1)^2.
A334239 (program): Number of r X s rectangles with composite side lengths such that r + s = 2n, r <= s and r | s.
A334240 (program): a(n) = exp(-n) * Sum_{k>=0} (k + 1)^n * n^k / k!.
A334242 (program): a(n) = exp(-n) * Sum_{k>=0} (k + n)^n * n^k / k!.
A334260 (program): Sum of the largest composite parts in the partitions of 2n into two parts.
A334277 (program): Perimeters of almost-equilateral Heronian triangles.
A334281 (program): Number of n-colorings of the vertices of the 4-dimensional cross polytope such that no two adjacent vertices have the same color.
A334293 (program): First quadrisection of Padovan sequence.
A334308 (program): Base phi Niven numbers: numbers divisible by the number of 1’s in their base phi representation (A055778).
A334316 (program): E.g.f. A(x) satisfies: A(x) = x * exp(A(x)) * (1 - A(x)).
A334320 (program): Number of even integers in base n with exactly two distinct digits.
A334321 (program): Non-palindromic primes.
A334341 (program): a(n) = Sum_{p|n, p prime} (n - p).
A334347 (program): Number of r X s rectangles such that r + s = 2n, where exactly one of r or s is a positive square.
A334349 (program): Total area of all r X s rectangles with integer side lengths such that r + s = n, r < s and (s - r) | (s * r).
A334361 (program): Number of r X s rectangles with squarefree side lengths such that r < s, r + s = 2n and r | s.
A334363 (program): Decimal expansion of Sum_{k>=0} 1/(4*k+1)!.
A334364 (program): Decimal expansion of Sum_{k>=0} 1/(4*k+2)!.
A334366 (program): Decimal expansion of Sum_{k>=0} 1/(4*k)!!.
A334367 (program): Decimal expansion of Sum_{k>=0} 1/(4*k+2)!!.
A334378 (program): Decimal expansion of Sum_{k>=0} 1/((2*k+1)!)^2.
A334379 (program): Decimal expansion of Sum_{k>=0} 1/((2*k)!)^2.
A334380 (program): Decimal expansion of Sum_{k>=0} (-1)^k/((2*k)!!)^2.
A334381 (program): Decimal expansion of Sum_{k>=0} 1/(2^k*(k!)^2).
A334383 (program): Decimal expansion of Sum_{k>=0} (-1)^k/(2^k*(k!)^2).
A334387 (program): The difference version of the ‘Decade transform’ : to obtain a(n) write n as a sum of its power-of-ten parts and then continue to calculate the absolute value of the difference between the adjacent parts until a single number remains.
A334391 (program): Numbers whose only palindromic divisor is 1.
A334395 (program): Partial products of A334393.
A334396 (program): Number of fault-free tilings of a 3 X n rectangle with squares and dominoes.
A334397 (program): Decimal expansion of (e - 2)/e.
A334403 (program): Harshad numbers with sum of digits equal to 18.
A334413 (program): First differences of A101803.
A334414 (program): First differences of A334415.
A334415 (program): Nearest integer to n*(2-phi), where phi is the golden ratio (A001622).
A334422 (program): Decimal expansion of Pi/128.
A334461 (program): a(n) is the number of partitions of n into consecutive parts that differ by 4.
A334463 (program): a(n) is the sum of all parts of all partitions of n into consecutive parts that differ by 3.
A334464 (program): a(n) is the total number of parts in all partitions of n into consecutive parts that differ by 4.
A334473 (program): The n-cowboy shootout problem: a(3^k) = 3^k, a((3^k)+b) = b if (3^k)+b <= 2*3^k, otherwise a((3^k)+b) = 2*b-3^k, where b is a positive integer.
A334490 (program): a(n) = Sum_{d|n} gcd(d, sigma(d)).
A334491 (program): a(n) = Product_{d|n} gcd(d, sigma(d)).
A334501 (program): Eventual period of a single cell in rule 190 cellular automaton in a cyclic universe of width n.
A334520 (program): Primes that are the sum of two cubes.
A334541 (program): a(n) is the number of partitions of n into consecutive parts that differ by 5.
A334551 (program): Number of fixed polyominoes with 2n-1 cells and width and height both equal to n.
A334562 (program): E.g.f.: exp(-(x + x^2 + x^3)).
A334563 (program): a(n) is the maximum number of 4-cycles possible in an n-vertex planar graph.
A334564 (program): E.g.f.: exp(-(x + x^2 + x^3 + x^4)).
A334565 (program): E.g.f.: exp(-(x + x^2 + x^3 + x^4 + x^5)).
A334569 (program): E.g.f.: exp(-(x + x^2/2 + x^3/3)).
A334570 (program): E.g.f.: exp(-(x + x^2/2 + x^3/3 + x^4/4)).
A334571 (program): E.g.f.: exp(-(x + x^2/2 + x^3/3 + x^4/4 + x^5/5)).
A334572 (program): Let x(n, k) be the exponent of prime(k) in the factorization of n, then a(n) = Max_{k} abs(x(n,k)- x(n-1,k)).
A334573 (program): Partial sums of A334572.
A334576 (program): a(n) is the X-coordinate of the n-th point of the space filling curve P defined in Comments section; sequence A334577 gives Y-coordinates.
A334577 (program): a(n) is the Y-coordinate of the n-th point of the space filling curve P defined in Comments section; sequence A334576 gives X-coordinates.
A334578 (program): Double subfactorials: a(n) = (-1)^floor(n/2) * n!! * Sum_{i=0..floor(n/2)} (-1)^i/(n-2*i)!!.
A334579 (program): a(n) = Sum_{d|n} gcd(tau(d), sigma(d)).
A334580 (program): Denominator of Sum_{k=1..n} (-1)^(k+1)/k^2.
A334582 (program): Denominator of Sum_{k=1..n} (-1)^(k+1)/k^3.
A334585 (program): Denominator of Sum_{k=1..n} (-1)^(k+1)/k^4.
A334595 (program): Binary interpretation of the right diagonal of the XOR-triangle with first row generated from the binary expansion of n.
A334603 (program): Period length of the fraction 1/11^n for n >= 1.
A334604 (program): Denominator of Sum_{k=1..n} (-1)^(k+1)/k^5.
A334605 (program): Denominator of Sum_{k=1..n} (-1)^(k+1)/k^6.
A334608 (program): a(n) is the total number of down-steps after the final up-step in all 3_1-Dyck paths of length 4*n (n up-steps and 3n down-steps).
A334609 (program): a(n) is the total number of down-steps after the final up-step in all 3_2-Dyck paths of length 4*n (n up-steps and 3*n down-steps).
A334610 (program): a(n) is the total number of down-steps after the final up-step in all 4_1-Dyck paths of length 5*n (n up-steps and 4*n down-steps).
A334611 (program): a(n) is the total number of down-steps after the final up-step in all 4_2-Dyck paths of length 5*n (n up-steps and 4*n down-steps).
A334612 (program): a(n) is the total number of down-steps after the final up-step in all 4_3-Dyck paths of length 5*n (n up-steps and 4*n down-steps).
A334614 (program): a(n) = pi(prime(n) - n) + n, where pi is the prime counting function.
A334625 (program): Maximal size of a subset T of S = {1,2,…,n} with a cyclic arrangement of T such that any three neighbors can be reordered in an arithmetic progression.
A334628 (program): Total area of all distinct rectangles whose length and width are relatively prime and L + W = n.
A334632 (program): Decimal expansion of Sum_{k>=0} (-1)^k / ((2*k)!)^2.
A334656 (program): a(n) is the number of words of length n on the alphabet {0,1,2} with the number of 0’s plus the number of 1’s congruent to the number of 2’s modulo 3.
A334657 (program): Dirichlet g.f.: 1 / zeta(s-2).
A334659 (program): Dirichlet g.f.: 1 / zeta(s-3).
A334660 (program): Dirichlet g.f.: 1 / zeta(s-4).
A334662 (program): a(n) = Sum_{d|n} gcd(tau(d), pod(d)), where pod(k) is the product of the divisors of k (A007955).
A334663 (program): a(n) = Sum_{d|n} gcd(sigma(d), pod(d)), where pod(k) is the product of the divisors of k (A007955).
A334664 (program): a(n) = Product_{d|n} gcd(d, tau(d)).
A334668 (program): Numerator of Sum_{k=1..n} (-1)^(k+1)/k^7.
A334669 (program): Denominator of Sum_{k=1..n} (-1)^(k+1)/k^7.
A334670 (program): a(n) = (2*n+1)!! * (Sum_{k=1..n} 1/(2*k+1)).
A334671 (program): Number of ways to write n as the sum of a squarefree number (A005117) and a square (A000290).
A334673 (program): a(n) = 23*a(n-1) - a(n-2) + 1 for n > 1, a(0)=0, a(1)=1.
A334680 (program): a(n) is the total number of down-steps after the final up-step in all 2-Dyck paths of length 3*n (n up-steps and 2*n down-steps).
A334682 (program): a(n) is the total number of down-steps after the final up-step in all 3-Dyck paths of length 4*n (n up-steps and 3*n down-steps).
A334694 (program): a(n) = (n/4)*(n^3+2*n^2+5*n+8).
A334702 (program): Array read by antidiagonals: T(n,k) = binomial(n*k,3), n>=0, k>=0.
A334703 (program): Triangle read by rows: T(n,k) = binomial(n*k,3) (0 <= k <= n).
A334706 (program): Number of collinear triples in a 4 X n rectangular grid.
A334714 (program): Partial sums of A335294.
A334715 (program): A(n,k) = !n + [n > 0] * (k * n!), where !n = A000166(n) is subfactorial of n and [] is an Iverson bracket; square array A(n,k), n>=0, k>=0, read by antidiagonals.
A334716 (program): a(n) = !n + n * n!, where !n = A000166(n) is subfactorial of n.
A334719 (program): a(n) is the total number of down-steps after the final up-step in all 4-Dyck paths of length 5*n (n up-steps and 4*n down-steps).
A334721 (program): Denominator of the product of n and the n-th harmonic alternating number, Sum_{k=1..n} (-1)^(k+1)/k.
A334724 (program): Denominator of the sum of all elements of the n X n matrix M with M[i,j] = (-1)^(i+j)*i/j for i,j = 1..n.
A334727 (program): Binary interpretation of the left diagonal of the XOR-triangle with first row generated from the binary expansion of n, with most significant bit given by first row.
A334729 (program): a(n) = Product_{d|n} gcd(tau(d), sigma(d)).
A334730 (program): a(n) = Product_{d|n} gcd(tau(d), pod(d)) where tau(k) is the number of divisors of k (A000005) and pod(k) is the product of divisors of k (A007955).
A334731 (program): a(n) = Product_{d|n} gcd(sigma(d), pod(d)) where sigma(k) is the sum of divisors of k (A000203) and pod(k) is the product of divisors of k (A007955).
A334732 (program): a(n) is the total number of parts in all partitions of n into consecutive parts that differ by 5.
A334733 (program): a(n) is the sum of all parts of all partitions of n into consecutive parts that differ by 5.
A334734 (program): Denominator of Sum_{k=1..n} k^4 / Product_{k=1..n} k^4.
A334735 (program): Denominator of Sum_{k=1..n} k^2 / Product_{k=1..n} k^2.
A334745 (program): Starting with a(1) = a(2) = 1, proceed in a square spiral, computing each term as the sum of diagonally adjacent prior terms.
A334759 (program): Perimeters of Pythagorean triangles with even side lengths.
A334762 (program): a(n) = ceiling (n / A000005(n)).
A334764 (program): a(n) = Product_{k=1..n} d(2*k - 1), where d() is the number of divisors function A000005.
A334767 (program): a(n) = Product_{k=1..n} d(2*k), where d() is the number of divisors function A000005.
A334768 (program): Self-convolution of A061397.
A334776 (program): Total number of peaks in all permutations of 2 indistinguishable copies of 1..n.
A334777 (program): Total number of local maxima in all permutations of 2 indistinguishable copies of 1..n.
A334781 (program): Array read by antidiagonals: T(n,k) = Sum_{i=1..n} binomial(1+i,2)^k.
A334782 (program): a(n) = Sum_{d|n} lcm(d, tau(d)).
A334783 (program): a(n) = Sum_{d|n} lcm(d, sigma(d)).
A334784 (program): a(n) = Sum_{d|n} lcm(tau(d), sigma(d)).
A334789 (program): a(n) = 2^log_2*(n) where log_2*(n) = A001069(n) is the number of log_2(log_2(…log_2(n))) iterations needed to reach < 2.
A334793 (program): a(n) = Sum_{d|n} lcm(tau(d), pod(d)) where tau(k) is the number of divisors of k (A000005) and pod(k) is the product of divisors of k (A007955).
A334794 (program): a(n) = Sum_{d|n} lcm(sigma(d), pod(d)) where sigma(k) is the sum of divisors of k (A000203) and pod(k) is the product of divisors of k (A007955).
A334795 (program): a(n) = Product_{d|n} lcm(d, tau(d)) where tau(k) is the number of divisors of k (A000005).
A334800 (program): a(n) is the number of values d*p less than n, where d is a divisor of n, p is a prime, and d*p is not a divisor of n.
A334802 (program): Positive integers of the form x^4 - y^4 that have exactly 4 divisors.
A334805 (program): a(n) = Product_{d|n} lcm(d, sigma(d)) where sigma(k) is the sum of divisors of k (A000203).
A334806 (program): a(n) = Product_{d|n} lcm(tau(d), sigma(d)) where tau(k) is the number of divisors of k (A000005) and sigma(k) is the sum of divisors of k (A000203).
A334807 (program): a(n) = Product_{d|n} lcm(tau(d), pod(d)) where tau(k) is the number of divisors of k (A000005) and pod(k) is the product of divisors of k (A007955).
A334809 (program): a(n) = Product_{d|n} lcm(sigma(d), pod(d)) where sigma(k) is the sum of divisors of k (A000203) and pod(k) is the product of divisors of k (A007955).
A334820 (program): Sequence is limit_{t->oo} s_t, where s_k = s_{k-1},s_{k-1}[k-1..end] starting with s_0 = s_0[0..1] = 0,1.
A334840 (program): a(1) = 1, a(n) = a(n-1)/gcd(a(n-1),n) if this gcd is > 1, else a(n) = 4*a(n-1).
A334841 (program): a(0) = 0; for n > 0, a(n) = (number of 1’s and 3’s in base 4 representation of n) - (number of 0’s and 2’s in base 4 representation of n).
A334843 (program): Decimal expansion of arclength between (0,0) and (Pi/6,1/2) on y = sin x.
A334852 (program): a(1) = 1, a(n) = a(n-1) / gcd(a(n-1),n) if this gcd is > 1, else a(n) = a(n-1) + 2.
A334854 (program): E.g.f. A(x) satisfies: A(x) = arctan(x * exp(A(x))).
A334863 (program): a(n) = A064097(A003961(n)).
A334880 (program): Numbers k such that gcd(k, k-th composite number) > 1.
A334891 (program): Number of ways to choose 4 points that form an square from the A000292(n) points in a regular tetrahedral grid where each side has n vertices.
A334907 (program): Comtet’s expansion of the e.g.f. (sqrt(1 + sqrt(8*s)) - sqrt(1 - sqrt(8*s)))/ sqrt(8*s * (1 - 8*s)).
A334908 (program): Area/6 of primitive Pythagorean triangles generated by {{2, 0}, {1, -1}}^n*{{2}, {1}}, for n >= 0.
A334909 (program): Area/6 of primitive Pythagorean triangles given in A334638 as triples.
A334912 (program): a(n) = numerator (2^(4*n-1) * (2^(4*n-2) - 1) * (Bernoulli(4*n-2) / (4*n-2)!) * ((2*n-2)! / Euler(2*n-2))^2).
A334913 (program): a(n) is the sum of digits of n in signed binary nonadjacent form.
A334914 (program): Least positive multiple of n that when written in base 10 uses only 0’s, 1’s, 2’s and 3’s.
A334919 (program): Numbers of the form i + j + 3*i*j for i,j >= 1 together with numbers of the form -i - j + 3*i*j for i,j >= 2.
A334921 (program): Expansion of Phi(x) = (1/(1+x))*Product_{k>=0} (1-(x/(1+x))^2^k).
A334922 (program): Square array T(n,k) = ((3/2)*n*k + (1/2)*A319929(n,k))/2, n >= 1, k >= 1, read by antidiagonals.
A334923 (program): Square array T(n,k) = ((5/2)*n*k - (1/2)*A319929(n,k))/2, n >= 1, k >= 1, read by antidiagonals.
A334924 (program): G.f.: Sum_{k>=1} x^(k^2*(k + 1)/2) / (1 - x^(k^2*(k + 1)/2)).
A334925 (program): G.f.: Sum_{k>=1} x^(k*(k^2 + 1)/2) / (1 - x^(k*(k^2 + 1)/2)).
A334926 (program): G.f.: Sum_{k>=1} x^(k*(2*k^2 + 1)/3) / (1 - x^(k*(2*k^2 + 1)/3)).
A334930 (program): Numbers that generate rotationally symmetrical XOR-triangles featuring singleton zero bits in a hexagonal arrangement.
A334940 (program): Partial sums of A230595.
A334948 (program): a(n) is the number of partitions of n into consecutive parts that differ by 6.
A334949 (program): a(n) is the total number of parts in all partitions of n into consecutive parts that differ by 6.
A334953 (program): a(n) is the sum of all parts of all partitions of n into consecutive parts that differ by 6.
A334954 (program): a(n) is 1 plus the number of divisors of n.
A334957 (program): Triangular array read by rows. T(n,k) is the number of labeled digraphs on n nodes with exactly k self loops, n>=0, 0<=k<=n.
A334958 (program): GCD of consecutive terms of the factorial times the alternating harmonic series.
A334969 (program): Heinz numbers of alternately strong integer partitions.
A334971 (program): a(n) is the least prime p such that p+2 is divisible by n-th prime.
A334976 (program): a(n) is the total number of down steps between the (n-1)-th and n-th up steps in all 2-Dyck paths of length 3*n. A 2-Dyck path is a nonnegative path with steps (1, 2), (1, -1) that starts and ends at y = 0.
A334977 (program): a(n) is the total number of down steps between the (n-1)-th and n-th up steps in all 2_1-Dyck paths of length 3*n. A 2_1-Dyck path is a lattice path with steps (1, 2), (1, -1) that starts and ends at y = 0 and stays above the line y = -1.
A334978 (program): a(n) is the total number of down steps between the (n-1)-th and n-th up steps in all 3-Dyck paths of length 4*n. A 3-Dyck path is a nonnegative lattice path with steps (1, 3), (1, -1) that starts and ends at y = 0.
A334979 (program): a(n) is the total number of down steps between the (n-1)-th and n-th up steps in all 3_1-Dyck paths of length 4*n. A 3_1-Dyck path is a lattice path with steps (1, 3), (1, -1) that starts and ends at y = 0 and stays above the line y = -1.
A334980 (program): a(n) is the total number of down steps between the (n-1)-th and n-th up steps in all 3_2-Dyck paths of length 4*n. A 3_2-Dyck path is a lattice path with steps (1, 3), (1, -1) that starts and ends at y = 0 and stays above the line y = -2.
A334987 (program): Sum of centered triangular numbers dividing n.
A334988 (program): Sum of tetrahedral numbers dividing n.
A334991 (program): a(n) = 4^n + 3 * 18^n.
A334992 (program): a(n) is the smallest number larger than a(n-1) whose a(i)-th binary digit is 0 for all i<n, with a(1)=1.
A334995 (program): Twice the area of triangle with coordinates (Fn, Fn+k), (Fn+2k, Fn+3k) and (Fn+4k, Fn+5k), where Fn is the n-th Fibonacci number A000045.
A335021 (program): a(n) = Sum_{d|n, 1 < d < n} (-1)^(d + 1).
A335022 (program): a(n) = Sum_{d|n, 1 < d < n} (-1)^(d + 1) * d.
A335023 (program): Ratios of consecutive terms of A334958.
A335024 (program): Ratios of consecutive terms of A056612.
A335025 (program): Largest side lengths of almost-equilateral Heronian triangles.
A335026 (program): a(n) = (n + 1)^2*a(n - 2) + a(n - 1), starting 0, 9, ….
A335031 (program): Complement of A334919.
A335032 (program): Dirichlet g.f.: zeta(s) * zeta(s-1) * Product_{p prime} (1 + p^(1 - s) - p^(-s)).
A335033 (program): a(n) is the smallest number larger than a(n-1) that is not a partial sum of 2^a(1),2^a(2),…,2^a(n-1), with a(1)=0.
A335048 (program): Minimum sum of primes (see Comments).
A335050 (program): Array read by descending antidiagonals, T(n,k) is the number of nodes in the pill tree with initial conditions (n,k), for n and k >= 0.
A335062 (program): a(n) = 1 - Sum_{d|n, d > 1} (-1)^d * a(n/d).
A335063 (program): a(n) = Sum_{k=0..n} (binomial(n,k) mod 2) * k.
A335064 (program): Let m = d*q + r be the Euclidean division of m by d. The terms m of this sequence satisfy that q, r, d are consecutive positive integer terms in a geometric progression with a noninteger common ratio > 1.
A335073 (program): a(n) = Sum_{k=1..n} 2^(bigomega(k) - omega(k)).
A335075 (program): Positions of 1’s when Kolakoski sequence is grouped into four independent numbers as 1, 2, 11, 22.
A335087 (program): Row sums of A335436.
A335090 (program): a(n) = ((2*n+1)!!)^2 * (Sum_{k=1..n} 1/(2*k+1)^2).
A335091 (program): a(n) = ((2*n+1)!!)^3 * (Sum_{k=1..n} 1/(2*k+1)^3).
A335092 (program): a(n) = ((2*n+1)!!)^4 * (Sum_{k=1..n} 1/(2*k+1)^4).
A335094 (program): Decimal expansion of (15 - 4*sqrt(2))/8.
A335107 (program): Least period of the length-n prefix of the Thue-Morse sequence A010060.
A335108 (program): Number of periods of the length-n prefix of the Thue-Morse sequence (A010060).
A335110 (program): a(n) = Sum_{k=0..n} (Stirling1(n,k) mod 2) * k.
A335111 (program): a(n) = n! * Sum_{k=0..n-1} (-2)^k / k!.
A335115 (program): a(2*n) = 2*n - a(n), a(2*n+1) = 2*n + 1.
A335129 (program): a(n) is the number of distinct lines created inside an n-gon when connecting vertex k to vertex 2k mod n.
A335131 (program): a(n) = Sum_{k=1..n} phi(k)*phi(k+1)*phi(k+2), where phi(k) = A000010(k) is Euler’s totient function.
A335137 (program): a(n) = floor(n*Im(2*e^(i*Pi/5))).
A335139 (program): a(n) = (prime(n + 1) +- k) / 2 where k is the smallest possible odd number such that a(n) is prime and a(n + 1) >= a(n).
A335147 (program): Perimeters of Heronian triangles whose middle side length divides their perimeter.
A335153 (program): a(1)=0; thereafter a(n) = (n-1)*sigma(n)-n*sigma(n-1) where sigma is the sum-of-divisors function A000203.
A335155 (program): Start with 1; if n is in the sequence, so are n+5 and 3*n.
A335167 (program): Nim n-th power of 8.
A335169 (program): Nim n-th power of 10.
A335182 (program): Sum of the refactorable divisors of n.
A335184 (program): a(n) is the number of subsets of {1,2,…,n} with at least two elements and the difference between successive elements at least 6.
A335187 (program): Total area of all trapezoids with bases p+q, q-p and height p*q with p,q prime, n = p+q and p < q.
A335206 (program): a(n) is the total binary weight of all persolus bitstrings of length n.
A335227 (program): G.f.: x / (Sum_{k>=1} k * x^k / (1 + x^k)).
A335228 (program): G.f.: x / (Sum_{k>=1} x^k / (1 + x^k)^2).
A335229 (program): Numbers expressible as the sum of two terms of A001950.
A335234 (program): Number of partitions of k_n into two parts (s,t) such that k_n | s*t, where k_n is the n-th nonsquarefree number (A013929).
A335242 (program): a(n) = 2*a(n-1) + a(n-3) for n >= 4, with initial values a(0) = 1, a(1) = 0, a(2) = 2, and a(3) = 3.
A335248 (program): Perimeters of isosceles Heronian triangles whose smallest two side lengths are equal.
A335249 (program): Perimeters of isosceles Heronian triangles whose largest two side lengths are equal.
A335257 (program): Numerators of expansion of arctanh(tan(x)) (odd powers only).
A335258 (program): Denominators of expansion of arctanh(tan(x)) (odd powers only).
A335259 (program): Triangle read by rows: T(n,k) = k^ceiling(n/k) for 1 <= k <= n.
A335262 (program): Triangle of triangular numbers, read by rows, constructed like this: Given a sequence t, start row 0 with t(0). Compute row n for n > 0 by reversing row n-1 and prepending t(n). The sequence t is here chosen as the triangular numbers.
A335265 (program): a(n) = Denominator(-4*n^2*Zeta(1 - n)^2*(1 - 2^n)) for n >= 1, a(0) = 1.
A335274 (program): a(n) = 2*a(n-1) + a(n-3), where a(0) = 0, a(1) = 1, a(2) = 4.
A335275 (program): Numbers k such that the largest square dividing k is a unitary divisor of k.
A335283 (program): a(n) = 1 + Sum_{d|n, n/d odd, d < n} a(d).
A335285 (program): a(n) is the greatest possible greatest part of any partition of n into prime parts.
A335294 (program): a(n) = pi(n) - pi(Sum_{k=1..n-1} a(k)) with a(1) = 1, where pi() is the prime counting function A000720.
A335298 (program): a(n) is the squared distance between the points P(n) and P(0) on a plane, n >= 0, such that the distance between P(n) and P(n+1) is n+1 and, going from P(n) to P(n+2), a 90-degree left turn is taken in P(n+1).
A335309 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+k,k) * n^(n-k).
A335310 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+k,k) * (-n)^(n-k).
A335312 (program): A(n, k) = k! [x^k] exp(2*x)*(y*sinh(x*y) + cosh(x*y)) and y = sqrt(n). Square array read by ascending antidiagonals, for n >= 0 and k >= 0.
A335322 (program): Triangle read by rows: T(n, k) = binomial(n, floor((n+k+1)/2) with k <= n.
A335323 (program): First lower diagonal of Parker’s triangle A047812.
A335324 (program): Square part of 4th-power-free part of n.
A335331 (program): a(n) = prime(k) where k is the n-th 7-smooth number.
A335334 (program): Sum of the integers in the reduced residue system of A002110(n).
A335338 (program): P_5(2n+1), the Legendre polynomial of order 5 at 2n+1.
A335340 (program): North-East paths from (0,0) to (n,n) with k cyclic descents.
A335341 (program): Sum of divisors of A003557(n).
A335344 (program): E.g.f.: exp(x^2/(2*(1 - x)^2)).
A335345 (program): E.g.f.: exp(x^2/(2*(1 - x)^3)).
A335354 (program): a(n) is the number of edges in the central polygon formed in a square by dividing each of its sides into n equal parts giving a total of 4*n nodes and drawing straight line segments from node k to node (k+n+1) mod 4*n, 0 <= k < 4*n.
A335365 (program): Numbers that are unreachable by the process of starting from 1 and adding 5 and/or multiplying by 3.
A335386 (program): Tri-unitary highly composite numbers: where the number of tri-unitary divisors (A335385) increases to a record.
A335401 (program): a(n) is the smallest positive number such that the decimal digits of n*a(n) are all 0, 1, 2 or 3.
A335402 (program): Numbers m such that the only normal integer partition of m whose run-lengths are a palindrome is (1)^m.
A335403 (program): If n = Product_{i=1..k} p_i^e_i then a(n) = Sum_{i=1..k} e_i * prime(p_i).
A335408 (program): Diameter of nearest neighbor interchange distance for free 3-trees.
A335415 (program): Decimal expansion of Sum_{k>=0} 1/cosh(Pi*k).
A335420 (program): a(n) = A000120(A163511(n)).
A335422 (program): a(n) = A005940(1+A163511(n)).
A335429 (program): Partial sums of A329697.
A335433 (program): Numbers whose multiset of prime indices is separable.
A335436 (program): Triangle read by rows: T(n,k) = 2*n+1 for k = 0 and otherwise T(n,k) = Sum_{i=n-k..n, j=0..i-n+k, i<>n or j<>k} T(i,j).
A335437 (program): Numbers k with a partition into two distinct parts (s,t) such that k | s*t.
A335439 (program): a(n) = n*(n-1)/2 + 2^(n-1) - 1.
A335447 (program): Number of (1,2)-matching permutations of the prime indices of n.
A335449 (program): Number of (1,2,1)-avoiding permutations of the prime indices of n.
A335450 (program): Number of (2,1,2)-avoiding permutations of the prime indices of n.
A335451 (program): Number of permutations of the prime indices of n with all equal parts contiguous and none appearing more than twice.
A335485 (program): Numbers k such that the k-th composition in standard order (A066099) is not weakly decreasing.
A335486 (program): Numbers k such that the k-th composition in standard order (A066099) is not weakly increasing.
A335487 (program): Number of (1,1)-matching permutations of the prime indices of n.
A335489 (program): Number of strict permutations of the prime indices of n.
A335500 (program): 2nd Lucas-Wythoff array (w(n,k)), by antidiagonals; see Comments.
A335509 (program): Number of patterns of length n matching the pattern (1,1,2).
A335511 (program): Number of (1,1,1)-avoiding permutations of the prime indices of n.
A335516 (program): Number of normal patterns contiguously matched by the prime indices of n in increasing or decreasing order, counting multiplicity.
A335519 (program): Number of contiguous divisors of n.
A335530 (program): Expansion of e.g.f. (1 - 2*log(1 + x))/(1 - 3*log(1 + x)).
A335531 (program): Expansion of e.g.f. 1/(1-3*log(1+x)).
A335534 (program): a(n) = tribonacci(n) modulo Fibonacci(n).
A335549 (program): Number of normal patterns matched by the multiset of prime indices of n in weakly increasing order.
A335550 (program): Number of minimal normal patterns avoided by the prime indices of n in increasing or decreasing order, counting multiplicity.
A335551 (program): Number of words of length n over the alphabet {0,1,2} that contain the substring 12 but not the substring 01.
A335559 (program): a(n) = 3*a(n-1) + 4*a(n-2) - 2*a(n-3) with a(0)=0, a(1)=1, a(2)=2.
A335567 (program): Number of distinct positive integer pairs (s,t) such that s <= t < n where neither s nor t divides n.
A335587 (program): a(n) is the sum of the numbers k such that 0 <= k <= n and n AND k = 0 (where AND denotes the bitwise AND operator).
A335595 (program): E.g.f.: exp(-x * (2 + x)) / (1 - x)^2.
A335599 (program): Sequence is limit_{k->oo} s_k, where s_k = s_{k-1}, s_{k-1}[k-1] + 2^(k-1), …, s_{k-1}[end] + 2^(k-1) starting with s_0 = s_0[0..1] = 0,0.
A335602 (program): Number of 3-regular cubic partitions of n.
A335603 (program): a(n) = p*q where p is the sequential number (or PrimePi, A000720) of the largest prime divisor of n, and q is the maximal exponent in the canonical representation of n (A051903).
A335607 (program): Rectangular array by antidiagonals: T(n,k) = floor(n + k*r), where r = sqrt(2).
A335608 (program): Number of sets (in the Hausdorff metric geometry) at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 2) missing one edge.
A335612 (program): Number of sets (in the Hausdorff metric geometry) at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 3) missing two edges, where the removed edges are incident to the same vertex in the three point part.
A335616 (program): a(n) is twice the number of partitions of n into consecutive parts, minus the number of partitions of n into consecutive parts that contain 1 as a part.
A335639 (program): Sum of the positive differences of the cubed parts in each partition of n into two parts.
A335647 (program): a(n) = binomial(4*n+1,n+1).
A335648 (program): Partial sums of A006010.
A335649 (program): a(n) is the frequency of multi-pairs in a sequence of multi-set designs with 2 blocks.
A335650 (program): Numbers that are multiples of 2,3,5, or 7 but not multiples of the product of any combination of 2,3,5, and 7.
A335652 (program): Numbers k such that Omega(k+1) = Omega(k) + 2, where Omega(k) = A001222(k) is the number of prime factors of k with multiplicity.
A335655 (program): Numbers k such that Omega(k+1) = Omega(k) + m, where Omega(k) = A001222(k) is the number of prime factors of k with multiplicity, case m = 3.
A335657 (program): Numbers whose prime factors (including repetitions) sum to an odd number.
A335660 (program): a(n) = n - A334714(n).
A335665 (program): Product of the refactorable divisors of n.
A335668 (program): Even composites m such that A002203(m)==2 (mod m).
A335690 (program): a(1) = 1, a(2) = a(3) = 2; a(n) = (a(n-1) + a(n-2) + 1)/a(n-3) (for n>3).
A335691 (program): A000166(n)^2.
A335692 (program): Inverse BINOMIAL transform of A335691.
A335693 (program): A000904(n) - (-1)^n.
A335694 (program): a(n) = 3*binomial(n,4) - 6*binomial(n,3) + 4*binomial(n,2) - 2.
A335699 (program): Irregular tree read by rows: take the Stern-Brocot tree A007305(n)/A007306(n) and set a(n) = A007306(n) - A007305(n) mod 3.
A335700 (program): A variant of A000179 and A102761.
A335708 (program): a(n) is the number of divisors of the n-th Niven number.
A335711 (program): The number of free polyominoes of width 2 and height n.
A335714 (program): The sum of the sizes (positions) of fixed points over all compositions of n.
A335718 (program): a(n) = 2*a(n-1) + 3*a(n-2) + 5*a(n-3), a(0) = 0, a(1) = 1, a(2) = 2.
A335719 (program): a(n) = 2*a(n-1) + 3*a(n-2) + 5*a(n-3), a(0) = 3, a(1) = 2, a(2) = 10.
A335720 (program): a(n) = 2*a(n-1) + 3*a(n-2) + 5*a(n-3), a(0) = 0, a(1) = 1, a(2) = 1.
A335741 (program): Number of Pell numbers (A000129) <= n.
A335746 (program): a(n) is the number of partitions of n into distinct parts such that the number of parts divisible by 3 is even.
A335749 (program): a(n) = n!*[x^n] exp(2*x)*(y*sinh(x*y) + cosh(x*y)) and y = sqrt(6).
A335750 (program): a(n) = numerator(Bernoulli(2*n)*(1/2 - n)! / sqrt(Pi)).
A335754 (program): a(n) is the number of overpartitions of n where overlined parts are not divisible by 3 and non-overlined parts are congruent to 1 modulo 3.
A335755 (program): a(n) is the number of overpartitions of n where overlined parts are not divisible by 3 and non-overlined parts are congruent to 2 modulo 3.
A335756 (program): A cup filling problem starting with 2 empty cups of sizes 3 and n, where a(n) is the number of unreachable states (see details in comments).
A335774 (program): Numbers k such that in prime factorization of k the second smallest factor is 7.
A335789 (program): a(n) = time to the nearest second at the n-th instant (n>=0) when the hour and minute hands on a clock face coincide, starting at time 0:00.
A335807 (program): Number of vertices in the n-th simplex graph of the complete graph on three vertices (K_3).
A335819 (program): E.g.f.: exp((3/2) * x * (2 + x)).
A335821 (program): Triangular array T(n, k) = n^2 - k^2, read by rows.
A335840 (program): Expansion of x*(1+2*x)/((1-2*x)*(1-x+4*x^2)).
A335841 (program): Number of distinct rectangles that can be made with one even and one odd side length that are divisors of 2n.
A335843 (program): a(n) is the number of n-digit positive integers with exactly two distinct base 10 digits.
A335851 (program): Numbers that are powerful in Gaussian integers.
A335857 (program): a(n) is the determinant of the n X n Hankel matrix A with A(i,j) = A000108(i+j+6) for 0<=i,j<=n-1.
A335858 (program): Nonnegative integers ordered by binary length and then lexicographically by run lengths (considering least significant runs first).
A335860 (program): Partial sums of A064097.
A335862 (program): Decimal expansion of the zero x1 of the cubic polynomial x^3 - 2*x^2 - 10*x - 6.
A335863 (program): Decimal expansion of the negative of the zero x2 of the cubic polynomial x^3 - 2*x^2 - 10*x - 6.
A335864 (program): Decimal expansion of the negative of the zero x3 of the cubic polynomial x^3 - 2*x^2 - 10*x - 6.
A335865 (program): Moduli a(n) = v(n) for the simple difference sets of Singer type of order m(n) (v(n), m(n)+1, 1) in the additive group modulo v(n) = m(n)^2 + m(n) + 1, with m(n) = A000961(n).
A335867 (program): a(n) = exp(-n) * Sum_{k>=0} n^k * (k - 1)^n / k!.
A335871 (program): a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} binomial(n,k) * binomial(n+(n-1)*k,k-1) for n > 0.
A335873 (program): Total number of points in all permutations of [n] that are fixed or reflected.
A335876 (program): a(1) = 2, and for n > 1, a(n) = n + (n/p), where p is largest prime dividing n, A006530(n).
A335882 (program): Numbers k for which A331410(k) = 2.
A335895 (program): Middle side of primitive triples, in nondecreasing order, for integer-sided triangles whose angles A < B < C are in arithmetic progression.
A335903 (program): Column 1 in the matrix of A279212 (whose indexing starts at 0).
A335909 (program): Parity of A323173: a(n) = A000035(A323173(n)).
A335915 (program): Fully multiplicative with a(2) = 1, and a(p) = A000265(p-1)*A000265(p+1) = A000265(p^2 - 1), for odd primes p.
A335927 (program): a(n+1) = Sum_{k=1..n} (a(k) + k*(n-k)), with a(1)=1.
A335940 (program): a(n) = n if n is prime, a(n) = 0 if n is a nontrivial power of a prime, and otherwise a(n) = max(|p-q| where p, q are distinct primes dividing n}.
A335945 (program): E.g.f. A(x) satisfies: A(x) = exp(x*A(x)/(1 + x)).
A335946 (program): a(n) = 1 + Sum_{k=0..n-1} binomial(n,k)^2 * a(k).
A335950 (program): Sparse rulers with length a(n) cannot be perfect rulers.
A335955 (program): a(n) = (4^n*(Z(-n, 1/4) - Z(-n, 3/4)) + Z(-n, 1)*(2^(n+1)-1))*A171977(n+1), where Z(n, c) is the Hurwitz zeta function.
A335956 (program): a(n) = (2^n - 1)*2^valuation(n, 2) for n > 0 and a(0) = 0.
A335962 (program): Numbers k such that k^2 + 1 and k^2 + 2 are both squarefree.
A335965 (program): a(n) = number of odd numbers in the n-th row of the Narayana triangle A001263.
A335979 (program): Number of partitions of n into exactly two parts with no decimal carries.
A335980 (program): Expansion of e.g.f. exp(2 * (1 - exp(-x)) + x).
A335981 (program): Expansion of e.g.f. exp(3 * (1 - exp(-x)) + x).
A335982 (program): Expansion of e.g.f. exp(4 * (1 - exp(-x)) + x).
A335997 (program): Triangle read by rows: T(n,k) = Product_{i=n-k+1..n} i! for 0 <= k <= n.
A335999 (program): a(1) = 1; for n >= 2, a(n) = least positive integer not in {a(1),…, a(n-1), b(1),…,b(n-1)}, where for n >=1, b(n) = n + 2 + least positive integer not in {a(1),…, a(n-1), a(n), b(1),…,b(n-1)}.
A336008 (program): Complement of A335999.
A336012 (program): a(n) is the number of chains from {} to a top element in the poset of even sized subsets of {1,2,…,n} ordered by inclusion.
A336017 (program): a(n) = floor(frac(Pi*n)*n), where frac denotes the fractional part.
A336018 (program): a(n) = floor(frac(log_2(n))*n), where frac denotes the fractional part.
A336024 (program): Expansion of e.g.f. (1 + sinh(x)) / cos(x).
A336030 (program): a(n) = Fibonacci(n-1) + Fibonacci(floor(n/2)).
A336040 (program): Characteristic function of refactorable numbers (A033950).
A336041 (program): Number of refactorable divisors of n.
A336061 (program): Numerators of coefficients associated with the second virial coefficient for rigid spheres with imbedded point dipoles.
A336064 (program): Numbers divisible by the maximal exponent in their prime factorization (A051903).
A336066 (program): Numbers k such that the exponent of the highest power of 2 dividing k (A007814) is a divisor of k.
A336094 (program): Digit of Pi multiplied by the next digit of Pi.
A336101 (program): Numbers divisible by exactly one odd prime.
A336102 (program): Number of inseparable multisets of size n covering an initial interval of positive integers.
A336103 (program): Number of separable multisets of size n covering an initial interval of positive integers.
A336109 (program): First column of dispersion array A120861.
A336112 (program): a(n) is the least number k such that the Sum_{i=0..k} sqrt(k) equals or exceeds n.
A336113 (program): a(n) is the numerator of Sum_{odd d|n} 1/d.
A336114 (program): The hafnian of a symmetric Toeplitz matrix of order 2*n, n>=2 with the first row (0,1,2,…,2,1); a(0)=a(1)=1.
A336119 (program): Numbers k such that A122111(k) [the conjugated prime factorization of k] is a square or twice a square.
A336122 (program): Numbers k for which A335884(k) = 2.
A336124 (program): a(n) = A122111(n) mod 4.
A336126 (program): Lexicographically earliest infinite sequence such that a(i) = a(j) => A000035(i) = A000035(j) and A007814(1+A000265(i)) = A007814(1+A000265(j)), for all i, j >= 1.
A336146 (program): Lexicographically earliest infinite sequence such that a(i) = a(j) => A000035(i) = A000035(j) and A000265(i) = A000265(j), for all i, j >= 1.
A336158 (program): The least number with the prime signature of the odd part of n: a(n) = A046523(A000265(n)).
A336163 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Sum_{j=0..n} k^j * binomial(n,j)^3.
A336165 (program): G.f. A(x) satisfies: A(x) = 1 + x * ((1 - x) * A(x))^2.
A336174 (program): Number of non-symmetric binary n X n matrices M over the reals such that M^2 is the transpose of M.
A336179 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Sum_{j=0..n} (-k)^j * binomial(n,j)^3.
A336180 (program): a(n) = Sum_{k=0..n} (-n)^k * binomial(n,k)^3.
A336181 (program): a(n) = Sum_{k=0..n} (-2)^k * binomial(n,k)^3.
A336182 (program): a(n) = Sum_{k=0..n} (-3)^k * binomial(n,k)^3.
A336186 (program): Side length of a square block of integers, with 1 at the top-left corner, on a diagonally numbered 2D board such that the sum of the integers in the square is a perfect square.
A336187 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Sum_{j=0..n} k^j * binomial(n,j)^k.
A336188 (program): a(n) = Sum_{k=0..n} n^k * binomial(n,k)^n.
A336194 (program): Table read by antidiagonals upwards: T(n,k) = (n - 1)*k^3 - 1, with n > 1 and k > 0.
A336195 (program): a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^3 * a(k).
A336196 (program): a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^4 * a(k).
A336197 (program): a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^5 * a(k).
A336199 (program): Decimal expansion of the distance between the centers of two unit-radius spheres such that the volume of intersection is equal to the sum of volumes of the two nonoverlapping parts.
A336201 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Sum_{j=0..n} (-k)^j * binomial(n,j)^k.
A336202 (program): a(n) = Sum_{k=0..n} (-n)^k * binomial(n,k)^n.
A336203 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Sum_{j=0..n} 2^j * binomial(n,j)^k.
A336204 (program): a(n) = Sum_{k=0..n} 2^k * binomial(n,k)^n.
A336212 (program): a(n) = Sum_{k=0..n} 3^k * binomial(n,k)^n.
A336213 (program): a(n) = Sum_{k=0..n} k^k * binomial(n,k)^n, with a(0)=1.
A336214 (program): a(n) = Sum_{k=0..n} k^n * binomial(n,k)^n, with a(0)=1.
A336217 (program): a(0) = 1; a(n) = 2 * Sum_{k=0..n-1} binomial(n,k)^2 * a(k).
A336222 (program): Numbers k such that the square root of the largest square dividing k has an even number of prime divisors (counted with multiplicity).
A336224 (program): Numbers k such that the largest square dividing k is a unitary divisor of k and its square root has an even number of prime divisors (counted with multiplicity).
A336225 (program): Table read by antidiagonals: T(n, k) = digitsum(n*k) with n >= 0 and k >= 0.
A336227 (program): a(0) = 1; a(n) = n * Sum_{k=0..n-1} binomial(n-1,k)^2 * a(k).
A336228 (program): a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^2 * (n-k) * a(k).
A336231 (program): Integers whose binary digit expansion has an even number of 0’s between any two consecutive 1’s.
A336234 (program): Edge length of ‘Prime squares’: sum the four numbers at the corners of a square drawn on a diagonally numbered 2D board, with 1 at the corner of the square. The sequence gives the size of the square such that the sum is a prime number.
A336236 (program): a(n) = prime(n-2) - a(n-2) for n > 2, starting with a(1)=1, a(2)=1.
A336241 (program): a(n) = (n!)^2 * Sum_{d|n} 1 / (d!)^2.
A336242 (program): a(n) = (n!)^2 * Sum_{d|n} (-1)^(d+1) / (d!)^2.
A336243 (program): a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^2 * (n-k-1)! * a(k).
A336246 (program): Array read by upwards antidiagonals: T(n,k) is the number of ways to place n persons on different seats such that each person number p, 1 <= p <= n, differs from the seat number s(p), 1 <= s(p) <= n+k, k >= 0.
A336247 (program): a(n) = (n!)^n * Sum_{k=0..n} 1 / (k!)^n.
A336248 (program): a(n) = (n!)^n * Sum_{k=0..n} (-1)^k / (k!)^n.
A336249 (program): a(n) = (n!)^n * Sum_{k=0..n} 1 / ((k!)^n * (n-k)!).
A336250 (program): a(n) = (n!)^n * Sum_{k=1..n} (-1)^(k+1) / k^n.
A336257 (program): a(n) = Catalan(n) mod (2*n+1).
A336258 (program): a(0) = 1; a(n) = (n!)^2 * Sum_{k=0..n-1} a(k) / (k! * (n-k))^2.
A336263 (program): Numbers of the form k + s + 2*k*s where k is a positive integer and s is a Sundaram number (A159919).
A336266 (program): Decimal expansion of (3/16)*Pi.
A336276 (program): a(n) = Sum_{k=1..n} mu(k)*k^2.
A336277 (program): a(n) = Sum_{k=1..n} mu(k)*k^3.
A336278 (program): a(n) = Sum_{k=1..n} mu(k)*k^4.
A336279 (program): a(n) = Sum_{k=1..n} mu(k)*k^5.
A336283 (program): Row sums of A192933.
A336286 (program): The hafnian of a symmetric Toeplitz matrix of order 2n, n>=2 with the first row (0,1,2,…,2,0); a(0)=a(1)=1.
A336288 (program): Numbers of squares formed by this procedure on n-th step: Step 1, draw a unit square. Step n, draw a unit square with center in every intersection of lines of the figure in step n-1.
A336291 (program): a(n) = (n!)^2 * Sum_{k=1..n} 1 / (k * ((n-k)!)^2).
A336292 (program): a(n) = (n!)^2 * Sum_{k=1..n} (-1)^(n-k) / (k * ((n-k)!)^2).
A336293 (program): a(n) = Sum_{k=0..n} binomial(n,k)^2 * binomial(2*k,k) * (n-k)!.
A336298 (program): Greatest prime < prime(n)/2.
A336299 (program): (Least prime > prime(n)/2) - (greatest prime < prime(n)/2).
A336302 (program): a(n) = n^2 mod ceiling(sqrt(n)).
A336305 (program): Alternating row sums of triangle A211343.
A336308 (program): Decimal expansion of (5/32)*Pi.
A336315 (program): The number of divisors in the conjugated prime factorization of n: a(n) = A000005(A122111(n)).
A336316 (program): The number of non-unitary divisors in the conjugated prime factorization of n: a(n) = A048105(A122111(n)).
A336318 (program): Square root of the largest square dividing n*d(n), where d(n) is the number of divisors of n, A000005.
A336319 (program): Squarefree part of n*d(n), where d(n) = number of divisors of n (A000005).
A336323 (program): Numbers composite(n) such that gcd(n,composite(n)) > 1.
A336337 (program): Total number of records over all length n ternary words (words on alphabet {0,1,2}).
A336338 (program): Numbers k such that gcd(k, composite(k)) is even.
A336339 (program): Numbers composite(n) such that gcd(n,composite(n)) is even.
A336340 (program): a(n) = (1/2)A336338(n).
A336341 (program): a(n) = (1/2)A336339(n).
A336351 (program): Number of cyclic arrangements of S = {1,2,…,6n - 3} such that any three neighbors can be reordered in an arithmetic progression.
A336356 (program): Characteristic function of A336359, numbers k for which A001222(A000203(k)) < A001222(k).
A336359 (program): Numbers k for which bigomega(sigma(k)) < bigomega(k), where bigomega (A001222) gives the number of prime factors with multiplicity, and sigma (A000203) gives the sum of divisors.
A336360 (program): Numbers k for which bigomega(sigma(k)) >= bigomega(k), where bigomega (A001222) gives the number of prime factors with multiplicity, and sigma (A000203) gives the sum of divisors.
A336370 (program): Numbers k such that gcd(k, prime(k) + prime(k-1)) = 1.
A336371 (program): Numbers k such that gcd(k, prime(k) + prime(k-1)) > 1.
A336372 (program): Primes p(n) such that gcd(n, prime(n)+prime(n-1)) = 1.
A336373 (program): Primes p(n) such that gcd(n, prime(n)+prime(n-1)) > 1.
A336374 (program): Numbers k such that gcd(k, prime(k) + prime(k+2)) = 1.
A336375 (program): Numbers k such that gcd(k, prime(k) + prime(k+2)) > 1.
A336376 (program): Primes p(n) such that gcd(n, prime(n)+prime(n+2)) = 1.
A336377 (program): Primes p(n) such that gcd(n, prime(n)+prime(n+2)) > 1.
A336378 (program): Numbers k such that gcd(k, prime(k-1) + prime(k+1)) = 1.
A336379 (program): Numbers k such that gcd(k, prime(k-1) + prime(k+1)) > 1.
A336380 (program): Primes p(n) such that gcd(n, prime(n-1)+prime(n+1)) = 1.
A336381 (program): Primes p(n) such that gcd(n, prime(n-1)+prime(n+1)) > 1.
A336386 (program): a(n) = bigomega(sigma(n)) - bigomega(n), where bigomega (A001222) gives the number of prime factors with multiplicity, and sigma (A000203) gives the sum of divisors.
A336387 (program): Number of prime divisors of n that do not divide sigma(n); a(1) = 0.
A336388 (program): Number of prime divisors of sigma(n) that divide n; a(1) = 0.
A336396 (program): a(n) = A329697(n) - A087436(n).
A336398 (program): Number of rational knots (or two-bridge knots) with n crossings (chiral pairs counted as distinct).
A336400 (program): The hafnian of a symmetric Toeplitz matrix of order 2*n, n>=2 with the first row (0,2,1,…,1,2); a(0)=1, a(1)=2.
A336407 (program): a(n) is the number of composites < n-th odd composite.
A336409 (program): Distance from prime(n) to the nearest odd composite that is < prime(n).
A336410 (program): Numbers k such that prime(k) - oc(k) = 2, where oc(k) is the greatest odd composite < prime(k).
A336411 (program): Numbers k such that prime(k) - oc(k) = 4, where oc(k) is the greatest odd composite < prime(k).
A336415 (program): Number of divisors of n! with equal prime multiplicities.
A336418 (program): Numbers with a factorial number of divisors.
A336426 (program): Numbers that cannot be written as a product of superprimorials {2, 12, 360, 75600, …}.
A336430 (program): Number of partitions of n into two positive integer parts that have the same number of decimal digits.
A336455 (program): a(n) = A335915(sigma(n)), where A335915 is a fully multiplicative sequence with a(2) = 1 and a(p) = A000265(p^2 - 1) for odd primes p, with A000265(k) giving the odd part of k.
A336456 (program): a(n) = A335915(sigma(sigma(n))), where A335915 is a fully multiplicative sequence with a(2) = 1 and a(p) = A000265(p^2 - 1) for odd primes p, with A000265(k) giving the odd part of k.
A336457 (program): a(n) = A065330(sigma(n)), where A065330 is fully multiplicative with a(2) = a(3) = 1, and a(p) = p for primes p > 3.
A336459 (program): a(n) = A065330(sigma(sigma(n))), where A065330 is fully multiplicative with a(2) = a(3) = 1, and a(p) = p for primes p > 3.
A336466 (program): Fully multiplicative with a(p) = A000265(p-1) for any prime p, where A000265(k) gives the odd part of k.
A336467 (program): Fully multiplicative with a(2) = 1 and a(p) = A000265(p+1) for odd primes p, with A000265(k) giving the odd part of k.
A336469 (program): a(n) = A329697(phi(n)), where A329697 is totally additive with a(2) = 0 and a(p) = 1 + a(p-1) for odd primes.
A336475 (program): Multiplicative with a(2^e) = 1, and for odd primes p, a(p^e) = (e+1)*p^e.
A336476 (program): a(n) = gcd(A000593(n), A336475(n)).
A336477 (program): a(n) = 1 if a regular n-gon is constructible with ruler (or, more precisely, an unmarked straightedge) and compass, 0 otherwise.
A336483 (program): Floor(n/10) + (5 times last digit of n).
A336487 (program): Numbers m such that the Fibonacci word (A003849) has an abelian cube of order m.
A336495 (program): a(n) = (-1)^n * Sum_{k=0..n} (-2)^k * binomial(n,k) * binomial(n^2+k+1,n)/(n^2+k+1).
A336497 (program): Numbers that cannot be written as a product of superfactorials A000178.
A336502 (program): Partial sums of A057003.
A336510 (program): a(n) = Sum_{p | A055204(n)} 2^(pi(p) - 1).
A336513 (program): a(n) = Sum_{i=1..n} Product_{j=(i-1)*n+1..i*n} j.
A336521 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) is the coefficient of x^(k*n) in expansion of ( (1 + x)/(1 - x) )^n.
A336522 (program): a(n) is the coefficient of x^(n^2) in expansion of ( (1 + x)/(1 - x) )^n.
A336524 (program): Triangular array read by rows. T(n,k) is the number of unlabeled binary trees with n internal nodes and exactly k distinguished external nodes (leaves) for 0 <= k <= n+1 and n >= 0.
A336529 (program): a(n) = (n^3+5*n+3)/3 + 2*floor(n/2) + a(n-2), with a(0)=1 and a(1)=3.
A336535 (program): a(n) = (m(n)^2 + 3)*(m(n)^2 + 7)/32, where m(n) = 2*n - 1.
A336537 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n^2+k+1,n)/(n^2+k+1).
A336538 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x)^3 * (2 + A(x)).
A336539 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x)^3 * (1 + 2 * A(x)).
A336540 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x)^4 * (2 + A(x)).
A336551 (program): a(n) = A003557(n) - 1.
A336563 (program): Sum of proper divisors of n that are divisible by every prime that divides n.
A336564 (program): a(n) = n - A308135(n), where A308135(n) is the sum of non-coreful divisors of n.
A336566 (program): a(n) = gcd(A336563(n), A336564(n)) = gcd(A057723(n)-n, n-A308135(n));
A336567 (program): Sum of proper divisors of {n divided by its largest squarefree divisor}.
A336568 (program): Numbers that are not a product of two numbers each having distinct prime multiplicities.
A336572 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x)^4 * (1 + 2 * A(x)).
A336577 (program): a(n) = Sum_{k=0..n} 2^k * binomial(n,k) * binomial(n^2+k+1,n)/(n^2+k+1).
A336578 (program): a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} 3^k * binomial(n,k) * binomial(n^2,k-1) for n > 0.
A336590 (program): Numbers k such that k/A008834(k) is squarefree, where A008834(k) is the largest cube dividing k.
A336591 (program): Numbers whose exponents in their prime factorization are either 1, 3, or both.
A336592 (program): Numbers k such that k/A008835(k) is cubefree, where A008835(k) is the largest 4th power dividing k.
A336593 (program): Numbers k such that k/A008835(k) is cubeful (A036966), where A008835(k) is the largest 4th power dividing k.
A336595 (program): Numbers whose number of divisors is divisible by 5.
A336596 (program): Numbers whose number of divisors is divisible by 7.
A336602 (program): a(n) = 8*a(n-1) - 21*a(n-2) + 20*a(n-3) - 5*a(n-4), with initial terms a(0)=1, a(1)=7, a(2)=35, a(3)=154.
A336606 (program): Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(x) / BesselJ(0,2*sqrt(x)).
A336608 (program): Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(-x) / BesselJ(0,2*sqrt(x)).
A336610 (program): Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(-sqrt(x) * BesselI(1,2*sqrt(x))).
A336614 (program): Number of n X n (0,1)-matrices A over the reals such that A^2 is the transpose of A.
A336615 (program): Numbers of the form p * m^2, where p is prime and m > 0 is not divisible by p.
A336623 (program): First member of the Diophantine pair (m, k) that satisfies 8*(m^2 + m) = k^2 + k; a(n) = m
A336624 (program): Triangular numbers that are one-eighth of other triangular numbers; T(t) such that 8*T(t)=T(u) for some u where T(k) is the k-th triangular number.
A336625 (program): Indices of triangular numbers that are eight times other triangular numbers.
A336626 (program): Triangular numbers that are eight times another triangular number.
A336627 (program): Coordination sequence for the Manhattan lattice.
A336630 (program): a(n) = 2*F(2*n+1) + 4*F(n+1)*F(n-1) for n > 0, with a(0) = 0 and F(n) = A000045(n).
A336634 (program): Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(-x) * BesselI(0,2*sqrt(x))^2.
A336642 (program): One less than the largest square dividing n: a(n) = A008833(n)-1.
A336643 (program): Squarefree kernel of n divided by the squarefree part of n: a(n) = rad(n) / core(n).
A336644 (program): a(n) = (n-rad(n)) / core(n), where rad(n) and core(n) give the squarefree kernel and squarefree part of n, respectively.
A336645 (program): a(n) = n - A326129(n).
A336646 (program): a(n) = n - A326144(n).
A336647 (program): a(n) = n - A336566(n).
A336649 (program): Sum of divisors of A336651(n) (odd part of n divided by its largest squarefree divisor).
A336650 (program): a(n) = p^e, where p is the smallest odd prime factor of n, and e is its exponent, with a(n) = 1 when n is a power of two.
A336651 (program): Odd part of n divided by its largest squarefree divisor.
A336652 (program): Sum of positive divisors of odd part of n that are divisible by every (odd) prime dividing it: a(n) = A057723(A000265(n)).
A336655 (program): Odd numbers k such that the multiplicative order of 2 modulo k is squarefree.
A336660 (program): a(n) is the maximal number of 1 X 1 squares in an arrangement of n squares, from 1 X 1 to n X n.
A336675 (program): Number of paths of length n starting at initial node of the path graph P_10.
A336678 (program): Number of paths of length n starting at initial node of the path graph P_11.
A336682 (program): a(n) is the number of iterations needed to reach a fixed point starting with n and repeatedly applying f(x) = x - (the product of the digits of x).
A336691 (program): Number of distinct prime factors of 1+sigma(n).
A336692 (program): Binary weight of 1+sigma(n).
A336693 (program): Period of binary representation of 1/(1+sigma(n)).
A336694 (program): a(n) = A329697(1+sigma(n)), where A329697 is totally additive with a(2) = 0 and a(p) = 1 + a(p-1) for odd primes.
A336695 (program): a(n) = A331410(1+sigma(n)), where A331410 is totally additive with a(2) = 0 and a(p) = 1 + a(p+1) for odd primes.
A336696 (program): Sum of odd divisors of 1+sigma(n).
A336698 (program): a(n) = A000265(1+A000265(sigma(n))), where A000265(k) gives the odd part of k.
A336699 (program): a(n) = A000265(1+A000265(sigma(A000265(n)))), where A000265(k) gives the odd part of k, and sigma is the sum of divisors function.
A336705 (program): Coordination sequence for the half-Manhattan lattice.
A336712 (program): a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} 2^(n-k) * binomial(n,k) * binomial(n+(n-1)*k,k-1) for n > 0.
A336722 (program): a(n) = gcd(tau(n), sigma(n), pod(n)) where tau(k) is the number of divisors of k (A000005), sigma(k) is the sum of divisors of k (A000203) and pod(k) is the product of divisors of k (A007955).
A336723 (program): a(n) = lcm(tau(n), sigma(n), pod(n)) where tau(k) is the number of divisors of k (A000005), sigma(k) is the sum of divisors of k (A000203) and pod(k) is the product of divisors of k (A007955).
A336727 (program): Square array T(n,k), n>=0, k>=0, read by antidiagonals, where T(0,k) = 1 and T(n,k) = (1/n) * Sum_{j=1..n} (-k)^(n-j) * binomial(n,j) * binomial(n,j-1) for n > 0.
A336728 (program): a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} (-n)^(n-k) * binomial(n,k) * binomial(n,k-1) for n > 0.
A336729 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x) / (1 + 3 * x * A(x)).
A336743 (program): a(n) is the product of the first n positive evil numbers.
A336746 (program): Triangle read by rows: T(n,k) = (n-k-1+H(k+1))*((k+1)!) for 0 <= k <= n where H(k+1) = Sum_{i=0..k} 1/(i+1) for k >= 0.
A336751 (program): Smallest side of integer-sided triangles whose sides a < b < c are in arithmetic progression.
A336753 (program): Largest side of integer-sided triangles whose sides a < b < c are in arithmetic progression.
A336754 (program): Perimeters in increasing order of integer-sided triangles whose sides a < b < c are in arithmetic progression.
A336756 (program): Perimeters in increasing order of primitive integer-sided triangles whose sides a < b < c are in arithmetic progression.
A336776 (program): a(n) is the least number of repetitions such that the result of the repeated execution of the multiplication f <- f*n started at f=1 produces an overflow, when the multiplication is performed using 32-bit single precision floats according to the IEEE 754 standard.
A336780 (program): a(n) is the least number of repetitions such that the result of the repeated execution of the multiplication f <- f*n started at f=1 produces an overflow, when the multiplication is performed using 64-bit double precision floats according to the IEEE 754 standard.
A336804 (program): a(n) = (n!)^2 * Sum_{k=0..n} 2^(n-k) / (k!)^2.
A336805 (program): a(n) = (n!)^2 * Sum_{k=0..n} 3^(n-k) / (k!)^2.
A336807 (program): a(n) = (n!)^2 * Sum_{k=0..n} 4^(n-k) / (k!)^2.
A336808 (program): a(n) = (n!)^2 * Sum_{k=0..n} 5^(n-k) / (k!)^2.
A336809 (program): a(n) = (n!)^2 * Sum_{k=0..n} (k+1) / ((n-k)!)^2.
A336819 (program): Odd values of D > 0 for which the generalized Ramanujan-Nagell equation x^2 + D = 2^m has two or more solutions in the positive integers.
A336828 (program): a(n) = Sum_{k=0..n} binomial(n,k)^2 * k^n.
A336829 (program): a(n) = Sum_{k=0..n} binomial(n+k,k)^n.
A336834 (program): a(n) = 1 if A005940(1+n) is deficient, 0 otherwise.
A336835 (program): Number of iterations of x -> A003961(x) needed before the result is deficient (sigma(x) < 2x), when starting from x=n.
A336837 (program): Numerator of ratio A336841(n)/A000005(n).
A336838 (program): Numerator of the arithmetic mean of the divisors of A003961(n).
A336839 (program): Denominator of the arithmetic mean of the divisors of A003961(n).
A336840 (program): Inverse Möbius transform of A048673.
A336841 (program): Prime-shifted analog of A094471: a(n) = A336845(n) - A003973(n).
A336842 (program): Number of trailing 1-bits in the binary representation of A003961(n): a(n) = A007814(1+A003961(n)).
A336843 (program): Period of binary representation of 1/A003961(n): a(n) = A007733(A003961(n)).
A336844 (program): a(n) = A336698(A003961(n)).
A336845 (program): a(n) = A000005(n) * A003961(n), where A003961 is the prime shift towards larger primes, and A000005 gives the number of divisors of n, and also of A003961(n).
A336846 (program): a(n) = gcd(sigma(A003961(n)), A000005(n)*A003961(n)).
A336847 (program): a(n) = A003973(n) - A336846(n).
A336848 (program): a(n) = A003973(n) / A336846(n).
A336849 (program): a(n) = A003961(n) / gcd(A003961(n), sigma(A003961(n))), where A003961 is the prime shift towards larger primes.
A336850 (program): a(n) = gcd(A003961(n), sigma(A003961(n))), where A003961 is the prime shift towards larger primes.
A336851 (program): a(n) = sigma(A003961(n)) - A003961(n), where A003961 is a prime shift towards larger primes, sigma is the sum of divisors.
A336852 (program): a(n) = sigma(A003961(n)) - sigma(n).
A336853 (program): a(n) = A003961(n) - n, where A003961 is the prime shift towards larger primes.
A336854 (program): a(n) = A336841(n)/2.
A336856 (program): Prime-shifted analog of gcd(d(n), sigma(n)): a(n) = gcd(A000005(n), A003973(n)).
A336857 (program): The digit sum of n*(n^2 + 1)/2.
A336860 (program): a(n) = 1 + the total remainder when repeatedly taking integer square roots until 1 is reached.
A336861 (program): a(n) = ceiling((n-1-sqrt(n+1))/2).
A336867 (program): Numbers k such that k! does not have distinct prime multiplicities.
A336868 (program): Indicator function for numbers k such that k! has distinct prime multiplicities.
A336873 (program): a(n) = Sum_{k=0..n} (binomial(n+k,k) * binomial(n,k))^n.
A336877 (program): The harmonic function on the Sierpinski gasket with vertices 0, 1, w = (-1)^(1/3) defined by the values a(0) = 0, a(1) = 1, a(w) = -1.
A336878 (program): Second differences of A336877, divided by 3.
A336882 (program): a(0) = 1; for k >= 0, 0 <= i < 2^k, a(2^k + i) = m_k * a(i), where m_k is the least odd number not in terms 0..2^k - 1.
A336898 (program): a(n) = numerator(n / (4^n - 2^n)) for n > 0 and a(0) = 1.
A336899 (program): a(n) = denominator(n / (4^n - 2^n)) for n > 0 and a(0) = 1.
A336917 (program): Number of iterations of x -> A252463(x) needed before the result is deficient, when starting from x=n.
A336918 (program): Numbers k such that A000005(k) divides A003973(k); numbers k for which A336839(k) = 1.
A336919 (program): Numbers k such that A000005(k) does not divide A003973(k); numbers k for which A336839(k) > 1.
A336921 (program): a(n) = A331410(n) - A087436(n).
A336923 (program): a(n) = 1 if sigma(2n) - sigma(n) is a power of 2, otherwise 0.
A336924 (program): a(n) = spf(1+sigma(n)), where spf is the smallest prime factor and sigma is the sum of divisors function.
A336928 (program): a(n) = A329697(sigma(n)), where A329697 is totally additive with a(2) = 0 and a(p) = 1 + a(p-1) for odd primes.
A336929 (program): a(n) = A331410(sigma(n)), where A331410 is totally additive with a(2) = 0 and a(p) = 1 + a(p+1) for odd primes.
A336930 (program): Numbers k such that the 2-adic valuation of A003973(k), the sum of divisors of the prime shifted k is equal to the 2-adic valuation of the number of divisors of k.
A336931 (program): Difference between the 2-adic valuation of A003973(n) [= the sum of divisors of the prime shifted n] and the 2-adic valuation of the number of divisors of n.
A336932 (program): The 2-adic valuation of A003973(n), the sum of divisors of prime shifted n.
A336937 (program): The 2-adic valuation of sigma(n), the sum of divisors of n.
A336940 (program): Number of odd divisors of n!.
A336945 (program): a(n) = binomial(3*n,n)/(2*n + 1) - 2*binomial(3*(n - 1),n - 1)/(2*n - 1) for n > 0 with a(0) = 1.
A336947 (program): E.g.f.: 1 / (exp(-2*x) - x).
A336948 (program): E.g.f.: 1 / (exp(-3*x) - x).
A336949 (program): a(n) = n! * [x^n] 1 / (exp(-n*x) - x).
A336950 (program): E.g.f.: 1 / (1 - x * exp(2*x)).
A336951 (program): E.g.f.: 1 / (1 - x * exp(3*x)).
A336952 (program): E.g.f.: 1 / (1 - x * exp(4*x)).
A336955 (program): a(n) = Sum_{k=0..n} k^k * binomial(n, k)^2.
A336958 (program): E.g.f.: 1 / (exp(2*x) - x).
A336959 (program): E.g.f.: 1 / (1 - x * exp(-2*x)).
A336960 (program): E.g.f.: 1 / (1 - x * (2 + x) * exp(x)).
A336961 (program): E.g.f.: exp(x * (2 + x) * exp(x)).
A336965 (program): a(n) is the product of the distinct prime numbers appearing in the prime tower factorization of n.
A336969 (program): a(n) = n! * [x^n] 1 / (exp(n*x) - x).
A336970 (program): G.f. A(x) satisfies: A(x) = 1 - x^2 * A(x/(1 - x)) / (1 - x).
A336971 (program): G.f. A(x) satisfies: A(x) = 1 - x^3 * A(x/(1 - x)) / (1 - x).
A336972 (program): Sum of the smallest two side lengths of all distinct integer-sided triangles with perimeter n.
A336973 (program): Sum of the smallest and largest side lengths of all distinct integer-sided triangles with perimeter n.
A336974 (program): Sum of the largest two side lengths of all distinct integer-sided triangles with perimeter n.
A336996 (program): Triangle of coefficients T(n,k) (n >= 0, 0 <= k <= 2*n), read by rows: n-th row is obtained by expanding (2 + x + x^2)^n.
A336997 (program): a(n) = n! * Sum_{d|n} 2^(d - 1) / d!.
A336998 (program): a(n) = n! * Sum_{d|n} 3^(d - 1) / d!.
A336999 (program): a(n) = n! * Sum_{d|n} n^d / d!.
A337000 (program): E.g.f.: 1 / ((1 - x)*(2 - exp(x))).
A337001 (program): a(n) = n! * Sum_{k=0..n} k^3 / k!.
A337002 (program): a(n) = n! * Sum_{k=0..n} k^4 / k!.
A337003 (program): a(n) = Sum_{k=1..n, gcd(n,k) = 1} binomial(n,k)^2.
A337004 (program): Turn sequence of the R5 dragon curve.
A337010 (program): a(n) = exp(-1/2) * Sum_{k>=0} (2*k + 3)^n / (2^k * k!).
A337011 (program): a(n) = 2^n * exp(-1/2) * Sum_{k>=0} (k + 2)^n / (2^k * k!).
A337012 (program): a(n) = exp(-1/2) * Sum_{k>=0} (2*k + n)^n / (2^k * k!).
A337022 (program): a(n) is the number of positive integers <= A070826(n) with at least one odd prime divisor <= prime(n).
A337024 (program): Number of ways to tile a 2n X 2n square with 1 X 1 white and n X n black squares.
A337025 (program): Number of n-state 2-symbol halt-free Turing machines.
A337027 (program): a(n) = (1/2) * Sum_{k>=0} (2*k + n)^n / 2^k.
A337030 (program): a(n) is the number of squarefree composite numbers < prime(n).
A337037 (program): Numbers whose every unordered factorization has a distinct sum of factors.
A337038 (program): a(n) = exp(-1/2) * Sum_{k>=0} (2*k - 1)^n / (2^k * k!).
A337039 (program): a(n) = exp(-1/3) * Sum_{k>=0} (3*k - 1)^n / (3^k * k!).
A337040 (program): a(n) = exp(-1/4) * Sum_{k>=0} (4*k - 1)^n / (4^k * k!).
A337041 (program): a(n) = exp(-1/5) * Sum_{k>=0} (5*k - 1)^n / (5^k * k!).
A337042 (program): a(n) = exp(-1/6) * Sum_{k>=0} (6*k - 1)^n / (6^k * k!).
A337046 (program): Integers n such that n! = x^2 + y^3 + z^6 where x, y and z are nonnegative integers, is soluble.
A337050 (program): Numbers without an exponent 2 in their prime factorization.
A337052 (program): Numbers k such that the powerful part of k has an even number of prime divisors counted with multiplicity.
A337053 (program): a(n) = exp(2) * Sum_{i>=0} Sum_{j>=0} (-1)^(i+j) * (i*j)^n / (i! * j!).
A337059 (program): E.g.f.: 1 / (2 + x^3/6 - exp(x)).
A337062 (program): E.g.f.: exp(1 + x^2/2 - exp(x)).
A337068 (program): a(n) is the least number of repetitions such that the result of the repeated execution of the division f <- f/n started at f=1 produces 0, when the division is performed using Commodore BASIC.
A337080 (program): Complement of A337037.
A337084 (program): a(n) is the smallest nonzero digit d whose product d*n will contain the digit d, or 0 if no such digit exists.
A337099 (program): Largest positive number using exactly n segments on a calculator display (when ‘6’ and ‘7’ are represented using 6 resp. 3 segments).
A337101 (program): Number of partitions of n into two positive parts (s,t), s <= t, such that the harmonic mean of s and t is an integer.
A337102 (program): Number of partitions of n into two positive integer parts (s,t), s<=t, such that the harmonic mean of the smallest and largest part is not an integer.
A337106 (program): Number of nontrivial divisors of n!.
A337110 (program): Number of length three 1..n vectors that contain their geometric mean.
A337120 (program): Factor complexity (number of subwords of length n) of the regular paperfolding sequence (A014577), and all generalized paperfolding sequences.
A337129 (program): Triangular array read by rows: T(n,0) = 2^n, T(n,k) = Sum_{i=n-k..n, j=0..i-n+k, i<>n or j<>k} T(i,j) for k > 0.
A337130 (program): a(n) is the sum of all products of pairs of numbers joined by the diagonals of an n-gon when its vertices are numbered from 1 to n in order.
A337131 (program): Row lengths of irregular triangle A335967.
A337132 (program): a(n) is the number of squares at distance n from the central square of a Vicsek fractal.
A337134 (program): a(n) = Sum_{k=1..n} floor(sqrt(2k-1)).
A337135 (program): a(1) = 1; for n > 1, a(n) = Sum_{d|n, d <= sqrt(n)} a(d).
A337140 (program): Numbers m = a + b with a and b positive integers whose product a*b = k^2 is a square.
A337141 (program): Numbers having at least one 6 in their representation in base 7.
A337142 (program): a(n) is the number of words of length n over the alphabet {0,1,2} with at least two 1’s and exactly one occurrence of the subword 22.
A337148 (program): Concatenation of sum n+(n+1) and product n*(n+1) in decimal.
A337151 (program): a(n) = (n!)^2 * Sum_{k=0..n} (-1)^(n-k) * (k+1) / ((n-k)!)^2.
A337152 (program): a(n) = 2^n * (n!)^2 * Sum_{k=0..n} 1 / ((-2)^k * (k!)^2).
A337153 (program): a(n) = 3^n * (n!)^2 * Sum_{k=0..n} 1 / ((-3)^k * (k!)^2).
A337154 (program): a(n) = 4^n * (n!)^2 * Sum_{k=0..n} 1 / ((-4)^k * (k!)^2).
A337155 (program): a(n) = 5^n * (n!)^2 * Sum_{k=0..n} 1 / ((-5)^k * (k!)^2).
A337167 (program): a(n) = 1 + 3 * Sum_{k=0..n-1} a(k) * a(n-k-1).
A337168 (program): a(n) = (-1)^n + 2 * Sum_{k=0..n-1} a(k) * a(n-k-1).
A337169 (program): a(n) = (-1)^n + 3 * Sum_{k=0..n-1} a(k) * a(n-k-1).
A337171 (program): a(n) = A004186(n) mod n.
A337173 (program): a(n) = Sum_{k=1..floor(n/2)} k^2 * (n-k)^2.
A337174 (program): Number of pairs of divisors of n (d1,d2) such that d1 <= d2 and d1*d2 >= n.
A337175 (program): Number of pairs of divisors of n, (d1,d2), such that d1 <= d2 and d1*d2 < n.
A337177 (program): Sum of the divisors d of n such that d is not equal to n/d.
A337178 (program): Number of biconnected geodetic graphs with n unlabeled vertices.
A337180 (program): a(n) = Sum_{d|n} d * gcd(d,n/d).
A337186 (program): a(n) = 1 + Sum_{k=0..n-2} binomial(n-2,k) * a(k).
A337191 (program): If cards numbered 1 through n are “Down Two Table” shuffled (top two put on bottom one at a time, third from top card dealt to table) until all of the cards are placed on the table, a(n) is the number of the last card dealt.
A337192 (program): Triangular array read by rows. T(n,k) is the number of elements of rank k in the order complex of the poset P = [n] X [n], n=0, k=0 or n>0, 0<=k<=2n-1.
A337193 (program): Total number of inversions in all permutations of [n] where the descent set equals the subset of odd elements in [n-1].
A337194 (program): a(n) = 1 + A000265(sigma(n)), where A000265 gives the odd part.
A337195 (program): The 2-adic valuation of 1+A000265(sigma(n)), where A000265 gives the odd part.
A337199 (program): Binary weight of A337194(n) = 1+A000265(sigma(n)), where A000265(k) gives the odd part of k.
A337203 (program): Sum of the divisors of the primorial inflation of n.
A337204 (program): Sum of the odd divisors of the primorial inflation of n.
A337217 (program): One half of the even numbers of A094739.
A337238 (program): Number k such that k and k+1 are both digitally balanced numbers in base 2 (A031443).
A337239 (program): Numbers having at least one 7 in their representation in base 8.
A337244 (program): Perimeters of integer-sided triangles such that the harmonic mean of all the side lengths and the harmonic mean of each pair of side lengths is an integer
A337246 (program): Sum of the first coordinates of all pairs of prime divisors of n, (p,q), such that p <= q.
A337250 (program): Numbers having at least one 3 in their representation in base 4.
A337252 (program): Digits of 2^n can be rearranged with no leading zeros to form t^2, for t not a power of 2.
A337256 (program): Number of strict chains of divisors of n.
A337257 (program): Number of even divisors of n!.
A337273 (program): Number of distinct positive integer pairs, (s,t), such that s < t < n where neither s nor t divides n.
A337277 (program): Stern’s triangle read by rows.
A337281 (program): a(n) = n*T(n), where T(n) = A000073(n) = n-th tribonacci number.
A337282 (program): Partial sums of A337281.
A337283 (program): a(n) = Sum_{i=0..n} i*T(i)^2, where T(i) = A000073(i) is the i-th tribonacci number.
A337284 (program): a(n) = Sum_{i=1..n} (i-1)*T(i)^2, where T(i) = A000073(i) is the i-th tribonacci number.
A337285 (program): a(n) = Sum_{i=1..n} (i-1)^2*T(i)^2, where T(i) = A000073(i) is the i-th tribonacci number.
A337286 (program): a(n) = Sum_{i=0..n} i^2*T(i)^2, where T(i) = A000073(i) is the i-th tribonacci number.
A337288 (program): Numbers k such that k is in A095096 and k+1 is in A020899.
A337289 (program): Numbers k such that k+1 is in A095096 and k is in A020899.
A337291 (program): a(n) = 3*binomial(4*n,n)/(4*n-1).
A337292 (program): a(n) = 4*binomial(5*n,n)/(5*n-1).
A337297 (program): Sum of the coordinates of all pairs of divisors of n, (d1,d2), such that d1 < d2.
A337298 (program): Sum of the coordinates of all relatively prime pairs of divisors of n, (d1,d2), such that d1 <= d2.
A337299 (program): Expansion of Product_{k>0} (1 - 2^(k-1)*x^k).
A337300 (program): Partial sums of the geometric Connell sequence A049039.
A337302 (program): Number of X-based filling of diagonals in a diagonal Latin square of order n with fixed main diagonal.
A337303 (program): Number of X-based filling of diagonals in a diagonal Latin square of order n.
A337307 (program): a(1) = 1; a(n) = 1 + Product_{k=1..n-1} a(k) (mod n-1).
A337313 (program): a(n) is the number of n-digit positive integers with exactly three distinct base 10 digits.
A337314 (program): a(n) is the number of n-digit positive integers with exactly four distinct base 10 digits.
A337319 (program): a(n) = Sum_{i = 1..floor(log_2(n))+1} g(frac(n/2^i)), where g(t) = [0 if t = 0, -1 if 0 < t < 1/2, 1 if t >= 1/2], and where frac(x) denotes the fractional part.
A337322 (program): Number of ordered pairs of divisors of n, (d1,d2), such that d2 is prime and d1 < d2.
A337323 (program): a(n) = gcd(n, tau(n), sigma(n), pod(n)) where tau(k) is the number of divisors of k (A000005), sigma(k) is the sum of divisors of k (A000203) and pod(k) is the product of divisors of k (A007955).
A337328 (program): Number of pairs of squarefree divisors of n, (d1,d2), such that d1 <= d2.
A337329 (program): Sum of the products of all pairs of divisors of n, (d1,d2), such that d1|n, d2|n, d1|d2 and d1<d2.
A337333 (program): Number of pairs of odd divisors of n, (d1,d2), such that d1 <= d2.
A337336 (program): a(n) = A048673(n^2).
A337345 (program): Number of divisors d of n for which A003961(d) > 2*d.
A337346 (program): Number of proper divisors d of n for which A003961(d) > 2*d.
A337348 (program): Numbers formed as the product of two numbers without consecutive equal binary digits and sharing no common bits between them.
A337349 (program): To get a(n), take 3*n+1 and divide out any power of 2; then multiply by 3, subtract 1 and divide out any power of 2.
A337350 (program): a(n) is the number of lattice paths from (0,0) to (2n,2n) using only the steps (1,0) and (0,1) and which do not touch any other points of the form (2k,2k).
A337360 (program): Sum of the coordinates of all pairs of divisors of n, (d1,d2), such that d1 <= d2.
A337362 (program): Number of pairs of divisors of n, (d1,d2), with d1 <= d2 such that d1 and d2 are nonconsecutive integers.
A337363 (program): a(n) = Sum_{d1|n, d2|n, d1<d2} (1 - [d1 + 1 = d2]), where [ ] is the Iverson bracket.
A337369 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of sqrt(2 / ( (1-2*(k+4)*x+((k-4)*x)^2) * (1+(k-4)*x+sqrt(1-2*(k+4)*x+((k-4)*x)^2)) )).
A337370 (program): Expansion of sqrt(2 / ( (1-12*x+4*x^2) * (1-2*x+sqrt(1-12*x+4*x^2)) )).
A337373 (program): Numbers k for which A003961(k) > 3*k.
A337374 (program): Numbers k for which A003961(k) > 4*k.
A337376 (program): Primorial deflation (numerator) of Doudna-tree.
A337377 (program): Primorial deflation (denominator) of Doudna-tree.
A337381 (program): Numbers k for which A003973(k) >= 2*sigma(k).
A337382 (program): Numbers k for which A003973(k) < 2*sigma(k).
A337383 (program): a(n) = 1 if sigma(A003961(n)) >= 2*sigma(n), 0 otherwise, where A003961 is the prime shift towards larger primes.
A337387 (program): a(n) = Sum_{k=0..n} n^(n-k) * binomial(2*k,k) * binomial(2*n+1,2*k).
A337388 (program): a(n) = Sum_{k=0..n} n^(n-k) * binomial(2*k,k) * binomial(2*n,2*k).
A337389 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of sqrt((1+(k-4)*x+sqrt(1-2*(k+4)*x+((k-4)*x)^2)) / (2 * (1-2*(k+4)*x+((k-4)*x)^2))).
A337390 (program): Expansion of sqrt((1-2*x+sqrt(1-12*x+4*x^2)) / (2 * (1-12*x+4*x^2))).
A337391 (program): a(n) is the smallest n-digit number divisible by n^3.
A337392 (program): Minimum m such that the convergence speed of m^^m is equal to n >= 2, where A317905(n) represents the convergence speed of m^^m (and m = A067251(n), the n-th non-multiple of 10).
A337393 (program): Expansion of sqrt((1-5*x+sqrt(1-6*x+25*x^2)) / (2 * (1-6*x+25*x^2))).
A337394 (program): Expansion of sqrt(2 / ( (1-6*x+25*x^2) * (1-5*x+sqrt(1-6*x+25*x^2)) )).
A337396 (program): Expansion of sqrt((1-8*x+sqrt(1+64*x^2)) / (2 * (1+64*x^2))).
A337397 (program): Expansion of sqrt(2 / ( (1+64*x^2) * (1-8*x+sqrt(1+64*x^2)) )).
A337402 (program): Decimal expansion of the length of third shortest diagonal in a regular 12-gon with unit edge length.
A337418 (program): Number of sets (in the Hausdorff metric geometry) at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 3) missing two edges, where the removed edges are not incident to the same vertex in the 3 point part but are incident to the same vertex in the other part.
A337419 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of sqrt((1-(k+4)*x+sqrt(1+2*(k-4)*x+((k+4)*x)^2)) / (2 * (1+2*(k-4)*x+((k+4)*x)^2))).
A337420 (program): a(n) = Sum_{k=0..n} (-n)^(n-k) * binomial(2*k,k) * binomial(2*n,2*k).
A337421 (program): Expansion of sqrt((1-6*x+sqrt(1-4*x+36*x^2)) / (2 * (1-4*x+36*x^2))).
A337422 (program): Expansion of sqrt((1-7*x+sqrt(1-2*x+49*x^2)) / (2 * (1-2*x+49*x^2))).
A337443 (program): E.g.f.: (1 + x) * exp(x) / (sec(x) + tan(x)).
A337444 (program): Expansion of e.g.f. (1 + 2*x) * exp(x) / (sec(x) + tan(x)).
A337445 (program): E.g.f.: 1 / ((sec(x) + tan(x)) * (1 - x)).
A337464 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of sqrt(2 / ( (1+2*(k-4)*x+((k+4)*x)^2) * (1-(k+4)*x+sqrt(1+2*(k-4)*x+((k+4)*x)^2)) )).
A337465 (program): a(n) = Sum_{k=0..n} (-n)^(n-k) * binomial(2*k,k) * binomial(2*n+1,2*k).
A337466 (program): Expansion of sqrt(2 / ( (1-4*x+36*x^2) * (1-6*x+sqrt(1-4*x+36*x^2)) )).
A337467 (program): Expansion of sqrt(2 / ( (1-2*x+49*x^2) * (1-7*x+sqrt(1-2*x+49*x^2)) )).
A337471 (program): Primorial inflation of n prime shifted once: a(n) = A003961(A108951(n)).
A337481 (program): Number of compositions of n that are neither strictly increasing nor strictly decreasing.
A337482 (program): Number of compositions of n that are neither strictly increasing nor weakly decreasing.
A337483 (program): Number of ordered triples of positive integers summing to n that are either weakly increasing or weakly decreasing.
A337484 (program): Number of ordered triples of positive integers summing to n that are neither strictly increasing nor strictly decreasing.
A337492 (program): a(n) = a(n-1) + 4*a(n-3) + 2*a(n-4) + 2*a(n-5); a(0) = a(1) = a(2) = 1, a(3) = 5, a(4) = 11.
A337493 (program): Decimal expansion of 10800/Pi, number of minutes of arc in a radian.
A337495 (program): Maximum number of preimages that a permutation of length n can have under the consecutive-123-avoiding stack-sorting map.
A337496 (program): Number of bases b for which the expansion of n in base b contains the largest digit possible (i.e., the digit b-1).
A337499 (program): a(n) is the number of ballot sequences of length n tied or won by at most 2 votes.
A337500 (program): a(n) is the number of ballot sequences of length n tied or won by at most 3 votes.
A337501 (program): Minimum number of painted cells in an n X n grid to avoid unpainted trominoes.
A337502 (program): Minimum number of painted cells in an n X n grid to avoid unpainted tetrominoes.
A337503 (program): Minimum number of painted cells in an n X n grid to avoid unpainted pentominoes.
A337505 (program): Number of sequences of length 2*n covering an initial interval of positive integers and splitting into n maximal anti-runs.
A337507 (program): Number of length-n sequences covering an initial interval of positive integers with exactly two maximal anti-runs, or with one pair of adjacent equal parts.
A337509 (program): Number of partitions of n into two distinct parts (s,t), such that (t-s) | n, and where n/(t-s) <= s < t.
A337512 (program): G.f. A(x) satisfies: A(x) = 1 - Sum_{k=1..3} (x * A(x))^k.
A337519 (program): Length of the shortest walk in an n X n grid graph that starts in one corner and visits every edge.
A337521 (program): a(n) = L(n)*a(n-1) + a(n-2) with a(0) = a(1) = 1 and L(n) the Lucas numbers A000032.
A337524 (program): a(n) = d(n) * (d(n) - 1), where d is the number of divisors of n (A000005).
A337527 (program): G.f.: Sum_{n>=0} (2^n + 1)^n * x^n / (1 + (2^n + 1)*x)^(n+1).
A337528 (program): G.f.: Sum_{n>=0} (2^n + 1)^n * x^n / (1 + (2^n - 1)*x)^(n+1).
A337532 (program): a(n) = Sum_{d1|n, d2|n, d1<=d2} [(d1 mod 2) = (d2 mod 2)], where [ ] is the Iverson bracket.
A337533 (program): 1 together with nonsquares whose square part’s square root is in the sequence.
A337535 (program): For n>1, a(n) is the least base b>2 such that the digits of n in base b contain the digit b-1; a(1)=1.
A337541 (program): Number of divisors d of n for which sigma(A003961(d)) >= 2*sigma(d), where sigma is the sum of divisors, and A003961(x) shifts the prime factorization of x one step towards larger primes.
A337544 (program): a(n) = 2*phi(A003961(n)) - A003961(n).
A337549 (program): a(n) = A003972(n) - n.
A337559 (program): Number of length three 1..n vectors that contain their harmonic mean.
A337564 (program): Number of sequences of length 2*n covering an initial interval of positive integers and splitting into n maximal runs.
A337566 (program): a(n) is the number of possible decompositions of the polynomial n * (x + x^2 + … + x^q), where q > 1, into a sum of k polynomials, not necessarily all different; each of these polynomials is to be of the form b_1 * x + b_2 * x^2 + … + b_q * x^q where each b_i is one of the numbers 1, 2, 3, …, q and no two b_i are equal.
A337567 (program): Let a(0) = 1, k(0) = 1. For n >= 1; if a(n-1) + k(n-1) is a prime, then a(n) = a(n-1) + k(n-1), k(n) = k(n-1); else a(n) = a(n-1) + k(n-1) + 1, k(n) = k(n-1) + 1.
A337569 (program): Decimal expansion of the real solution to x^3 = 3 - x.
A337570 (program): Decimal expansion of the real positive solution to x^4 = 4-x.
A337571 (program): Decimal expansion of the real positive solution to x^4 = x+4.
A337572 (program): Numbers having at least one 4 in their representation in base 5.
A337582 (program): Numbers m such that m AND (m*2^k) is zero or a power of 2 for any k > 0 (where AND denotes the bitwise AND operator).
A337588 (program): Number of distinct positive integer pairs, (s,t), such that s < t < n where neither s nor t divides n, but s | t.
A337616 (program): Row sums of A337967.
A337623 (program): a(n) is the least positive multiple of 2*n-1 containing only the digits 0 and 1 in base n.
A337624 (program): a(n) is the least positive integer in base n that when multiplied by 2n-1 will contain only the digits 0 and 1.
A337631 (program): a(n) is the sum of the squares of diameters of all nonempty subsets of {1,2,…,n}.
A337635 (program): Number of numbers k <= n such that k is in A095096 and k+1 is in A020899.
A337636 (program): Number of numbers k <= n such that k+1 is in A095096 and k is in A020899.
A337640 (program): a(n) = one-half of the number of cells in the central rectangle of the graph described in row 2n+1 of A333288.
A337666 (program): Numbers k such that any two parts of the k-th composition in standard order (A066099) have a common divisor > 1.
A337674 (program): Numbers k whose prime divisors are all less than or equal to the number of divisors of k.
A337686 (program): a(n) is the least multiplier k such that n*k has twice as many divisors as n.
A337690 (program): a(n) is the number of primitive nondeficient numbers (A006039) dividing n.
A337692 (program): a(n) is the sum of all positive integers whose digits in base n are strictly decreasing.
A337694 (program): Numbers with no two relatively prime prime indices.
A337698 (program): Number of compositions of n that are not strictly increasing.
A337710 (program): Decimal expansion of 8*Pi^6/63 = 5!*zeta(6).
A337711 (program): Decimal expansion of (7/120)*Pi^4 = (21/4)*zeta(4).
A337723 (program): a(n) = prime(n-2) - ceiling(a(n-2)/2); a(1)=0, a(2)=1.
A337724 (program): a(n) = prime(n-2) - floor(a(n-2)/2); a(1)=0, a(2)=1.
A337725 (program): a(n) = (3*n+1)! * Sum_{k=0..n} 1 / (3*k+1)!.
A337726 (program): a(n) = (3*n+2)! * Sum_{k=0..n} 1 / (3*k+2)!.
A337727 (program): a(n) = (4*n)! * Sum_{k=0..n} 1 / (4*k)!.
A337728 (program): a(n) = (4*n+1)! * Sum_{k=0..n} 1 / (4*k+1)!.
A337729 (program): a(n) = (4*n+2)! * Sum_{k=0..n} 1 / (4*k+2)!.
A337730 (program): a(n) = (4*n+3)! * Sum_{k=0..n} 1 / (4*k+3)!.
A337747 (program): Maximal number of 4-point circles passing through n points on a plane.
A337749 (program): a(n) = n! * Sum_{k=0..floor(n/2)} (-1)^k / (n-2*k)!.
A337750 (program): a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^k / (n-3*k)!.
A337751 (program): a(n) = n! * Sum_{k=0..floor(n/4)} (-1)^k / (n-4*k)!.
A337753 (program): The number of n-digit numbers which are divisible by 3 and where all decimal digits are odd.
A337759 (program): Squares that are the sum of 3 distinct nonzero squares.
A337771 (program): Number of positive integer pairs, (s,t), with s,t composite, such that s < t < n, and neither s nor t divides n.
A337788 (program): The number of primes between n exclusive and n+primepi(n) inclusive.
A337821 (program): For n >= 0, a(4n+1) = 0, a(4n+3) = a(2n+1) + 1, a(2n+2) = a(n+1).
A337823 (program): a(n) = prime(n-1) - floor(a(n-1)/2); a(1)=1.
A337827 (program): a(n) is the number of 2n-bead necklaces with exactly n different colored beads.
A337835 (program): a(1) = 0 and for n > 1, a(n+1) = k - a(n) where k is the number of terms equal to a(n) among the first n terms.
A337843 (program): a(n) is n + the number of digits in the decimal expansion of n.
A337851 (program): a(n) = (2^n + 2)^n.
A337852 (program): a(n) = (2^(n+1) + 1)^n.
A337855 (program): Number of n-digit positive integers that are the product of two integers ending with 5.
A337864 (program): a(n) is the number formed by removing from n each digit if it is a duplicate of the previous digit, from left to right.
A337869 (program): The number of random walks on the simple square lattice that return to the origin (0,0) after 2n steps and do not pass through (0,0) or (1,0) at intermediate steps.
A337870 (program): The number of random walks on the simple square lattice that start at the origin (0,0) and pass through (1,0) after 2n+1 steps before having returned to the origin.
A337877 (program): Numbers of the form p^2*q where p and q are primes and p <= q.
A337878 (program): a(n) is the smallest m > 0 such that the n-th prime divides Jacobsthal(m).
A337879 (program): a(n) is the length of the n-th line segment to draw the squares of the Fibonacci spiral without lifting the pencil, including superpositions.
A337895 (program): Number of oriented colorings of the tetrahedral facets (or vertices) of a regular 4-dimensional simplex using n or fewer colors.
A337896 (program): Number of chiral pairs of colorings of the 8 triangular faces of a regular octahedron or the 8 vertices of a cube using n or fewer colors.
A337897 (program): Number of achiral colorings of the 8 triangular faces of a regular octahedron or the 8 vertices of a cube using n or fewer colors.
A337898 (program): Number of achiral colorings of the 6 square faces of a cube or the 6 vertices of a regular octahedron using n or fewer colors.
A337899 (program): Number of chiral pairs of colorings of the edges of a regular tetrahedron using n or fewer colors.
A337900 (program): The number of walks of length 2n on the square lattice that start from the origin (0,0) and end at the vertex (2,0).
A337901 (program): The number of walks of length 2n+1 on the square lattice that start from the origin (0,0) and end at the vertex (3,0).
A337902 (program): The number of walks of length 2n+1 on the square lattice that start from the origin (0,0) and end at the vertex (2,1).
A337905 (program): The number of walks of n steps on the hexagonal lattice that start at the origin and end at the adjacent vertex (1,0).
A337909 (program): Distinct terms of A080079 in the order in which they appear.
A337921 (program): a(n) is the sum of (3^n mod 2^k) for k such that 2^k < 3^n.
A337923 (program): a(n) is the exponent of the highest power of 2 dividing the n-th Fibonacci number.
A337927 (program): a(n) = n / GCD (n, reverse of n).
A337928 (program): Numbers w such that (F(2n+1)^2, -F(2n)^2, -w) are primitive solutions of the Diophantine equation 2*x^3 + 2*y^3 + z^3 = 1, where F(n) is the n-th Fibonacci number (A000045).
A337929 (program): Numbers w such that (F(2*n-1)^2, -F(2*n)^2, w) are primitive solutions of the Diophantine equation 2*x^3 + 2*y^3 + z^3 = 1, where F(n) is the n-th Fibonacci number (A000045).
A337932 (program): Number of ways to write n as the sum of two deficient numbers (A005100).
A337934 (program): Sums of two distinct abundant numbers.
A337937 (program): a(n) = Euler totient function phi = A000010 evaluated at N(n) = floor((3*n-1)/2) = A001651(n), for n >= 1.
A337938 (program): Irregular triangle read by rows: T(n, k) gives the primitive period of the sequence {k (Modd n)}_{k >= 0}, for n >= 1.
A337940 (program): Triangle read by rows: T(n, k) = T(n+2) - T(n-k), with the triangular numbers T = A000217, for n >= 1, k = 1, 2, …, n.
A337945 (program): Numbers m with a solution (s,t,k) such that s^2 + t^2 = k*m, s + t = m, 1 <= s <= t and 1 <= k <= m - 1.
A337949 (program): a(n) = 2^(n*(n-1)/2) + 2^(n*(n+1)/2) for n > 0, with a(0) = 1.
A337951 (program): a(n) = 4^(n*(n-1)/2) + 4^(n*(n+1)/2) for n > 0, with a(0) = 1.
A337957 (program): Number of unoriented colorings of the 8 cubic facets of a tesseract or of the 8 vertices of a hyperoctahedron.
A337958 (program): Number of achiral colorings of the 8 cubic facets of a tesseract or of the 8 vertices of a hyperoctahedron.
A337966 (program): Triangle read by rows, coefficients of polynomials over {-1, 0, 1}. Also a triangle-to-triangle transformation U -> T(U) applied to the triangle U(n, k) = 1.
A337969 (program): a(n) = 3^(n*(n-1)/2) + 3^(n*(n+1)/2) for n > 0, with a(0) = 1.
A337971 (program): a(n) = 5^(n*(n-1)/2) + 5^(n*(n+1)/2) for n > 0, with a(0) = 1.
A337976 (program): Number of partitions of n into two distinct parts (s,t), such that s | t, (t-s) | n, and where n/(t-s) <= s < t.
A337978 (program): a(n) = n + pi(n) - pi(n + pi(n)), where pi(n) is the prime count of n (n>=1).
A337979 (program): Define a map f(n):= n-> n + pi(n) - pi(n + pi(n)), where pi(n) is the prime count of n (n>=1). a(n) is the number of steps for n to reach 1 under repeated iteration of f.
A337985 (program): a(n) is the exponent of the highest power of 2 dividing the n-th Bell number.
A337997 (program): Triangle read by rows, generalized Eulerian polynomials evaluated at x = 1.
A338020 (program): a(n) is the number of circles of positive integer area with radii less than n and greater than n - 1.
A338021 (program): Number of partitions of n into two parts (s,t) such that s <= t and t | s*n.
A338038 (program): a(n) is the sum of the primes and exponents in the prime factorization of n, but ignoring 1-exponents.
A338041 (program): Draw n rays from each of two distinct points in the plane; a(n) is the number of regions thus created. See Comments for details.
A338042 (program): Draw n rays from each of two distinct points in the plane; a(n) is the number of vertices thus created. See Comments for details.
A338043 (program): Draw n rays from each of two distinct points in the plane; a(n) is the number of edges thus created. See Comments for details.
A338045 (program): G.f.: Sum_{k>=0} x^(2^k) / (1 - x^(2^k))^3.
A338046 (program): G.f.: Sum_{k>=0} x^(2^k) / (1 - x^(2^k))^4.
A338062 (program): Numbers k such that the Enots Wolley sequence A336957(k) is odd.
A338064 (program): Numbers k such that the Enots Wolley sequence A336957(k) is even.
A338075 (program): Diagonal terms in the expansion of (1+x*y*z)/(1-x-y-z).
A338076 (program): Diagonal terms in the expansion of 1/(1-x-2*y-3*z).
A338077 (program): Diagonal terms in the expansion of (1+x*y+y*z+z*x)/(1-x-y-z).
A338086 (program): Duplicate the ternary digits of n, so each 0, 1 or 2 becomes 00, 11 or 22 respectively.
A338090 (program): Numbers having at least one 8 in their representation in base 9.
A338100 (program): Number of spanning trees in the n X 2 king graph.
A338101 (program): Smallest odd prime dividing n is a(n)-th prime, or 0 if no such prime exists.
A338108 (program): Numbers that follow from the alternating series a(n) = d(1) - d(2) + d(3) - d(4) + … + (-1)^(n+1) d(n), where d(k) denotes the k-th term of the digit sequence of Euler’s number e.
A338109 (program): a(n)/A002939(n+1) is the Kirchhoff index of the join of the disjoint union of two complete graphs on n vertices with the empty graph on n+1 vertices.
A338110 (program): Number of spanning trees in the join of the disjoint union of two complete graphs each on n vertices with the empty graph on n vertices.
A338112 (program): Least number that is both the sum and product of n distinct positive integers.
A338117 (program): Number of partitions of n into two parts (s,t) such that (t-s) | n, where s < t.
A338128 (program): a(n) is the least k > 1 such that the base n representation of k^k ends with that of k.
A338130 (program): Positive numbers k such that the ternary representation of k^k ends with that of k.
A338131 (program): Triangle read by rows, T(n, k) = k^(n - k) + Sum_{i = 1..n-k} k^(n - k - i)*2^(i - 1), for 0 <= k <= n.
A338138 (program): Nested cube root (b(n) + (b(n-1) + … + (b(1))^(1/3)…)^(1/3))^(1/3), where b(n) = A338137(n).
A338153 (program): a(n) is the number of acyclic orientations of the edges of the n-prism.
A338157 (program): Numbers that follow from the alternating series a(n) = d(1) - d(2) + d(3) -d(4) + … + (-1)^(n+1) d(n), where d(k) denotes the k-th term of the digit sequence of the Golden Ratio.
A338164 (program): Dirichlet g.f.: (zeta(s-2) / zeta(s))^2.
A338165 (program): Dirichlet g.f.: (zeta(s-3) / zeta(s))^2.
A338170 (program): a(n) is the number of divisors d of n such that tau(d) divides sigma(d).
A338171 (program): a(n) is the sum of those divisors d of n such that tau(d) divides sigma(d).
A338172 (program): a(n) is the product of those divisors d of n such that tau(d) divides sigma(d).
A338186 (program): Expansion of (2-6*x-12*x^2)/((1-x)^2*(1-9*x)).
A338187 (program): E.g.f. A(x) satisfies: A(x) = 1 + Integral (x/A(x)^3)’ / (x/A(x)^4)’ dx.
A338188 (program): E.g.f. A(x) satisfies: A(x) = 1 + Integral (x/A(x)^8)’ / (x/A(x)^9)’ dx.
A338192 (program): Sum of Fibonacci and tribonacci numbers: a(n) = A000073(n) + A000045(n).
A338193 (program): E.g.f. A(x) satisfies: A(x) = 1 + Integral (x/A(x))’ / (x/A(x)^2)’ dx.
A338198 (program): Triangle read by rows, T(n,k) = ((k+1)*2^(n-k)-(k-2)*(-1)^(n-k))/3 for 0 <= k <= n.
A338199 (program): a(n) = v(1 + F(4*n - 3)), where F(x) = (3*x + 1)/2^v(3*x + 1), x is any odd natural number, and v(y) is the 2-adic valuation of y.
A338200 (program): The number of similarity classes of pointed reflection spaces of residue two in an n-dimensional vector space over GF(2).
A338204 (program): a(n) is the sum of odd-indexed terms (of every row) of the first n rows of the triangle A237591.
A338206 (program): Inverse of A160016.
A338215 (program): a(n) = A095117(A062298(n)).
A338220 (program): Numbers k such that the Motzkin number A001006(k) is divisible by 5.
A338225 (program): a(n) = F(n+3) * F(n+1) + (-1)^n where F(n) = A000045(n) are the Fibonacci numbers.
A338226 (program): a(n) = Sum_{i=0..n-1} i*10^i - Sum_{i=0..n-1} (n-1-i)*10^i.
A338227 (program): a(n) = x(n) mod floor(sqrt(x(n))), where x(n) = floor((n^2)/2).
A338228 (program): Number of numbers less than or equal to n whose square does not divide n.
A338229 (program): Number of ternary strings of length n that contain at least one 0 and at most two 1’s.
A338230 (program): Number of ternary strings of length n that contain at least two 0’s and at most one 1.
A338231 (program): Sum of the numbers less than or equal to n whose square does not divide n.
A338232 (program): Number of ternary strings of length n that contain at least two 0’s and at most two 1’s.
A338233 (program): Number of numbers less than n whose square does not divide n.
A338234 (program): Sum of the numbers less than n whose square does not divide n.
A338236 (program): Number of numbers less than or equal to sqrt(n) whose square does not divide n.
A338241 (program): For any m >= 0, a(3*m) = 3*a(m), a(3*m+1) = 1-3*a(m), a(3*m+2) = 3*a(m)-1.
A338242 (program): a(n) = -A338241(2*n) for any n >= 0.
A338243 (program): a(0) = 0, a(n) = A338241(2*n-1) for any n > 0.
A338245 (program): Nonnegative values in A117966, in order of appearance.
A338246 (program): Nonpositive values in A117966, in order of appearance and negated.
A338247 (program): Inverse permutation to A338245.
A338248 (program): Nonnegative values in A053985, in order of appearance.
A338249 (program): Nonpositive values in A053985, in order of appearance and negated.
A338251 (program): Nonnegative values in A317050, in order of appearance.
A338252 (program): Nonpositive values in A317050, in order of appearance and negated.
A338280 (program): Triangle T read by rows: T(n, k) = k*n^(n-k-1) with 0 < k < n.
A338281 (program): a(n) is the sum of n and the largest proper divisor of n.
A338284 (program): a(n) is the smallest nonsquare m such that the second partial quotient in the continued fraction for sqrt(m) equals n.
A338291 (program): Matrix inverse of the rascal triangle (A077028), read across rows..
A338295 (program): For n > 1, a(n) is the largest base b <= n such that the digits of n in base b contain the digit b-1; a(1) = 1.
A338321 (program): Trace of complement matrix for polynomial triangle centers of degree n (on the Nagel line).
A338329 (program): First differences of A326118.
A338337 (program): Coefficient of x^(6*n)*y^(6*n)*z^(6*n) in the expansion of 1/(1-x-y^2-z^3).
A338353 (program): A (0,1)-matrix in the first quadrant read by downward antidiagonals: an example of a non-uniformly recurrent 2-D word having uniformly recurrent rows and columns.
A338354 (program): A (0,1)-matrix in the first quadrant read by downward antidiagonals: an example of a uniformly recurrent 2-D word in which row 0 is non-recurrent.
A338356 (program): Indices of records in A283312.
A338361 (program): Indices of primes in A283312.
A338363 (program): a(n) = n + pi(n) - pi(floor(n/2)), where pi = A000720.
A338364 (program): a(n) = Product_{k=1..n} phi(prime(k)-1).
A338369 (program): Triangle read by rows: T(n,k) = (Sum_{i=0..n-k}(1+k*i)^3)/(Sum_{i=0..n-k} (1+k*i)) for 0 <= k <= n.
A338372 (program): T(n, m) = Sum_{k=1..(m+3)/2} C(m-k+2, k-1)*C(n+1, k-1)*C(n-m+k-1, k-1)*C(2*n-2*k+4, 2*m-4*k+5)/(C(2*k-2, k-1)*C(2*m-2*k+4, 2*k-2))/2, triangle read by rows.
A338373 (program): Numbers k such that bigomega(2*k + 1) >= 4.
A338375 (program): Number of digits in (2n)! / (2^n * n!).
A338399 (program): Inverse boustrophedon transform of the Fibonacci numbers.
A338429 (program): Maximum number of copies of a 1234 permutation pattern in an alternating (or zig-zag) permutation of length n + 5.
A338430 (program): Number of numbers less than sqrt(n) whose square does not divide n.
A338432 (program): Triangle read by rows: T(n, k) = (n - k + 1)^2 + 2*k^2, for n >= 1, and k = 1, 2, …, n.
A338434 (program): Sum of the numbers less than or equal to sqrt(n) whose square does not divide n.
A338435 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = n!*LaguerreL(n, -k*n).
A338448 (program): E.g.f.: 1 / (1 - x - log(1 - x)).
A338467 (program): a(n+1) = prime(n) + 2*n - a(n). a(1) = 1.
A338490 (program): Sum of indices of distinct odd prime factors of n.
A338506 (program): a(n) is the number of subsets of divisors of n.
A338510 (program): a(n) is smallest number in column n >= 0 of the triangle in A247687.
A338519 (program): Integers that can be expressed as a product d*tau(d), where tau is the number of divisors function, in a single way.
A338522 (program): Number of cyclic Latin squares of order n.
A338523 (program): Triangle T(n,m) = (2*m*n+2*n-2*m^2+1)*C(2*n+2,2*m+1)/(4*n+2).
A338524 (program): prime(n) Gray code decoding.
A338529 (program): a(n) = prime(n+2)*prime(n+3)-prime(n)*prime(n+1).
A338530 (program): a(n) = (prime(n) + a(n-1)) mod prime(n-1), a(1) = 1.
A338539 (program): Numbers having exactly two non-unitary prime factors.
A338544 (program): a(n) = (5*floor((n-1)/2)^2 + (4+(-1)^n)*floor((n-1)/2)) / 2.
A338546 (program): For n > 0, a(n) is the number of 1’s among the first T(n) terms of the sequence 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, …, k 1’s, k 0’s, where T(n) is the n-th triangular number.
A338550 (program): Number of binary trees of height n such that the number of nodes at depth d equals d+1 for every d = 0..n.
A338563 (program): a(n) = lcm(n, tau(n), sigma(n)) where tau(k) is the number of divisors of k (A000005) and sigma(k) is the sum of divisors of k (A000203).
A338576 (program): a(n) = n * pod(n) where pod(n) = the product of divisors of n (A007955).
A338588 (program): a(n)/A002939(n+1) is the Kirchhoff index of the disjoint union of two complete graphs each on n and n+1 vertices with the empty graph on n+1 vertices.
A338589 (program): Sum of the remainders (s*t mod n), where s + t = n and 1 <= s <= t.
A338595 (program): Denominators of resistance values < 1 ohm that can be obtained from a network of exactly 5 one-ohm resistors, but not from any network with fewer than 5 one-ohm resistors. Numerators are in A338580.
A338610 (program): Integers m such that there exist one prime p and one positive integer k, for which the expression k^3 + k^2*p is a perfect cube m^3.
A338616 (program): a(n) is twice the number of parts in all partitions of n into consecutive parts.
A338623 (program): a(n) is the length of the longest block of consecutive terms appearing twice (possibly with overlap) among the first n terms of the Thue-Morse sequence (A010060).
A338630 (program): Least number of odd primes that add up to n, or 0 if no such representation is possible.
A338639 (program): a(0) = 1; for n > 0, a(n) = -Sum_{d|n, d < n} a(d - 1).
A338647 (program): a(n) = Sum_{k=1..n} 2^(k/gcd(n,k) - 1).
A338648 (program): Number of divisors of n which are greater than 4.
A338649 (program): Number of divisors of n which are greater than 5.
A338650 (program): Number of divisors of n which are greater than 6.
A338651 (program): Number of divisors of n which are greater than 7.
A338652 (program): Number of divisors of n which are greater than 8.
A338653 (program): Number of divisors of n which are greater than 9.
A338654 (program): T(n, k) = 2^n * Product_{j=1..k}((j/2)^((-1)^(j - 1)). Triangle read by rows, for 0 <= k <= n.
A338658 (program): a(n) = Sum_{d|n} d * binomial(d+n/d-1, d).
A338661 (program): a(n) = Sum_{d|n} d^n * binomial(d+n/d-2, d-1).
A338662 (program): a(n) = Sum_{d|n} (n/d)^d * binomial(d+n/d-1, d).
A338663 (program): a(n) = Sum_{d|n} (n/d)^n * binomial(d+n/d-1, d).
A338666 (program): a(1)=1 and a(2)=2. For all n > 2, a(n) is the smallest number > a(n-1) by a number > the difference between a(n-1) and a(n-2) so that consecutive terms of sequence are always relatively prime.
A338667 (program): Numbers that are the sum of two positive cubes in exactly one way.
A338680 (program): Numbers that do not occur as differences of consecutive terms of A338666.
A338682 (program): a(n) = Sum_{d|n} (-1)^(d-1) * binomial(d+n/d-1, d).
A338685 (program): a(n) = Sum_{d|n} d^n * binomial(d, n/d).
A338690 (program): Inverse Moebius transform of A209615.
A338691 (program): Positions of (-1)’s in A209615.
A338692 (program): Positions of 1’s in A209615.
A338694 (program): a(n) = Sum_{d|n} d^d * binomial(d, n/d).
A338695 (program): a(n) = Sum_{d|n} 2^(d-1) * binomial(d, n/d).
A338717 (program): a(n) = sum of 4th powers of entries in row n of Stern’s triangle A337277.
A338718 (program): Define b(1)=1 and for n>1, b(n)=n/b(n-1); then a(n) = floor(b(n)).
A338719 (program): Define b(1)=1 and for n>1, b(n)=n/b(n-1); then a(n) = ceiling(b(n)).
A338720 (program): Define b(1)=1 and for n>1, b(n)=n/b(n-1); then a(n) = nearest integer to b(n).
A338722 (program): Row sums in triangle A338721.
A338723 (program): Alternating row sums in triangle A338721.
A338726 (program): a(n) = Catalan(n) + 2^n - n - 1.
A338727 (program): a(n) = C(n+1)^2 - 2*C(n+1)*C(n) + C(n)^2, where C() is a Catalan number.
A338730 (program): Generating function Sum_{n >= 1} a(n)*x^n = Sum_{k>=1} k*x^(k*(3*k+1)/2)/(1-x^k).
A338731 (program): Generating function Sum_{n >= 0} a(n)*x^n = Sum_{k>=1} x^(k*(3*k+1)/2)/(1-x^k).
A338732 (program): Generating function Sum_{n >= 0} a(n)*x^n = Sum_{k>=1} x^(k*(3*k+1))/(1-x^k).
A338733 (program): Partial sums of A054843.
A338735 (program): a(n) = Bell(n) + n - 2 (cf. A000110).
A338754 (program): Duplicate each decimal digit of n, so 0 -> 00, …, 9 -> 99.
A338758 (program): a(n) is the sum of even-indexed terms (of every row) of first n rows of the triangle A237591.
A338760 (program): Subword complexity of a certain infinite word.
A338761 (program): Subword complexity of a certain infinite word.
A338790 (program): a(n) = rad(n)^2 - sigma(n), where rad(n) is the squarefree kernel of n (A007947) and sigma(n) is the sum of divisors of n (A000203).
A338795 (program): Each term of A003215 (centered hexagonal numbers) is multiplied by the corresponding term of A003154 (centered dodecagonal numbers).
A338796 (program): Triangle T read by rows: T(n, k) is the k-th row sum of the symmetric Toeplitz matrix M(n) whose first row consists of a single zero followed by successive positive integers repeated (A004526).
A338798 (program): a(n) = Sum_{k=1..n-1} lcm(lcm(n, k), lcm(n, n-k)).
A338803 (program): Product of the nonzero digits of (n written in base 5).
A338814 (program): Expansion of e.g.f. log(Product_{k>0} (1 + x^k)^(1/k)).
A338817 (program): Matrix inverse of triangle A176270, read by rows.
A338824 (program): Lexicographically earliest sequence of nonnegative integers such that for any distinct m and n, a(m) OR a(m+1) <> a(n) OR a(n+1) (where OR denotes the bitwise OR operator).
A338848 (program): Number of compositions (ordered partitions) of n into distinct powers of 3.
A338852 (program): a(n) = (7*floor(a(n-1)/3)) + (a(n-1) mod 3) with a(1) = 3.
A338854 (program): Product of the nonzero digits of (n written in base 4).
A338857 (program): With S(n,k) = Sum_{n<=j<=k} 1/(2*j+1), a(n)=k+1 such that S(n,k-1) < 1 <= S(n,k) for n>=0 and a(0)=1.
A338862 (program): a(n) is the number of polynomials of degree 2*n over the field GF(2) that have no factors of odd degree.
A338863 (program): Product of the nonzero digits of (n written in base 6).
A338878 (program): Numerators in a set of expansions of the single-term Machin-like formula for Pi.
A338880 (program): Product of the nonzero digits of (n written in base 7).
A338881 (program): Product of the nonzero digits of (n written in base 8).
A338882 (program): Product of the nonzero digits of (n written in base 9).
A338888 (program): a(n) = (a(n-2) bitwise-OR a(n-1)) + 1; a(1)=0, a(2)=0.
A338894 (program): Number of ordered pairs (x,y): 1 <= x, y <= n*n, such that x*y is a square.
A338896 (program): Inradii of Pythagorean triples of A338895.
A338900 (program): Difference between the two prime indices of the n-th squarefree semiprime.
A338901 (program): Position of the first appearance of prime(n) as a factor in the list of squarefree semiprimes.
A338902 (program): Number of integer partitions of the n-th semiprime into semiprimes.
A338907 (program): Semiprimes whose prime indices sum to an odd number.
A338908 (program): Squarefree semiprimes whose prime indices sum to an even number.
A338912 (program): Lesser prime index of the n-th semiprime.
A338913 (program): Greater prime index of the n-th semiprime.
A338920 (program): a(n) is the number of times it takes to iteratively subtract m from n where m is the largest nonzero proper suffix of n less than or equal to the remainder until no further subtraction is possible.
A338929 (program): a(n) is the smallest prime number p larger than A072668(n) such that p is equal to 1 (mod A072668(n)).
A338935 (program): a(n) = Sum_{d|n} (d^2 mod n).
A338937 (program): a(n+1) = A001414(a(n)) + A001414(a(n-1)) with a(0)=1, a(1)=2.
A338939 (program): a(n) is the number of partitions n = a + b such that a*b is a perfect square.
A338947 (program): Number of vertices of a hexagonal tessellation that lie on subsequent circles centered at a vertex of one hexagon.
A338971 (program): Linear representation of the complete labeled binary trees of all integer heights, where the nodes at level i, 0 <= i <= n, of a binary tree with height n are labeled with the number n-i.
A338979 (program): a(n) = Sum_{k=0..n} n^k * binomial(n,k) * Catalan(k).
A338991 (program): a(n) = Sum_{k=1..floor(n/2)} (n-2*k) * floor((n-k)/k).
A338995 (program): Triangle T(n,m):=binomial(n+3*m+2,n-m).
A338996 (program): Numbers of squares and rectangles of all sizes in 3*n*(n+1)/2-ominoes in form of three-quarters of Aztec diamonds.
A338997 (program): Number of (i,j,k) in {1,2,…,n}^3 such that gcd(n,i) = gcd(n,j) = gcd(n,k).
A339001 (program): a(n) = (-1)^n * Sum_{k=0..n} (-n)^k * binomial(n,k) * Catalan(k).
A339012 (program): Written in factorial base, n ends in a(n) consecutive non-0 digits.
A339013 (program): Class number m containing n in a partitioning of the natural numbers into classes B_m by William J. Keith.
A339014 (program): E.g.f.: exp(2 * (exp(x) - 1 - x - x^2 / 2)).
A339017 (program): E.g.f.: exp(2 * (exp(x) - 1 - x - x^2 / 2 - x^3 / 6)).
A339023 (program): Replace each digit d in the decimal representation of n with the digital root of n*d.
A339026 (program): Number of pairs (x,y): 1 <= x < y <= n*n, such that x*y is a square.
A339027 (program): E.g.f.: exp(2 * (exp(x) - 1 - x - x^2 / 2 - x^3 / 6 - x^4 / 24)).
A339031 (program): T(n, k) = k*P(n, k), where P(n, k) is the number of partitions of an n-set with k blocks, the largest of which has the size n - k + 1. Triangle T(n, k) for 0 <= k <= n, read by rows.
A339032 (program): Expansion of (4*x^5 - 9*x^4 + 17*x^3 - 15*x^2 + 6*x - 1)/((2*x - 1)^2*(x - 1)^3).
A339034 (program): Row sums of A339033.
A339048 (program): a(n) = 2*n^2 + 9.
A339049 (program): a(n) = A000010(2*n + 1)/A053447(n), for n >= 0.
A339050 (program): Triangle read by rows T(n, m) = F(2*m-1)*(n-m) + F(2*m), for 1 <= m <= n, where F = A000045 (Fibonacci).
A339051 (program): Even bisection of the infinite Fibonacci word A096270.
A339052 (program): Odd bisection of the infinite Fibonacci word A096270.
A339053 (program): a(n) = least k such that the first n-block in A339051 occurs in A339052 beginning at the k-th term.
A339057 (program): a(n) = (-1)^(n + 1)*3^(2*n + 1)*Euler(2*n + 1, 1/3)*2^(valuation_{2}(2*(n + 1))), the Steinhaus-Euler sequence S_{3}(n).
A339076 (program): Numbers which are coprime to their digital sum (A007953).
A339094 (program): Number of (unordered) ways of making change for n US Dollars using the current US denominations of 1$, 2$, 5$, 10$, 20$, 50$ and 100$ bills.
A339106 (program): Triangle read by rows: T(n,k) = A000203(n-k+1)*A000041(k-1), n >= 1, 1 <= k <= n.
A339114 (program): Least semiprime whose prime indices sum to n.
A339116 (program): Triangle of all squarefree semiprimes grouped by greater prime factor, read by rows.
A339124 (program): a(n) is the number of squares at distance n from the central square of a golden square fractal.
A339136 (program): Number of (undirected) cycles in the graph C_3 X P_n.
A339146 (program): a(n) = a(floor(n / 5)) * (n mod 5 + 1); initial terms are 1.
A339183 (program): Number of partitions of n into two parts such that the smaller part is a nonzero square.
A339184 (program): Number of partitions of n into two parts such that the larger part is a nonzero square.
A339187 (program): a(n) is the maximum of f(s) for all binary sequences s of length n where f(s) denote the duplication distance between s and its root.
A339191 (program): Partial products of squarefree semiprimes (A006881).
A339194 (program): Sum of all squarefree semiprimes with greater prime factor prime(n).
A339196 (program): Number of (undirected) cycles on the n X 2 king graph.
A339217 (program): a(n) = Sum_{k=1..n} floor((2*n-k)/k).
A339236 (program): Irregular triangle of incomplete Leonardo numbers read by rows. T(n, k) = 2*Sum_{j=0..k} binomial(n-j, j)) -1, for n>=0 and 0<=k<=floor(n/2).
A339240 (program): a(n) = n*2^(2*n-2) + n*binomial(2*n,n)/2.
A339247 (program): The primes that yield twice a prime when each bit of their binary expansion is inverted.
A339252 (program): a(0) = 1, a(1) = 4, a(2) = 11, and a(n) = 4*a(n-1) - 4*a(n-2) for n >= 3.
A339255 (program): Leading digit of n in base 5.
A339256 (program): Leading digit of n in base 6.
A339265 (program): Expansion of Product_{n >= 1} (1 - x^(2*n))*(1 - x^(2*n-1))*(1 - x^(2*n+1)).
A339267 (program): Level of the Calkin-Wilf tree in which the n-th convergent of the continued fraction for e appears.
A339273 (program): Sums of two nonzero even squares.
A339276 (program): Nearest integer to the fourth root of n.
A339277 (program): Number of partitions of 2*n into powers of 2 where every part appears at least 2 times.
A339279 (program): Number of partitions of 3*n into powers of 3 where every part appears at least 2 times.
A339308 (program): Partial sums of products of proper divisors of n (A007956).
A339311 (program): a(n) = Sum_{k=1..n} (k!)^n.
A339332 (program): Sums of antidiagonals in A283683.
A339350 (program): Triangle read by rows. T(n,k) = Sum_{j=0..k} binomial(k-j+2, 2)*T(n-1, j), for n>=0, 0<=k<=n, with T(0,0)=1 and T(n,n)=0 for n>0.
A339353 (program): G.f.: Sum_{k>=1} k^2 * x^(k*(k + 1)) / (1 - x^k).
A339354 (program): G.f.: Sum_{k>=1} k^3 * x^(k*(k + 1)) / (1 - x^k).
A339355 (program): Maximum number of copies of a 12345 permutation pattern in an alternating (or zig-zag) permutation of length n + 7.
A339356 (program): Maximum number of copies of a 123456 permutation pattern in an alternating (or zig-zag) permutation of length n + 9.
A339358 (program): Maximum number of copies of a 1234567 permutation pattern in an alternating (or zig-zag) permutation of length n + 11.
A339360 (program): Sum of all squarefree numbers with greatest prime factor prime(n).
A339361 (program): Product of prime indices of the n-th squarefree semiprime.
A339362 (program): Sum of prime indices of the n-th squarefree semiprime.
A339363 (program): a(n) = Sum_{k=1..floor(sqrt(n))} floor(sqrt(n-k)).
A339370 (program): a(n) = Sum_{k=1..floor(n/2)} (n-k) * floor((n-k)/k).
A339377 (program): Number of triples (x, y, z) of natural numbers satisfying x+y = n and 2*x*y = z^2.
A339378 (program): Let n be a positive integer. For each prime divisor p of n, consider the highest power of p which does not exceed n. The sum a(n) of these powers is defined as the power-sum of n.
A339387 (program): a(n) = Sum_{k=1..n} (lcm(n,k)/gcd(n,k) mod k).
A339391 (program): Maximum, over all binary strings w of length n, of the size of the smallest string attractor for w.
A339392 (program): Numerators of the probability that when a stick is broken up at n-1 points independently and uniformly chosen at random along its length there exist 3 of the n pieces that can form a triangle.
A339393 (program): Denominators of the probability that when a stick is broken up at n-1 points independently and uniformly chosen at random along its length there exist 3 of the n pieces that can form a triangle.
A339399 (program): Pairwise listing of the partitions of k into two parts (s,t), with 0 < s <= t ordered by increasing values of s and where k = 2,3,… .
A339401 (program): a(n) = numerator of (1/e)^n * Sum_{k>=0}(n^k*k^n)/(n!*k!).
A339402 (program): a(n) = denominator of (1/e)^n * Sum_{k>=0}(n^k*k^n)/(n!*k!).
A339408 (program): Number of compositions (ordered partitions) of n into an even number of primes.
A339411 (program): Product of partial sums of odd squares.
A339416 (program): Number of compositions (ordered partitions) of n into an even number of triangular numbers.
A339417 (program): Number of compositions (ordered partitions) of n into an odd number of triangular numbers.
A339422 (program): G.f.: 1 / (1 + Sum_{k>=0} x^(2^k)).
A339423 (program): If n = p_1 * … * p_m with primes p_i <= p_{i+1}, a(n) = Sum_{k<m} Product_{j <= k} p_j.
A339436 (program): If n = p_1 * … * p_m with primes p_i <= p_{i+1}, a(n) = Sum_{j=1..m-1} p_1*…*p_j + Sum_{j=2..m} p_j*…*p_m.
A339437 (program): Numbers k such that A339436(k) is prime.
A339443 (program): Pairwise listing of the partitions of k into two parts (s,t), with 0 < t <= s ordered by decreasing values of s and where k = 2,3,… .
A339448 (program): a(n) = (prime(n) - a(n-1)) mod 3; a(0)=0.
A339451 (program): Gray-code-like sequence in which, at each step, the least significant bit that has never been toggled from the previous value, is toggled.
A339461 (program): Number of Fibonacci divisors of n^2 + 1.
A339464 (program): a(n) = (prime(n)-1) / gpf(prime(n)-1) where gpf(m) is the greatest prime factor of m, A006530.
A339470 (program): Decimal expansion of log(phi)^2, where phi is the golden ratio (A002390^2).
A339480 (program): Numbers of the form (k^2 - 2) / 2 where k - 1 and k + 1 are both odd composite numbers.
A339481 (program): a(n) = Sum_{d|n} d^(n-d) * binomial(d+n/d-2, d-1).
A339482 (program): a(n) = Sum_{d|n} d^(n-d+1) * binomial(d+n/d-2, d-1).
A339483 (program): Number of regular polygons that can be drawn with vertices on a centered hexagonal grid with side length n.
A339486 (program): Number of possible destination squares after n knight’s moves on an 8x8 chessboard beginning on a corner square.
A339487 (program): a(n) is the area of the n-gon with vertices (3^i, 5^i) for 0 <= i <= n-1.
A339488 (program): a(n) = H(n-1, n, n+1) where H(a, b, c) = (a + b + c)*(a + b - c)*(b + c - a)*(c + a - b) is Heron’s polynomial.
A339492 (program): T(n, k) = tau(k) + floor(n/k) - 1, where tau = A000005. Triangle read by rows.
A339495 (program): Row sums of A339494.
A339516 (program): a(n+1) = (a(n) - 2*(n-1)) * (2*n-1), where a(1)=1.
A339531 (program): Numbers b > 1 such that the smallest two primes, i.e., 2 and 3 are base-b Wieferich primes.
A339549 (program): a(n) is the product of the binary weights (A000120) of the divisors of n.
A339558 (program): Number of divisors of 2n that are the average of a pair of twin primes.
A339561 (program): Products of distinct squarefree semiprimes.
A339570 (program): Denote the van der Corput sequence of fractions 1/2, 1/4, 3/4, 1/8, 5/8, 3/8, 7/8, 1/16, … (A030101/A062383) by v(n), n >= 1. Then a(n) = denominator of v(A014486(n)).
A339572 (program): If n even, a(n) = A000071(n/2+1); if n odd, a(n) = A001610((n-1)/2).
A339573 (program): a(n) = floor(n*(n+1)/6) - 1.
A339576 (program): Row sums of triangle A236104.
A339577 (program): a(n) = product of nonzero entries in row n of A235791.
A339579 (program): a(n) = least nonnegative integer k such that n*2^k - 1 is composite.
A339584 (program): A ternary sequence: a(n) = 1 if n is in A003156, 2 if n is in A003157, 3 if n is in A003158.
A339597 (program): When 2*n+1 first appears in A086799.
A339600 (program): a(0) = a(1) = 1, a(2) = 3, a(3) = 6, a(n) = a(n-1) + 6*a(n-3) + 2*a(n-4) for n >= 4.
A339601 (program): Starting from x_0 = n, iterate by dividing with 3 (discarding any remainder), until zero is reached: x_1 = floor(x_0/3), x_2 = floor(x_1/3), etc. Then a(n) = Sum_{i=0..} (x_i AND 2^i), where AND is bitwise-and.
A339609 (program): Consider a triangle drawn on the perimeter of a triangular lattice with side length n. a(n) is the number of regions inside the triangle after drawing unit circles centered at each lattice point inside the triangle.
A339610 (program): Expansion of x*(2 - x - x^2 - 2*x^3)/(1 - x - x^2)^2.
A339621 (program): Sum of Fibonacci divisors of n^2 + 1.
A339623 (program): Consider a square drawn on the perimeter of a square lattice with side length n. a(n) is the number of regions inside the square after drawing unit circles centered at each interior lattice point of the square.
A339637 (program): Numbers congruent to 1 (mod 3) that are the quotient of two Cantor numbers (A005823).
A339640 (program): a(n) = (A062772(n) + A054270(n)) / 2 - A001248(n).
A339653 (program): a(n) is 0 if the smallest base-n Wieferich prime is < n, 1 if it is > n and 2 if no base-n Wieferich prime exists.
A339661 (program): Number of factorizations of n into distinct squarefree semiprimes.
A339662 (program): Greatest gap in the partition with Heinz number n.
A339669 (program): Number of Fibonacci divisors of Lucas(n)^2 + 1.
A339684 (program): a(n) = Sum_{d|n} 4^(d-1).
A339685 (program): a(n) = Sum_{d|n} 5^(d-1).
A339686 (program): a(n) = Sum_{d|n} 6^(d-1).
A339687 (program): a(n) = Sum_{d|n} 7^(d-1).
A339688 (program): a(n) = Sum_{d|n} 8^(d-1).
A339689 (program): a(n) = Sum_{d|n} 9^(d-1).
A339690 (program): Positive integers of the form 4^i*9^j*k with gcd(k,6)=1.
A339710 (program): a(n) = Sum_{k=0..n} binomial(n, k)*binomial(2*n + k, k)*2^k.
A339711 (program): a(n) = A178901(n)/n.
A339712 (program): a(n) = Sum_{d|n} d^(d+n/d-1) * binomial(d+n/d-2, d-1).
A339713 (program): a(n) = (a(n-2) concatenate a(n-1)) for n > 2, with a(1)=1, a(2)=10.
A339740 (program): Non-products of distinct primes or squarefree semiprimes.
A339741 (program): Products of distinct primes or squarefree semiprimes.
A339744 (program): Numbers k such that rad(k)^2 < sigma(k), where rad(k) is the squarefree kernel of k (A007947) and sigma(k) is the sum of divisors of k (A000203).
A339746 (program): Positive integers of the form 2^i*3^j*k, gcd(k,6)=1, and i == j (mod 3).
A339747 (program): a(n) = (5^(valuation(n, 5) + 1) - 1) / 4.
A339748 (program): a(n) = (6^(valuation(n, 6) + 1) - 1) / 5.
A339749 (program): a(n) is the greatest k > 0 such that 1+n, 1+2*n, …, 1+n*k are pairwise coprime.
A339760 (program): Number of (undirected) Hamiltonian paths in the 2 X n king graph.
A339765 (program): a(n) = 2*floor(n*phi) - 3*n, where phi = (1+sqrt(5))/2.
A339767 (program): a(n) = 2*gpf(n) - Sum_{p | n, p prime} p*m(p), where gpf(n) = A006530(n) is the greatest prime factor of n and m(p) is the multiplicity of p in the prime factorization of n.
A339771 (program): a(n) = Sum_{i=0..n} Sum_{j=0..n} 2^max(i,j).
A339804 (program): a(n) = Sum_{k=1..floor(n/2)} k * (n-k) * floor((n-k)/k).
A339809 (program): a(n) = A019565(n) - 1.
A339810 (program): a(n) = A046523(A019565(n) - 1).
A339812 (program): Number of prime divisors of (A019565(n) - 1), counted with multiplicity.
A339813 (program): The exponent of the highest power of 2 dividing (A019565(n) - 1).
A339814 (program): The exponent of the highest power of 2 dividing (A019565(2n) - 1).
A339817 (program): Squarefree numbers k > 1 for which the 2-adic valuation of phi(k) does not exceed the 2-adic valuation of k-1.
A339820 (program): a(n) = phi(A019565(n)), where phi is Euler totient function.
A339821 (program): a(n) = phi(A019565(2n)), where phi is Euler totient function.
A339822 (program): The exponent of the highest power of 2 dividing A339821(n).
A339823 (program): a(n) = A056239(n) - A000523(n).
A339824 (program): Even bisection of the infinite Fibonacci word A003849.
A339825 (program): Odd bisection of the infinite Fibonacci word A003849.
A339828 (program): a(n) = 4*a(n-1) - 2*a(n-2) + a(n-3) - 4*a(n-4) + a(n-5) for n >= 6, where a(1) = 1, a(2) = 3, a(3) = 5, a(4) = 16, a(5) = 53.
A339848 (program): Number of distinct free polyominoes that fit in an n X n square but are not a proper sub-polyomino of any polyomino that fits in the square.
A339850 (program): Number of Hamiltonian circuits within parallelograms of size 3 X n on the triangular lattice.
A339871 (program): Number of primes p for which the p-adic valuation of phi(n) exceeds the p-adic valuation of n-1, with a(1) = 0 by convention.
A339872 (program): Index k of the least prime(k) such that prime(k)-adic valuation of phi(n) exceeds the prime(k)-adic valuation of n-1, or 0 if no such k exists (for example, when n = 1 or a prime).
A339873 (program): a(n) = 1 + n - A143771(n).
A339879 (program): Numbers k for which k-1 is a multiple of A053575(k) [the odd part of phi(k)].
A339884 (program): Triangle read by rows: T(n, m) gives the number of partitions of n with m parts and parts from {1, 2, 3}.
A339887 (program): Number of factorizations of n into primes or squarefree semiprimes.
A339893 (program): a(n) = A000523(n) - A001222(n); floor(log_2(n)) minus the number of prime divisors of n, counted with multiplicity.
A339894 (program): a(n) = A000523(A122111(n)).
A339896 (program): a(n) = A056239(n) - A339894(n).
A339902 (program): Number of prime divisors of A339821(n), counted with multiplicity.
A339903 (program): Fully multiplicative with a(p) = A000265(q-1), where q = A151800(p), the next prime > p.
A339904 (program): The odd part of {Euler totient function phi applied to the prime shifted n}: a(n) = A000265(A000010(A003961(n))).
A339905 (program): Fully multiplicative with a(prime(k)) = prime(k+1) - 1.
A339910 (program): After 1, numbers k > 1 such that k has less prime divisors than k-1, when they are counted with multiplicity.
A339913 (program): a(n) = x/gcd(n,x), where x = 1+A060681(n).
A339915 (program): Number of divisors of n with the same number of decimal digits as n.
A339916 (program): The sum of 2^((d-1)/2) over all divisors of 2n+1.
A339918 (program): a(n) = Sum_{k=1..n} floor(3*n/k).
A339919 (program): a(n) = Sum_{k=1..n} (floor(3*n/k) - 3*floor(n/k)).
A339950 (program): Numbers k such that all k-sections of the infinite Fibonacci word A014675 have just two different run-lengths.
A339952 (program): Numbers that are the sum of an even square > 0 and an odd square.
A339963 (program): Numbers k such that gcd(k+1, sigma(k)) is 2.
A339964 (program): a(n) = gcd(sigma(n), n+1).
A339965 (program): a(n) = sigma(n) / gcd(sigma(n),n+1).
A339966 (program): a(n) = (n+1) / gcd(sigma(n),n+1).
A339967 (program): a(n) = gcd(sigma(n), n+2).
A339968 (program): Numbers k such that sigma(k) and k+2 are relatively prime, where sigma gives the sum of divisors of k.
A339969 (program): a(n) = gcd(n, A005940(1+n)).
A339970 (program): a(n) = A329697(A019565(2n)).
A339971 (program): Odd part of A339821(n).
A339977 (program): Sums of two distinct odd squares.
A339993 (program): Sums of two positive even cubes.
A339994 (program): Sums of two distinct nonzero even cubes.
A339995 (program): Numbers that are the sum of an odd cube and a nonzero even cube.
A340008 (program): a(n) is the image of n under the map: n -> n/2 if n is even, n-> n^2 - 1 if n is an odd prime, otherwise n -> n - 1.
A340044 (program): Numbers that are the sum of a square s and a fourth power t such that 0 < s <= t.
A340046 (program): Numbers that are the sum of a square s and a fourth power t such that 0 < s < t.
A340051 (program): Mixed-radix representation of n where the least significant digit is in base 3 and other digits are in base 2.
A340058 (program): Composite numbers c such that phi(c)/phi(mind(c)) mod phi(c)/phi(maxd(c)) = 0, where phi is the Euler function, mind(c) is the smallest nontrivial divisor of c, maxd(c) is the largest nontrivial divisor of c.
A340068 (program): a(n) is the number of integers in the set {n+1,n+2, . . . ,2n} whose representation in base 2 contain exactly three digits 1’s.
A340070 (program): a(n) = gcd(A003415(n), A069359(n)).
A340071 (program): a(n) = gcd(A003961(n)-1, phi(A003961(n))), where A003961 shifts the prime factorization of n one step towards larger primes.
A340072 (program): a(n) = phi(x) / gcd(x-1, phi(x)), where x = A003961(n), i.e., n with its prime factorization shifted one step towards larger primes.
A340073 (program): a(n) = (x-1) / gcd(x-1, phi(x)), where x = A003961(n), i.e., n with its prime factorization shifted one step towards larger primes.
A340074 (program): a(n) = gcd(A003961(n)-1, A339904(n)).
A340075 (program): The odd part of A340072(n).
A340076 (program): Positions of ones in A340075.
A340077 (program): Odd numbers k for which k-1 is a multiple of A053575(k) [the odd part of phi(k)].
A340078 (program): a(n) = gcd(n, 1+A018804(n)), where A018804(n) = Sum_{k=1..n} gcd(k, n).
A340079 (program): a(n) = n / gcd(n, 1+A018804(n)), where A018804(n) = Sum_{k=1..n} gcd(k, n).
A340080 (program): a(n) = (1+A018804(n)) / gcd(n, 1+A018804(n)), where A018804(n) = Sum_{k=1..n} gcd(k, n).
A340081 (program): a(n) = gcd(n-1, A003958(n)).
A340082 (program): a(n) = A003958(n) / gcd(n-1, A003958(n)).
A340083 (program): a(n) = (n-1) / gcd(n-1, A003958(n)).
A340084 (program): a(n) = gcd(n-1, A336466(n)); Odd part of A340081(n).
A340085 (program): a(n) = A336466(n) / gcd(n-1, A336466(n)); Odd part of A340082(n).
A340086 (program): a(1) = 0, for n > 1, a(n) = A000265(n-1) / gcd(n-1, A336466(n)).
A340087 (program): a(n) = gcd(n-1, A091732(n)), where A091732 is an infinitary analog of Euler’s phi function.
A340088 (program): a(n) = A091732(n) / gcd(n-1, A091732(n)), where A091732 is an infinitary analog of Euler’s phi function.
A340089 (program): a(n) = (n-1) / gcd(n-1, A091732(n)), where A091732 is an infinitary analog of Euler’s phi function.
A340102 (program): Number of factorizations of 2n + 1 into an odd number of odd factors > 1.
A340128 (program): a(n) = (n*prime(n)) mod prime(n+1).
A340130 (program): Number of convex polygons on the lines of a triangular grid with edge length n.
A340134 (program): a(n+1) = a(n-2*a(n)) + 1, starting with a(1) = a(2) = 0.
A340152 (program): Numbers k such that k and k+1 are both cubefree numbers (A004709).
A340154 (program): Primes p such that p == 5 (mod 6) and p+1 is squarefree.
A340156 (program): Square array read by upward antidiagonals: T(n, k) is the number of n-ary strings of length k containing 00.
A340161 (program): a(n) is the smallest number k for which the set {k + 1, k + 2, …, k + k} contains exactly n elements with exactly three 1-bits (A014311).
A340163 (program): For n>=1, smallest integer k such that for all m>=k: m^(1/n)+(m+1)^(1/n) >= (2^n*m+2^(n-1)-1)^(1/n).
A340169 (program): a(n) is the number of strings of length n over the alphabet {a,b,c} with the number of a’s divisible by 3, and the number of b’s and c’s is at most 3.
A340171 (program): List of X-coordinates of point moving along one of the arms of a counterclockwise double square spiral; A340172 gives Y-coordinates.
A340172 (program): List of Y-coordinates of point moving along one of the arms of a counterclockwise double square spiral; A340171 gives X-coordinates.
A340173 (program): Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(4,n) (with n at least 3) missing two edges, where the two removed edges are not incident to the same vertex in the 4-point set but are incident to the same vertex in the other set.
A340184 (program): n with the rightmost occurrence of the smallest digit of n deleted.
A340192 (program): a(n) = Sum_{d|n} A063994(d), where A063994(x) = Product_{primes p dividing x} gcd(p-1, x-1).
A340193 (program): a(n) = n - (Sum_{d|n} A063994(d)).
A340194 (program): a(n) = A337544(A003961(n)).
A340195 (program): a(n) = Sum_{divisors d of n} A049559(d), where A049559(x) = gcd(phi(x), x-1).
A340196 (program): a(n) = n - A340195(n).
A340199 (program): Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 3) missing two edges, where the two removed edges are not incident to the same vertex in the 3-point set and are also not incident to the same vertex in the other set.
A340203 (program): Number of primes in A339399 among the values of A339399(k) for k = 1..n.
A340215 (program): Consider constructing binary words that begin with 0 such that the subword 00, whenever it appears, is followed by 111. Then a(n) counts such words at length n (including those where the string 111 is yet being completed - see Example).
A340216 (program): Decimal expansion of the sum of the reciprocals of the squares of the positive triangular numbers.
A340217 (program): Consider binary words that begin with 1 such that the subword 00, whenever it appears, is followed by 111. Then a(n) counts such words at length n (including those where the string 111 is yet being completed - see Example).
A340227 (program): Number of pairs of divisors of n, (d1,d2), such that d1 < d2 and d1*d2 is squarefree.
A340228 (program): a(n) is the sum of the lengths of all the segments used to draw a rectangle of height 2^(n-1) and width n divided into 2^(n-1) rectangles of unit height, in turn, divided into rectangles of unit height and lengths corresponding to the parts of the compositions of n.
A340234 (program): Number of harmonious graphs with n edges and at most n vertices, allowing self-loops.
A340242 (program): Square array read by upward antidiagonals: T(n,k) is the number of n-ary strings of length k containing 000.
A340251 (program): a(n) is the index of the bit that was inverted in A340250(n) to get A340250(n+1).
A340257 (program): a(n) = 2^n * (1+n*(n+1)/2).
A340260 (program): T(n, k) = Sum_{j=1..k} [n mod j <> 1], where [] are the Iverson brackets. Table read by rows.
A340261 (program): T(n, k) is the number of integers that are less than or equal to k that do not divide n. Triangle read by rows, for 0 <= k <= n.
A340262 (program): T(n, k) = multinomial(n + k/2; n, k/2) if k is even else 0. Triangle read by rows, for 0 <= k <= n.
A340266 (program): The number of degrees of freedom in a quadrilateral cell for a serendipity finite element space of order n.
A340268 (program): Composite numbers k>1 such that (s-1) | (d-1) for each d | k, where s = lpf(k) = A020639(k).
A340275 (program): Number of partitions of n into 3 parts whose smallest two parts are relatively prime.
A340276 (program): Number of partitions of n into 3 parts whose largest two parts are relatively prime.
A340278 (program): Number of partitions of n into 3 parts whose smallest and largest parts are relatively prime.
A340301 (program): a(n) = n * floor(log_2(n)).
A340309 (program): Number of ordered pairs of vertices which have two different shortest paths between them in the n-Hanoi graph (3 pegs, n discs).
A340317 (program): (Product of primes <= n) read modulo n.
A340323 (program): Multiplicative with a(p^e) = (p + 1) * (p - 1)^(e - 1).
A340326 (program): a(n) = a(n-2) + (-1)^n*a(n-1) + n*(1-(-1)^n) with a(0) = a(1) = 1.
A340332 (program): E.g.f.: Sum_{n>=0} x^n * exp(3*2^n*x) / n!.
A340335 (program): E.g.f.: Sum_{n>=0} x^n * exp(2^n*x).
A340336 (program): E.g.f.: Sum_{n>=0} x^n * cosh(2^n*x).
A340337 (program): E.g.f.: Sum_{n>=0} x^n * sinh(2^n*x).
A340346 (program): The largest divisor of n that is a term of A055932 (numbers divisible by all primes smaller than their largest prime factor).
A340363 (program): a(n) = 1 if n is of the form of 2^i * p^j, with p an odd prime and i, j >= 0, otherwise 0.
A340368 (program): Multiplicative with a(p^e) = (p - 1) * (p + 1)^(e-1).
A340369 (program): a(n) = 1 if n has at most 3 prime factors when counted with multiplicity, 0 otherwise.
A340371 (program): a(n) = 1 if the odd part of n is noncomposite, 0 otherwise.
A340373 (program): a(n) = 1 if n is of the form of 2^i * p^j, with p an odd prime, and i>=0, j>=1, otherwise 0.
A340374 (program): a(n) = 1 if the odd part of n satisfies Korselt’s criterion (is in A324050), 0 otherwise.
A340375 (program): a(n) = 1 if n is of the form 2^i - 2^j with i >= j, and 0 otherwise.
A340376 (program): Numbers k such that there are no 1-digits in the ternary expansion of A048673(k).
A340377 (program): Numbers k such that there are no 2-digits in the ternary expansion of A048673(k).
A340378 (program): Number of 1-digits in the ternary representation of A048673(n).
A340379 (program): Number of 2-digits in the ternary representation of A048673(n).
A340380 (program): Numbers whose odd part is a squarefree semiprime (A006881); numbers of the form 2^k * p * q, with k >= 0, and distinct odd primes p and q.
A340386 (program): Heinz numbers of integer partitions with an odd number of parts, the greatest of which is odd.
A340395 (program): a(n) = A340131(A001006(n)).
A340399 (program): a(n) is the least Fibonacci number >= 2^n.
A340400 (program): a(n) is the greatest Fibonacci number < 2^(n+1).
A340424 (program): Triangle read by rows: T(n,k) = A024916(n-k+1)*A002865(k-1), 1 <= k <= n.
A340433 (program): Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(4,n) (with n at least 4) missing three edges, where all three removed edges are incident to different vertices in the 4-point set but all three removed edges are incident to the same vertex in the other set.
A340436 (program): Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 4) missing three edges, where exactly two of the removed edges are incident to the same vertex in the 3-point set but none of the removed edges are incident to the same vertex in the other set.
A340445 (program): Number of partitions of n into 3 parts that are not all the same.
A340448 (program): Radio number of the cycle graph C_n.
A340451 (program): E.g.f.: Sum_{n>=0} x^n * cosh(2^n*x) / n!.
A340452 (program): E.g.f.: Sum_{n>=0} x^n * sinh(2^n*x) / n!.
A340456 (program): G.f.: Sum_{n>=0} x^n/(1 - x^(5*n+1)) - x^3*Sum_{n>=0} x^(4*n)/(1 - x^(5*n+4)).
A340461 (program): a(n) = 2*sigma(phi(n)) - n.
A340473 (program): a(n) = n! [x^n] W(-W(x))/(-W(x)), where W(x) is the Lambert W function.
A340479 (program): a(n) = R(n) + digsum(n).
A340492 (program): a(n) = A000041(n)*A000070(n-1), n >= 1.
A340493 (program): Sequence whose partial sums give A340492.
A340494 (program): Index where n first appears in A340488.
A340495 (program): Records in first differences of A340494.
A340497 (program): Index where 2*n first appears in A340488.
A340498 (program): Where 2^n appears in A340488 for the first time.
A340503 (program): Fixed under 0 -> 02, 1 -> 32, 2 -> 01, 3 -> 31.
A340504 (program): Fixed under 0 -> 03, 1 -> 23, 2 -> 21, 3 -> 01.
A340507 (program): a(n) = floor(sqrt(2*n)) - A003056(n).
A340508 (program): Let ped(n) denote the number of partitions of n in which the even parts are distinct (A001935); a(n) = ped(9*n+7).
A340509 (program): a(n) = 3*A005382(n)-1.
A340515 (program): a(n) = minimal order of a group in which all groups of order <= n can be embedded.
A340516 (program): Let p_i (i=1..m) denote the primes <= n, and let e_i be the maximum number such that p_i^e_i <= n; then a(n) = Product_{i=1..m} p_i^(2*e_i-1).
A340519 (program): Smallest order of a non-abelian group with a center of order n.
A340520 (program): a(n) = 2*A006463(n) + 1.
A340521 (program): List of possible orders of automorphism groups of finite groups.
A340524 (program): Triangle read by rows: T(n,k) = A000005(n-k+1)*A002865(k-1), 1 <= k <= n.
A340525 (program): Triangle read by rows: T(n,k) = A006218(n-k+1)*A002865(k-1), 1 <= k <= n.
A340526 (program): Triangle read by rows: T(n,k) = A006218(n-k+1)*A000041(k-1), 1 <= k <= n.
A340527 (program): Triangle read by rows: T(n,k) = A024916(n-k+1)*A000041(k-1), 1 <= k <= n.
A340528 (program): Radio number of the path graph P_n.
A340536 (program): Digital root of 2*n^2.
A340542 (program): Number of Fibonacci divisors of Fibonacci(n)^2 + 1.
A340550 (program): Number of main classes of doubly symmetric diagonal Latin squares of order n.
A340554 (program): T(n, k) = [x^k] hypergeom([-2^n/2, -2^n/2 - 1/2], [1/2], x). Triangle read by rows, T(n, k) for n >= 0.
A340565 (program): Decimal expansion of the Product_{lesser twin primes p == 5 (mod 6)} 1/(1 - 1/p^2).
A340567 (program): Total number of ascents in all faro permutations of length n.
A340568 (program): Total number of consecutive triples matching the pattern 132 in all faro permutations of length n.
A340569 (program): Total number of consecutive triples matching the pattern 123 in all faro permutations of length n.
A340583 (program): Triangle read by rows: T(n,k) = A002865(n-k)*A000203(k), 1 <= k <= n.
A340588 (program): Squares of perfect powers.
A340602 (program): Heinz numbers of integer partitions of even rank.
A340603 (program): Heinz numbers of integer partitions of odd rank.
A340604 (program): Heinz numbers of integer partitions of odd positive rank.
A340605 (program): Heinz numbers of integer partitions of even positive rank.
A340615 (program): a(n) = k/2 if k is even, otherwise (3k+1)/2, where k = n + floor((n+1)/5).
A340616 (program): Decimal expansion of sqrt(3)-sqrt(2).
A340619 (program): n appears A006519(n) times.
A340625 (program): a(n) = Sum_{d|n, d odd, d <= n/d} binomial(n/d, d).
A340626 (program): a(n) = Sum_{d|n, d odd} binomial(d+n/d-1, d).
A340627 (program): a(n) = (11*2^n - 2*(-1)^n)/3 for n >= 0.
A340631 (program): a(n) is the minimum number of pebbles such that any assignment of those pebbles on a complete graph with n vertices is a next-player winning game in the two-player impartial pebbling game.
A340632 (program): a(n) in binary is a run of 1-bits from the most significant 1-bit of n down to the least significant 1-bit of n, inclusive.
A340646 (program): a(n) = (prime(n)^n) mod prime(n+1).
A340648 (program): a(n) is the maximum number of nonzero entries in an n X n sign-restricted matrix.
A340649 (program): a(n) = (n*prime(n+1)) mod prime(n).
A340660 (program): A000079 is the first row. For the second row, subtract A001045. For the third row, subtract A001045 from the second one, etc. The resulting array is read by ascending antidiagonals.
A340670 (program): Number of complex base i-1 points which can be represented within n bits and negated within those n bits.
A340673 (program): If n is of the form s^(2^e), where s is a squarefree number, and e >= 0, then a(n) is the (1+e)-th prime, otherwise a(n) = 1.
A340674 (program): Numbers of the form s^(2^e), where s is a squarefree number, and e >= 1.
A340675 (program): Exponential of Mangoldt function conjugated by Tek’s flip: a(n) = A225546(A014963(A225546(n))).
A340676 (program): If n is of the form s^(2^e), where s is a squarefree number, and e >= 0, then a(n) = 1+e, otherwise a(n) = 0.
A340677 (program): a(n) = A007947(n) / gcd(A007947(n), A008472(n)).
A340678 (program): a(n) = A008472(n) / gcd(A007947(n), A008472(n)).
A340679 (program): If n is a power of prime then a(n) = 1, otherwise a(n) = product of the distinct prime factors of n.
A340681 (program): The closure under squaring of A051144, the nonsquarefree nonsquares.
A340682 (program): The closure under squaring of the nonunit squarefree numbers.
A340683 (program): a(n) = A007949((A003961(A003961(n))+1)/2), where A003961 shifts the prime factorization of n one step towards larger primes, and A007949(x) gives the exponent of largest power of 3 dividing x.
A340691 (program): Greatest image of A001222 over the prime indices of n.
A340709 (program): Let k = n/2 + floor(n/4) if n is even, otherwise (3n+1)/2; then a(n) = A093545(k).
A340714 (program): a(n) is the sum of (n-2*j) for j < n/2 coprime to n.
A340718 (program): a(n) is the least k such that A340717(k) = n.
A340740 (program): a(n) is the sum of all the remainders when n is divided by positive integers less than n/2 and coprime to n.
A340741 (program): Numbers k such that A340740(k) is prime.
A340745 (program): a(n) is the number of “add the square” iterations required to reach or exceed 1 starting at 1/n.
A340757 (program): Counterexamples to a conjecture of Ramanujan about congruences related to the partition function.
A340760 (program): Number of partitions of n into 4 parts whose largest 3 parts have the same parity.
A340761 (program): Number of partitions of n into 4 parts whose ‘middle’ two parts have the same parity.
A340763 (program): Number of primes p <= n that are congruent to 1 modulo 3.
A340764 (program): Number of primes p <= n that are congruent to 2 modulo 3.
A340767 (program): Number of primes p <= 6*n + 5 that are congruent to 2 modulo 3.
A340768 (program): Third-smallest divisor of n-th composite number.
A340769 (program): The third-smallest divisor of n-th square number, n>1.
A340774 (program): Dirichlet g.f.: Sum_{n>0} a(n)/n^s = zeta(s-1) * zeta(2*s-1).
A340776 (program): G.f.: Sum_{n>=0} x^n/(1 - x*(1+x)^(n+1)).
A340781 (program): a(n) = (n - 1)*prime(n + 1) mod prime(n).
A340784 (program): Heinz numbers of even-length integer partitions of even numbers.
A340787 (program): Heinz numbers of integer partitions of positive rank.
A340788 (program): Heinz numbers of integer partitions of negative rank.
A340789 (program): a(n) = (n!)^2 * Sum_{k=1..n} (-1)^(k+1) / (k!)^2.
A340792 (program): List in which n appears ceiling(d(n)/2) = A038548(n) times, where d(n) is the number of divisors of n.
A340793 (program): Sequence whose partial sums give A000203.
A340801 (program): a(n) is the image of n under the map f defined as f(n) = n^2 - 2 if n is an odd prime, f(n) = n/2 if n is even, and f(n) = n - 1 otherwise.
A340804 (program): Triangle read by rows: T(n, k) = 1 + k*(n - 1) + (2*k - n - 1)*(k mod 2) with 0 < k <= n.
A340806 (program): a(n) = Sum_{k=1..n-1} (k^n mod n).
A340822 (program): a(n) = exp(-1) * Sum_{k>=0} (k*(k + n))^n / k!.
A340823 (program): a(n) = exp(-1) * Sum_{k>=0} (k*(k - n))^n / k!.
A340835 (program): a(n) is the least k such that the digit reversal of k is greater than or equal to n.
A340836 (program): a(n) is the least k such that the binary reversal of k is greater than or equal to n.
A340837 (program): a(n) = (1/2) * Sum_{k>=0} (k*(k - 1))^n / 2^k.
A340838 (program): a(n) = (1/2) * Sum_{k>=0} (k*(k + n))^n / 2^k.
A340849 (program): a(n) = A001045(n) + A052928(n).
A340850 (program): Dirichlet g.f.: Sum_{n>0} a(n)/n^s = zeta(s) * zeta(s-2) / (zeta(s-1))^2.
A340854 (program): Numbers that cannot be factored into factors > 1, the least of which is odd.
A340855 (program): Numbers that can be factored into factors > 1, the least of which is odd.
A340862 (program): Number of times the number n turns up in pseudo-Fibonacci sequences starting with [k, 1] (with k >= 1), excluding the starting terms.
A340863 (program): a(n) = n!*LaguerreL(n, -n^2).
A340867 (program): a(n) = (prime(n) - a(n-1)) mod 4; a(0)=0.
A340881 (program): Row sums of A340880.
A340883 (program): Row sums of A340882.
A340886 (program): a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^2 * 2^(n-k-1) * a(k).
A340887 (program): a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^2 * 3^(n-k-1) * a(k).
A340888 (program): a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^2 * 4^(n-k-1) * a(k).
A340898 (program): Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 4) missing three edges, where all three removed edges are incident to the same vertex in the 3-point set.
A340901 (program): Additive with a(p^e) = (-p)^e.
A340928 (program): Least image of A001222 applied to the prime indices of n.
A340929 (program): Heinz numbers of integer partitions of odd negative rank.
A340930 (program): Heinz numbers of integer partitions of even negative rank.
A340931 (program): Heinz numbers of integer partitions of odd numbers into an odd number of parts.
A340932 (program): Numbers whose least prime index is odd. Heinz numbers of integer partitions whose last part is odd.
A340933 (program): Numbers whose least prime index is even. Heinz numbers of integer partitions whose last part is even.
A340945 (program): List of Y-coordinates of point moving along one of the arms of a counterclockwise square spiral with four arms; A340944 gives X-coordinates.
A340959 (program): Table read by antidiagonals of the smallest prime >= n^k, n >= 1 and k >= 0.
A340968 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Sum_{j=0..n} k^j*binomial(n,j)*Catalan(j).
A340970 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Sum_{j=0..n} k^j*binomial(n,j)*binomial(2*j,j).
A340971 (program): a(n) = Sum_{k=0..n} n^k * binomial(n,k) * binomial(2*k,k).
A340972 (program): a(n) = Sum_{k=0..n} (-n)^k * binomial(n,k) * binomial(2*k,k).
A340973 (program): Generating function Sum_{n >= 0} a(n)*x^n = 1/sqrt((1-x)*(1-13*x)).
A341002 (program): Numbers whose sum of even digits and sum of odd digits differ by 1.
A341003 (program): Numbers whose sum of even digits and sum of odd digits differ by 2.
A341004 (program): Numbers whose sum of even digits and sum of odd digits differ by 3.
A341005 (program): Numbers whose sum of even digits and sum of odd digits differ by 4.
A341006 (program): Numbers whose sum of even digits and sum of odd digits differ by 5.
A341007 (program): Numbers whose sum of even digits and sum of odd digits differ by 6.
A341008 (program): Numbers whose sum of even digits and sum of odd digits differ by 7.
A341009 (program): Numbers whose sum of even digits and sum of odd digits differ by 8.
A341010 (program): Numbers whose sum of even digits and sum of odd digits differ by 9.
A341014 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Sum_{j=0..n} k^j * j! * binomial(n,j)^2.
A341016 (program): Numbers k such that A124440(k) is a multiple of A066840(k).
A341020 (program): INVERT transform of the binary weight.
A341033 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. exp(x/(1-k*x)).
A341036 (program): a(n) = Sum_{k=1..n} gcd(k,n)^(k-2).
A341038 (program): a(n) = Sum_{i+j<=m+1} d_i * d_j, where d_1 < … < d_m are the divisors of n.
A341042 (program): Multiplicative projection of odd part of n.
A341043 (program): a(n) = 16*n^3 - 36*n^2 + 30*n - 9.
A341055 (program): Inverse permutation to A341054.
A341062 (program): Sequence whose partial sums give A000005.
A341091 (program): Triangle read by rows: Coefficients for calculation of the sum of all the finite differences from order zero to order k. Sum_{n=0..k} T(n,k)*b(n) = b(0) + b(1) + … + b(k) + (b(1) - b(0)) + … + (b(k) - b(k-1)) + (((b(2) - b(1))-((b(1) - b(0))) + … .
A341092 (program): Rows of Pascal’s triangle which contain a 3-term arithmetic progression of a certain form: a(n) = (2n^2 + 22n + 37 + (2n + 3)*(-1)^n)/8.
A341099 (program): Numbers divisible by at least three terms of A008864.
A341103 (program): T(n, k) = Sum_{j=0..k}(binomial(n + k - j, 2*k) - binomial(n + j - 1, 2*k)) for n > 0 and T(0, 0) = 1. Triangle read by rows, T(n, k) for 0 <= k <= n.
A341104 (program): a(n) = [x^n] (x - 1)^4/((1 - 2*x)*(x^2 - 3*x + 1)).
A341110 (program): Row sums of A341111.
A341132 (program): Number of partitions of n into 2 distinct prime powers (including 1).
A341155 (program): Number of partitions of n into 2 distinct nonzero decimal palindromes.
A341185 (program): a(n) = Sum_{k=0..n} k^n * k! * binomial(n,k)^2.
A341191 (program): Number of ways to write n as an ordered sum of 2 nonzero decimal palindromes.
A341196 (program): a(n) = Sum_{k=0..n} k^4 * (n-k)! * binomial(n,k)^2.
A341197 (program): a(n) = Sum_{k=0..n} k^n * (n-k)! * binomial(n,k)^2.
A341208 (program): a(n) = F(n+4) * F(n+1) - 4 * (-1)^n where F(n) = A000045(n) are the Fibonacci numbers.
A341209 (program): a(n) = (n^3 + 6*n^2 + 17*n + 6)/6.
A341216 (program): Triangle read by columns T(n,k) k > n >= 1: Last survivor positions in a modified Josephus problem for n numbers, where after each deletion the counting starts over at the lowest existing number n, rather than continuing from the current position.
A341232 (program): Numerator of the expected fraction of guests without a napkin in Conway’s napkin problem with n guests.
A341233 (program): Denominator of the expected fraction of guests without a napkin in Conway’s napkin problem with n guests.
A341239 (program): a(n) = floor(r*floor(s*n)), where r = 1 + sqrt(2) and s = sqrt(2).
A341240 (program): a(n) = 4*a(n-1) - 2*a(n-2) + a(n-3) - 4*a(n-4) + 2*a(n-5) for n >= 7, where a(1) = 1, a(2) = 2, a(3) = 4, a(4) = 12, a(5) = 38, a(6) = 127.
A341248 (program): a(n) = 5*a(n-1) - 4*a(n-3) for n >= 4, where a(1) = 1, a(2) = 4, a(3) = 18.
A341249 (program): a(n) = floor(r*floor(s*n)), where r = 2 + sqrt(2) and s = sqrt(2).
A341250 (program): a(n) = 5*a(n-1) - 4*a(n-3) for n >= 4, where a(1) = 1, a(2) = 3, a(3) = 13.
A341254 (program): a(n) = floor(r*floor(r*n)), where r = (2 + sqrt(5))/2.
A341255 (program): Let f(n) = floor(r*floor(r*n)) = A341254(n), where r = (2 + sqrt(5))/2). Let a(1) = 1. Then a(n) = f(a(n-1)) for n >= 2.
A341256 (program): Concatenation of all 01-words in the order induced by A004526; see Comments.
A341257 (program): Positions of palindromes in the ordering of all 01-words defined at A341256.
A341259 (program): Number of 0’s in n-th word defined at A341258.
A341276 (program): a(n) = 1 + 3*n*(n+1) - Sum_{k=1..n} d(k), where d(k) is the number of divisors of k.
A341282 (program): Numbers k such that there is no k-digit number m with the property that the binary expansion of m begins with the base-10 digits of m.
A341300 (program): a(n) = n!+(n-1)!+(n-2)!+(n-3)!+n-3.
A341301 (program): a(n) = ceiling(n^2 - 7*n/3 + 19/3).
A341302 (program): a(n) = n! + (n-1)! + n-2.
A341307 (program): Expansion of (x^9+x^8+2*x^7+x^6+2*x^5+2*x^4+x^3+x^2+1)/(1-x^6)^2.
A341308 (program): Row sums of triangle A249223.
A341309 (program): Sum of odd divisors of n that are <= A003056(n).
A341310 (program): Sum of odd divisors of n that are > A003056(n).
A341311 (program): G.f. = (1+x^2+2*x^3+3*x^4+4*x^5+3*x^6+4*x^7+3*x^8+2*x^9+x^10)/(1-x^6)^2.
A341312 (program): a(n) = a(n-1) + a(n-3) unless a(n-1) and a(n-3) are both even in which case a(n) = (a(n-1) + a(n-3))/2, with a(0) = a(1) = a(2) = 1.
A341313 (program): a(n) = (a(n-1) + a(n-3))/2^m, where 2^m is the highest power of 2 that divides both a(n-1) and a(n-3), with a(0) = a(1) = a(2) = 1.
A341314 (program): Array read by antidiagonals: T(n,k) = (n+k)/gcd(n,k), n>=0, k>=0.
A341315 (program): Triangle read by rows: T(n,k) = (n+k)/gcd(n,k), n>=0, 0<=k<=n.
A341316 (program): Row sums in A341315.
A341330 (program): a(n) = Sum_{k=1..n} (-k)^(k+1).
A341331 (program): a(n) = n^n - (n-1)^n - (n-2)^n - … - 1^n.
A341343 (program): Dirichlet g.f.: Sum_{n>=1} a(n)/n^s = (zeta(s))^3 / (zeta(3*s))^2.
A341345 (program): a(n) = A048673(n) mod 3.
A341346 (program): a(n) = A048673(2n-1) mod 3.
A341347 (program): a(n) = (1+A003961(A003961(n)))/2 mod 3, where A003961 shifts the prime factorization of n one step towards larger primes.
A341349 (program): Numbers k for which A254049(k) is not a multiple of 3.
A341350 (program): Numbers k for which A254049(k) [= A048673(2k-1)] is a multiple of 3.
A341353 (program): Greatest k such that 3^k divides A156552(n); the 3-adic valuation of A156552(n).
A341354 (program): Greatest k such that 3^k divides A156552(2*n); number of trailing 1-digits in the ternary expansion of A156552(n).
A341356 (program): The most significant digit in A097801-base.
A341361 (program): a(n) is the smallest abundant number of the form 2^e * prime(n).
A341389 (program): Characteristic function of A158705, nonnegative integers with an odd number of even powers of 2 in their base-2 representation.
A341392 (program): a(n) = A284005(n) / (1 + A000120(n))!.
A341396 (program): Number of integer solutions to (x_1)^2 + (x_2)^2 + … + (x_7)^2 <= n.
A341397 (program): Number of integer solutions to (x_1)^2 + (x_2)^2 + … + (x_8)^2 <= n.
A341398 (program): Number of integer solutions to (x_1)^2 + (x_2)^2 + … + (x_9)^2 <= n.
A341399 (program): Number of integer solutions to (x_1)^2 + (x_2)^2 + … + (x_10)^2 <= n.
A341400 (program): Number of nonnegative solutions to (x_1)^2 + (x_2)^2 + … + (x_5)^2 <= n.
A341401 (program): Number of nonnegative solutions to (x_1)^2 + (x_2)^2 + … + (x_6)^2 <= n.
A341402 (program): Number of nonnegative solutions to (x_1)^2 + (x_2)^2 + … + (x_7)^2 <= n.
A341403 (program): Number of nonnegative solutions to (x_1)^2 + (x_2)^2 + … + (x_8)^2 <= n.
A341407 (program): INVERT transform of pi (A000720).
A341409 (program): a(n) = (Sum_{k=1..3} k^n) mod n.
A341410 (program): a(n) = (Sum_{k=1..4} k^n) mod n.
A341411 (program): a(n) = (Sum_{k=1..5} k^n) mod n.
A341412 (program): a(n) = (Sum_{k=1..6} k^n) mod n.
A341413 (program): a(n) = (Sum_{k=1..7} k^n) mod n.
A341414 (program): a(n) = (Fibonacci(n)*Lucas(n)) mod 10.
A341420 (program): The positive integer numbers k represented properly by the binary quadratic form x^2 + 4*y^2.
A341441 (program): Total number of triangles visible in a regular (2n+1)-gon with all diagonals drawn.
A341449 (program): Heinz numbers of integer partitions into odd parts > 1.
A341463 (program): a(n) = (-1)^(n+1) * (3^n+1)/2.
A341470 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Sum_{j=0..n} binomial(k*n,n-j) * binomial(k*n+j,j).
A341491 (program): a(n) = binomial(6*n, n) * hypergeom([-5*n, -n], [-6*n], -1).
A341507 (program): Number of nonempty subsets S of {1,2,…,n} in which all elements are strictly less than the sum of the other elements of S.
A341509 (program): a(n) = 2^j if n is of the form 2^i - 2^j with i > j, and 0 otherwise.
A341513 (program): Sum of digits in A097801-base.
A341514 (program): Number of trailing zeros in A097801-base.
A341517 (program): a(n) = mu(A327859(n)), where mu is the Möbius function, A008683.
A341518 (program): Numbers k such that the primorial base representation of their arithmetic derivative do not contain digits larger than 1.
A341519 (program): Number of prime factors (with multiplicity) shared by A003961(n) and A003973(n): a(n) = bigomega(gcd(A003961(n), sigma(A003961(n)))).
A341522 (program): a(n) = A156552(3*A005940(1+n)).
A341523 (program): Number of prime factors (with multiplicity) shared by n and sigma(n): a(n) = bigomega(gcd(n, sigma(n))).
A341524 (program): Number of prime factors in A017666(n), counted with multiplicity: a(n) = bigomega(n) - bigomega(gcd(n, sigma(n)).
A341525 (program): Numerator of A003973(n) / A003961(n).
A341528 (program): a(n) = n * sigma(A003961(n)), where A003961 shifts the prime factorization of n one step towards larger primes, and sigma is the sum of the divisors of n.
A341529 (program): a(n) = sigma(n) * A003961(n), where A003961 shifts the prime factorization of n one step towards larger primes, and sigma is the sum of the divisors of n.
A341538 (program): One of the two successive approximations up to 2^n for 2-adic integer sqrt(17). This is the 1 (mod 4) case.
A341539 (program): One of the two successive approximations up to 2^n for 2-adic integer sqrt(17). This is the 3 (mod 4) case.
A341540 (program): Expansion of the 2-adic integer sqrt(17) that ends in 11.
A341543 (program): a(n) = sqrt( Product_{j=1..n} Product_{k=1..2} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/2)^2) ).
A341544 (program): a(n) = sqrt( Product_{j=1..n} Product_{k=1..4} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/4)^2) ).
A341549 (program): a(n) = Sum_{k=1..n} (-1)^(n+k)*A087322(n,k).
A341552 (program): Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 4) missing three edges, where all three removed edges are incident to different vertices in the 3 point set but exactly two removed edges are incident to the same vertex in the other set.
A341579 (program): Number of steps needed to solve the Towers of Hanoi exchanging disks puzzle with 3 pegs and n disks.
A341580 (program): Number of steps needed to reach position “YZ^(n-1)” in the Towers of Hanoi exchanging disks puzzle with 3 pegs and n disks.
A341581 (program): Number of steps needed to move the largest disk out from a stack of n disks in the Towers of Hanoi exchanging disks puzzle with 3 pegs.
A341582 (program): Number of simple moves of the smallest disk in the solution to the Towers of Hanoi exchanging disks puzzle with 3 pegs and n disks.
A341583 (program): Geometric length of the solution to the Towers of Hanoi exchanging disks puzzle with 3 pegs and n disks.
A341590 (program): a(n) = (Sum_{j=1..3} StirlingS1(3,j)*(2^j-1)^n)/3!.
A341591 (program): Number of superior prime divisors of n.
A341592 (program): Number of squarefree superior divisors of n.
A341593 (program): Number of superior prime-power divisors of n.
A341594 (program): Number of strictly superior odd divisors of n.
A341595 (program): Number of strictly superior squarefree divisors of n.
A341596 (program): Number of strictly inferior squarefree divisors of n.
A341597 (program): a(n) = A144066(n+3,3).
A341600 (program): One of the two successive approximations up to 2^n for 2-adic integer sqrt(-3/5). This is the 1 (mod 4) case.
A341601 (program): One of the two successive approximations up to 2^n for 2-adic integer sqrt(-3/5). This is the 3 (mod 4) case.
A341602 (program): Expansion of the 2-adic integer sqrt(-3/5) that ends in 01.
A341603 (program): Expansion of the 2-adic integer sqrt(-3/5) that ends in 11.
A341609 (program): Characteristic function of A337372: a(n) = 1 if A337345(n) = 1, otherwise 0.
A341619 (program): Characteristic function of primitive nondeficient numbers (A006039): a(n) = 1 if proper multiples of n are all abundant, and proper divisors of n are all deficient, 0 otherwise.
A341620 (program): Number of nondeficient divisors of n.
A341625 (program): a(n) = 1 if the arithmetic derivative of n is less than n, otherwise 0.
A341629 (program): Characteristic function of A055932: a(n) = 1 if n is a number all of whose prime divisors are consecutive primes starting at 2, otherwise 0.
A341635 (program): a(n) = Sum_{d|n} phi(d) * mu(d) * mu(n/d).
A341636 (program): a(n) = Sum_{d|n} phi(d) * tau(d) * tau(n/d).
A341637 (program): a(n) = Sum_{d|n} phi(d) * sigma(d) * sigma(n/d).
A341638 (program): a(n) = Sum_{d|n} phi(d) * sigma(d) * tau(n/d).
A341642 (program): Number of strictly superior prime divisors of n.
A341643 (program): The unique strictly superior prime divisor of each number that has one.
A341644 (program): Number of strictly superior prime-power divisors of n.
A341646 (program): Numbers with a strictly superior squarefree divisor.
A341655 (program): a(n) is the number of divisors of prime(n)^2 - 1.
A341656 (program): a(n) is the number of divisors of prime(n)^4 - 1.
A341657 (program): a(n) is the number of divisors of prime(n)^6 - 1.
A341660 (program): Primes p such that p^2 - 1 has fewer than 32 divisors.
A341663 (program): a(n) is the number of divisors of prime(n)^3 - 1.
A341664 (program): a(n) is the number of divisors of prime(n)^5 - 1.
A341671 (program): Solutions y of the Diophantine equation 3*(x^2+x+1) = y^2.
A341675 (program): Number of superior odd divisors of n.
A341676 (program): The unique superior prime divisor of each number that has one.
A341677 (program): Number of strictly inferior prime-power divisors of n.
A341680 (program): Successive approximations up to 2^n for the 2-adic integer Sum_{k>=0} k!.
A341681 (program): Successive approximations up to 3^n for the 3-adic integer Sum_{k>=0} k!.
A341682 (program): Successive approximations up to 5^n for the 5-adic integer Sum_{k>=0} k!.
A341683 (program): Successive approximations up to 7^n for the 7-adic integer Sum_{k>=0} k!.
A341684 (program): Expansion of the 2-adic integer Sum_{k>=0} k!.
A341686 (program): Expansion of the 5-adic integer Sum_{k>=0} k!.
A341687 (program): Expansion of the 7-adic integer Sum_{k>=0} k!.
A341691 (program): a(0) = 0, and for any n > 0, a(n) = n - a(k) where k is the greatest number < n such that n AND a(k) = a(k) (where AND denotes the bitwise AND operator).
A341700 (program): Sum of the primes p satisfying n < p <= 2n.
A341703 (program): a(n) = 6*binomial(n,4) + 2*binomial(n,2) + 1.
A341704 (program): a(n) = 20*binomial(n,6) + 2*binomial(n,3) + 1.
A341705 (program): a(n) = 70*binomial(n,8) + 2*binomial(n,4) + 1.
A341706 (program): Row 2 of semigroup multiplication table shown in A341317 and A341318.
A341714 (program): Coefficients in the expansion of Product_{m>=1} (1 - q^(13*m))/(1 - q^m).
A341718 (program): Subtract 1 from each term of A004094 (the powers of 2 written backwards).
A341723 (program): Triangle read by rows: coefficients of expansion of certain weighted sums P_1(n,k) of Fibonacci numbers as a sum of powers.
A341725 (program): Triangle read by rows: coefficients in expansion of Asveld’s polynomials p_j(x).
A341726 (program): Column 1 of A341723.
A341735 (program): a(n) = A007678(2*n+1).
A341736 (program): a(n) is the label of the square of the n-th element in the semigroup S = {(0,0), (i,j): i >= j >= 1}.
A341740 (program): a(n) is the maximum value of the magic constant in a normal magic triangle of order n.
A341744 (program): a(0)=1, a(1)=2; for n > 1, a(n) = a(n - a(n-2)) + n.
A341765 (program): Let b(2*m) be the number of even gaps 2*m between successive odd primes from 3 up to prime(n). Let k1 = sum of all b(2*m) when m == 1 (mod 3) and let k2 = sum of all b(2*m) when m == 2 (mod 3). Then a(n) = k1 - k2.
A341768 (program): a(n) = n * (binomial(n,2) - 2).
A341772 (program): a(n) = Sum_{d|n} phi(d) * J_2(n/d).
A341781 (program): Refactorable numbers (or tau numbers, A033950) k such that k/tau(k) is even, where tau(k) = A000005(k).
A341815 (program): a(n) = Sum_{k=0..n} binomial(n,k)^3 * k^n.
A341822 (program): Length of the longest 2-increasing sequence of positive integer triples with entries <= n.
A341828 (program): Difference of consecutive odd squarefree semiprimes.
A341831 (program): Dirichlet g.f.: 1 / zeta(s)^5.
A341832 (program): Dirichlet g.f.: 1 / zeta(s)^6.
A341833 (program): Dirichlet g.f.: 1 / zeta(s)^7.
A341834 (program): Dirichlet g.f.: 1 / zeta(s)^8.
A341835 (program): Dirichlet g.f.: 1 / zeta(s)^9.
A341836 (program): Dirichlet g.f.: 1 / zeta(s)^10.
A341837 (program): If n = Product (p_j^k_j) then a(n) = Product ((-1)^k_j * binomial(n, k_j)).
A341854 (program): Number of triangulations of a fixed hexagon with n internal nodes.
A341859 (program): Decimal expansion of 4 - (8/5)*sqrt(5).
A341861 (program): Number of primes among the (p-1)/2 numbers {2*p+1, 4*p+1, …, (p-1)*p+1}, p = prime(n).
A341865 (program): The cardinality of the largest multiset of positive integers whose product and sum equals n.
A341866 (program): The cardinality of the smallest (nontrivial, except for prime n) multiset of positive integers whose product and sum equal n.
A341867 (program): Square array read by downward antidiagonals: T(m,n) = Sum_{i=0..m, j=0..n} binomial(m,i)*binomial(n,j)*binomial(i+j,i).
A341869 (program): For any k, the cumulative sum of the terms a(1) + a(2) + a(3) + … + a(k) and the cumulative sum of their digits so far are odd. This is the lexicographically earliest sequence of distinct terms > 0 with this property.
A341885 (program): a(n) is the sum of A000217(p) over the prime factors p of n, counted with multiplicity.
A341893 (program): Indices of triangular numbers that are one-tenth of other triangular numbers.
A341896 (program): a(n) is the number of words of length n over the alphabet {a,b,c} with an even number of appearances of the letter ‘a’ and the sum of appearances of the letters ‘b’ and ‘c’ add up to at most 3.
A341900 (program): Partial sums of A005165.
A341902 (program): Least k > 1 such that (n^3+k)/(n+k) is an integer.
A341905 (program): a(n) = a(n-1) + a(n-2) + 2*a(n-3) with a(0) = 3, a(1) = 0, a(2) = 2.
A341915 (program): For any nonnegative number n with runs in binary expansion (r_1, …, r_w), a(n) = Sum_{k = 1..w} 2^(r_1 + … + r_k - 1).
A341916 (program): Inverse permutation to A341915.
A341927 (program): Bisection of the numerators of the convergents of cf(1,4,1,6,1,6,…,6,1).
A341928 (program): a(n) = F(n+4) * F(n+2) + 7 * (-1)^n where F(n) = A000045(n) are the Fibonacci numbers.
A341929 (program): Bisection of the numerators of the convergents of cf (1,1,6,1,6,1,…,6,1).
A341933 (program): a(n) = A023896(n) mod A000203(n).
A341938 (program): Numbers m such that the geometric mean of tau(m) and phi(m) is an integer where phi is the Euler totient function (A000010) and tau is the number of divisors function (A000005).
A341943 (program): Fixed points of A341915.
A341945 (program): Number of partitions of n into 2 primes (counting 1 as a prime).
A341952 (program): Let x = (prime(n+1) - prime(n))/2 modulo 3 for n >= 2, then a(n) = -1 if x = 2, otherwise a(n) = x.
A341953 (program): Replace each digit d in the decimal representation of n with the digital root of d^n.
A341961 (program): G.f. A(x) satisfies: A(x) = (1 + x*A(x))*(1 + 2*x*A(x)) / (1 - x*A(x))^2.
A341962 (program): G.f. B(x) satisfies: B(x) = (1 - x^2*B(x)^2) / (1 - 2*x*B(x))^2.
A341963 (program): G.f. C(x) satisfies: C(x) = (1 - x*C(x))*(1 - 2*x*C(x)) / (1 - 3*x*C(x))^2.
A341973 (program): Number of partitions of n into 2 distinct primes (counting 1 as a prime).
A341982 (program): Number of ways to write n as an ordered sum of 2 primes (counting 1 as a prime).
A341994 (program): a(n) = 1 if the arithmetic derivative (A003415) of n is a squarefree number (A005117) > 1, otherwise 0.
A341995 (program): a(n) = 1 if the arithmetic derivative (A003415) of n is a prime, otherwise 0.
A341996 (program): a(n) = 1 if there is at least one such prime p that p^p divides the arithmetic derivative of n, A003415(n); a(0) = a(1) = 0 by convention.
A341997 (program): a(n) = A327936(A003415(n)).
A341998 (program): Arithmetic derivative of n divided by its largest squarefree divisor: a(n) = A003557(A003415(n)).
A341999 (program): a(n) = 1 if the k-th arithmetic derivative is nonzero for all k >= 0, otherwise 0.
A342001 (program): Arithmetic derivative without its inherited divisor; the arithmetic derivative of n divided by A003557(n), which is a common divisor of both n and A003415(n).
A342002 (program): Čiurlionis sequence: Arithmetic derivative without its inherited divisor applied to the primorial base exp-function: a(n) = A342001(A276086(n)).
A342003 (program): Maximal exponent in the prime factorization of the arithmetic derivative of n: a(n) = A051903(A003415(n)).
A342007 (program): Multiplicative with a(p^e) = p^floor(e/p).
A342008 (program): Numbers k such that Euler totient phi(k) is a multiple of the arithmetic derivative of k.
A342014 (program): Arithmetic derivative of n, taken modulo n: a(n) = A003415(n) mod n.
A342015 (program): a(n) = A003415(A276086(n)) mod A276086(n).
A342016 (program): Difference between the arithmetic derivative of A276086(n) and A276086(n) itself, which is the prime product form of primorial base expansion of n.
A342023 (program): a(n) = 1 if there is a prime p such that p^p divides n, otherwise 0.
A342024 (program): a(n) = 1 if prime(k)^(k+1) divides n for some k, otherwise 0.
A342025 (program): a(n) = 1 if n has the same numbers of prime factors of forms 4*k+1 and 4*k+3 when counted with multiplicity, otherwise 0.
A342036 (program): Palindromes of even length only using 0 or 1.
A342040 (program): Binary palindromes of odd length.
A342050 (program): Numbers k which have an odd number of trailing zeros in their primorial base representation A049345(k).
A342051 (program): Numbers k which have an even number of trailing zeros in their primorial base representation A049345(k).
A342062 (program): a(n) is the number of divisors of prime(n)^8 - 1.
A342073 (program): Number of n-colorings of the vertices of the 5-dimensional cross polytope such that no two adjacent vertices have the same color.
A342074 (program): Number of n-colorings of the vertices of the 6-dimensional cross polytope such that no two adjacent vertices have the same color.
A342075 (program): Number of n-colorings of the vertices of the 7-dimensional cross polytope such that no two adjacent vertices have the same color.
A342081 (program): Numbers without an inferior odd divisor > 1.
A342082 (program): Numbers with an inferior odd divisor > 1.
A342083 (program): Number of chains of strictly inferior divisors from n to 1.
A342086 (program): Number of strict factorizations of divisors of n.
A342087 (program): Number of chains of divisors starting with n and having no adjacent parts x <= y^2.
A342088 (program): Triangle read by rows: T(n,k) is the number of n-colorings of the vertices of the k-dimensional cross polytope such that no two adjacent vertices have the same color. 0 <= k <= n.
A342089 (program): Numbers that have two representations as the sum of distinct non-consecutive Lucas numbers (A000032).
A342099 (program): Product of first n tangent numbers.
A342101 (program): Remove middle term and append, starting with [1, 2, 3].
A342107 (program): a(n) = Sum_{k=0..n} (4*k)!/k!^4.
A342112 (program): Drop the final digit of n^5.
A342120 (program): Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of g.f. 1/(1 - k*x - k*x^2).
A342122 (program): a(n) is the remainder when the binary reverse of n is divided by n.
A342126 (program): The binary expansion of a(n) corresponds to that of n where all the 1’s have been replaced by 0’s except in the first run of 1’s.
A342129 (program): Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of g.f. 1/(1 - k*x + k*x^2).
A342131 (program): a(n) = n/2 + floor(n/4) if n is even, otherwise (3*n+1)/2.
A342133 (program): Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of g.f. 1/(1 - 2*k*x + k*x^2).
A342134 (program): Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of g.f. 1/(1 - 2*k*x - k*x^2).
A342138 (program): Array T(n,k) = (n+k)*(3*n+3*k-5)/2 + (3*k+1), read by ascending antidiagonals.
A342148 (program): Infinite square matrix A(m,n) = F(m) mod n, m,n >= 1, where F = Fibonacci = A000045, read by falling antidiagonals.
A342149 (program): Infinite square matrix A(m,n) = F(m+1) mod (n+1), m,n >= 1, where F = Fibonacci = A000045, read by falling antidiagonals.
A342156 (program): For n > 2, a(n) = 0,1,2, or 3 when (prime(n+1) mod 6, prime(n) mod 6) = (1,1),(1,5),(5,1), or (5,5), respectively.
A342159 (program): Number of words of length n, over the alphabet {a,b,c}, which have an odd number of a’s and the number of b’s plus the number of c’s is less than or equal to 3.
A342161 (program): Expansion of the exponential generating function (tanh(x) - sech(x) + 1) * exp(x).
A342165 (program): A fractal-like sequence: erase the terms that have a prime index, the non-erased terms rebuild the original sequence.
A342166 (program): Product of first n Fubini numbers.
A342167 (program): a(n) = U(n, (n+2)/2) where U(n, x) is a Chebyshev polynomial of the 2nd kind.
A342168 (program): a(n) = U(n, (n+3)/2) where U(n, x) is a Chebyshev polynomial of the 2nd kind.
A342170 (program): Product of first n little Schröder numbers.
A342173 (program): a(n) = Sum_{j=1..n-1} floor(prime(n)/prime(j)).
A342177 (program): Product of first n Motzkin numbers.
A342178 (program): Product of first n central Delannoy numbers.
A342182 (program): Sum_{n>=0} a(n) * x^n / (n!)^2 = 1 / (1 - x * BesselI(0,2*sqrt(x))).
A342190 (program): Numbers k such that A001065(k) = sigma(k) - k is the sum of 2 squares.
A342196 (program): a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k)^2 * a(k-1).
A342197 (program): a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k)^3 * a(k-1).
A342198 (program): a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k)^4 * a(k-1).
A342199 (program): a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k)^5 * a(k-1).
A342205 (program): a(n) = T(n,n+1) where T(n,x) is a Chebyshev polynomial of the first kind.
A342206 (program): a(n) = T(n,n+2) where T(n,x) is a Chebyshev polynomial of the first kind.
A342207 (program): a(n) = U(n,n+1) where U(n,x) is a Chebyshev polynomial of the second kind.
A342210 (program): Product of first n secant numbers.
A342213 (program): Largest number of maximal planar node-induced subgraphs of an n-node graph.
A342234 (program): a(n) = (27^n - 9^n)/2 - 12^n + 6^n.
A342235 (program): Coordination sequence of David Eppstein’s “Tetrastix” graph.
A342253 (program): a(n) = (n-6)*sqrt((n-5)^2) + 2*n + 31.
A342279 (program): A bisection of A000201: a(n) = A000201(2*n+1).
A342280 (program): a(n) = A001952(2*n+1).
A342281 (program): A bisection of A001951: a(n) = A001951(2*n+1).
A342286 (program): a(n) = number of n-variable nondegenerate self-reflecting truth-tables.
A342287 (program): a(n) = number of n-variable nondegenerate self-dual truth-tables.
A342288 (program): a(n) = C(n)*C(n+2), where C(n) is the n-th Catalan number A000108(n).
A342294 (program): a(n) = Sum_{k = 0..n} binomial(n,k)^11.
A342295 (program): a(n) = Sum_{k = 0..n} binomial(n,k)^12.
A342311 (program): T(n, k) = (n - k + 2)*binomial(2*n, n + k - 2). Triangle read by rows, T(n, k) for 0 <= k <= n.
A342314 (program): T(n, k) = [x^k] 2^n*(Euler(n, x/2) + Euler(n, x)), where Euler(n, x) are the Euler polynomials. Triangle read by rows, T(n, k) for 0 <= k <= n.
A342315 (program): T(n, k) = [x^k] 2^n*(Euler(n, x) - Euler(n, x/2)), where Euler(n, x) are the Euler polynomials. Triangle read by rows, T(n, k) for 0 <= k <= n.
A342350 (program): Numbers k such that lcm(1,2,3,…,k)/21 equals the denominator of the k-th harmonic number H(k).
A342352 (program): Expansion of e.g.f. (exp(x)-1)*(exp(x) - x^2/2 - x - 1).
A342354 (program): M(n,k) = 2*n^2 + 2*k + 1 for 0 <= k <= n and M(n,k) = 2*k^2 + 4*k - 2*n + 1 for 0 <= n <= k; square array M(n,k) read by ascending antidiagonals (n, k >= 0).
A342362 (program): Expansion of the o.g.f. (1 + 8*x + 10*x^2 + 8*x^3 + x^4)/((1 - x)^4*(1 + x)^2).
A342363 (program): First differences of A341282.
A342369 (program): If n is congruent to 2 (mod 3), then a(n) = (2*n - 1)/3; otherwise, a(n) = 2*n.
A342370 (program): a(n) = Sum_{k=1..n} gcd(k,n)^(k-1).
A342371 (program): Partial sums of A051697.
A342379 (program): Expansion of e.g.f. (exp(x)-1)*(exp(x) - x^3/6 - x^2/2 - x - 1).
A342380 (program): Expansion of e.g.f. (exp(x)-1)*(exp(x) - x^4/24 - x^3/6 - x^2/2 - x - 1).
A342381 (program): Triangle read by rows: T(n,k) is the number of symmetries of the n-dimensional hypercube that fix exactly 2*k facets; n,k >= 0
A342385 (program): Triangle with n>=0 as first column and main diagonal. The (n+2)-th column is (n+1)*A028310(n).
A342389 (program): a(n) = Sum_{k=1..n} k^gcd(k,n).
A342394 (program): a(n) = Sum_{k=1..n} k^(gcd(k,n) - 1).
A342395 (program): a(n) = Sum_{k=1..n} k^(n/gcd(k,n)).
A342396 (program): a(n) = Sum_{k=1..n} k^(n/gcd(k,n) - 1).
A342397 (program): Expansion of the o.g.f. (2*x^2 + 3*x + 2)*x/((x + 1)^2*(x - 1)^4).
A342403 (program): a(1) = 1; a(n) = -Sum_{d|n, d < n} d * a(d).
A342404 (program): a(n) = binomial(n,2)*(2^(n-2) - n + 1).
A342410 (program): The binary expansion of a(n) corresponds to that of n where all the 1’s have been replaced by 0’s except in the last run of 1’s.
A342411 (program): a(n) = Sum_{k=1..n} (n/gcd(k,n))^(n/gcd(k,n) - 2).
A342412 (program): a(n) = Sum_{k=1..n} (n/gcd(k,n))^(n-2).
A342413 (program): a(n) = gcd(phi(n), A003415(n)), where A003415(n) is the arithmetic derivative of n, and phi is Euler totient function.
A342414 (program): a(n) = A003415(n) / gcd(phi(n),A003415(n)), where A003415(n) is the arithmetic derivative of n, and phi is Euler totient function.
A342415 (program): a(n) = phi(n) / gcd(phi(n),A003415(n)), where A003415(n) is the arithmetic derivative of n, and phi is Euler totient function.
A342416 (program): a(n) = gcd(A173557(n), A342001(n)).
A342420 (program): a(n) = Sum_{k=1..n} (n/gcd(k,n))^(n/gcd(k,n)).
A342421 (program): a(n) = Sum_{k=1..n} (n/gcd(k,n))^(gcd(k,n) - 1).
A342422 (program): a(n) = Sum_{k=1..n} (n/gcd(k,n))^gcd(k,n).
A342423 (program): a(n) = Sum_{k=1..n} gcd(k,n)^gcd(k,n).
A342424 (program): a(n) = Sum_{k=1..n} gcd(k,n)^(n/gcd(k,n)).
A342432 (program): a(n) = Sum_{k=1..n} gcd(k,n)^(n-2).
A342433 (program): a(n) = Sum_{k=1..n} gcd(k,n)^(n-1).
A342435 (program): a(n) = Sum_{k=1..n} gcd(k,n)^(gcd(k,n) - 2).
A342436 (program): a(n) = Sum_{k=1..n} gcd(k,n)^(gcd(k,n) - 1).
A342437 (program): a(n) = Sum_{k=1..n} gcd(k,n)^(n/gcd(k,n) - 1).
A342448 (program): Partial sums of A066194.
A342449 (program): a(n) = Sum_{k=1..n} gcd(k,n)^k.
A342455 (program): The fifth powers of primorials: a(n) = A002110(n)^5.
A342456 (program): A276086 applied to the primorial inflation of Doudna-tree, where A276086(n) is the prime product form of primorial base expansion of n.
A342457 (program): Terms of A342456 prime-shifted so far towards lower primes that they become even: a(n) = 2*A246277(A342456(n)).
A342458 (program): a(n) = gcd(A001615(n), A003415(n)), where A001615 is Dedekind psi, and A003415 is the arithmetic derivative of n.
A342459 (program): a(n) = gcd(A048250(n), A342001(n)).
A342460 (program): a(n) = 1 if n > 1 and is divisible by the sum of its prime factors (with repetition), otherwise 0.
A342461 (program): Number of nonzero digits when A329886(n) is written in primorial base, where A329886 is the primorial inflation of Doudna-tree.
A342462 (program): Sum of digits when A329886(n) is written in primorial base, where A329886 is the primorial inflation of Doudna-tree.
A342463 (program): a(n) = A342001(A342456(n)); “wild part” of the arithmetic derivative of A342456(n).
A342464 (program): Largest digit value when A329886(n) is written in primorial base, where A329886 is the primorial inflation of Doudna-tree.
A342466 (program): a(n) = A336466(1+A000265(sigma(n))), where A336466 is fully multiplicative with a(p) = A000265(p-1) for p prime, and A000265(k) is the odd part of k.
A342470 (program): a(n) = Sum_{d|n} phi(d)^4.
A342473 (program): a(n) = Sum_{d|n} phi(d)^d.
A342477 (program): The squarefree part of the powerful numbers: a(n) = A007913(A001694(n)).
A342482 (program): a(n) = n*(2^(n-1) - n - 1).
A342483 (program): a(n) = binomial(n,2)*(2^(n-2) - n).
A342527 (program): Number of compositions of n with alternating parts equal.
A342534 (program): a(n) = Sum_{k=1..n} phi(gcd(k, n))^2.
A342543 (program): a(n) = Sum_{k=1..n} phi(gcd(k, n))^gcd(k, n).
A342550 (program): For n>=3, a(n) is the sum of the indices of n seen as an m-gonal number.
A342553 (program): Least integer m > 2*n such that m-2*n and m+2*n are both squares, for n>1.
A342567 (program): a(n) = (prime(n)^2 - prime(n-1)*prime(n+1))/2, n >= 3.
A342568 (program): 1/a(n) is the current through the resistor at the central rung of an electrical ladder network made of 6*n+1 one-ohm resistors, fed by 1 volt at diametrically opposite ends of the ladder.
A342573 (program): The number of ordered n-tuples consisting of n permutations (not necessarily distinct) such that the first element of each of them is the same.
A342603 (program): a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 6*a(n) + a(n+1).
A342604 (program): a(n) = Sum_{j=1..n} A003718(j-1)*prime(j).
A342610 (program): a(0) = 0, a(1) = 1; a(2*n) = 5*a(n), a(2*n+1) = a(n) + a(n+1).
A342611 (program): a(0) = 0, a(1) = 1; a(2*n) = 7*a(n), a(2*n+1) = a(n) + a(n+1).
A342614 (program): a(0) = 0, a(1) = 1; a(2*n) = 8*a(n), a(2*n+1) = a(n) + a(n+1).
A342615 (program): a(0) = 0, a(1) = 1; a(2*n) = 9*a(n), a(2*n+1) = a(n) + a(n+1).
A342621 (program): Sum of the partition number of the prime factors of n with multiplicity.
A342628 (program): a(n) = Sum_{d|n} d^(n-d).
A342629 (program): a(n) = Sum_{d|n} (n/d)^(n-d).
A342633 (program): a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 3*a(n) + a(n+1).
A342634 (program): a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 4*a(n) + a(n+1).
A342635 (program): a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 5*a(n) + a(n+1).
A342636 (program): a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 7*a(n) + a(n+1).
A342637 (program): a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 8*a(n) + a(n+1).
A342638 (program): a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 9*a(n) + a(n+1).
A342643 (program): a(n) = [x^n] x * Product_{j>=0} (1 + x^(2^j) + n*x^(2^(j+1))).
A342653 (program): a(n) = mu(A156552(n)), where mu is Möbius mu function.
A342654 (program): a(n) = A005940(1+A324104(n)); Euler totient phi conjugated by A156552.
A342655 (program): Number of prime factors (counted with multiplicity) in A156552(n).
A342656 (program): a(n) = A087436(A156552(n)); Number of odd prime factors in A156552(n), counted with repetitions.
A342661 (program): a(n) = n * sigma(A064989(n)), where A064989 is multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p, and sigma gives the sum of the divisors of its argument.
A342662 (program): a(n) = sigma(n) * A064989(n), where A064989 is multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p, and sigma is the sum of the divisors of n.
A342671 (program): a(n) = gcd(sigma(n), A003961(n)), where A003961 is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors of n.
A342672 (program): a(n) = lcm(sigma(n), A003961(n)), where A003961 is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors of n.
A342673 (program): a(n) = gcd(n, sigma(A003961(n))), where A003961 is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors of n.
A342675 (program): a(n) = Sum_{d|n} d^(n-d+1).
A342676 (program): a(n) is the number of lunar primes less than or equal to n.
A342677 (program): a(n) = Sum_{d|n} (n/d)^(n-d+1).
A342693 (program): a(n) = Sum_{d|n} mu(d) * floor(n/d^2).
A342696 (program): a(n) = floor(n/12).
A342697 (program): For any number n with binary expansion Sum_{k >= 0} b(k) * 2^k, the binary expansion of a(n) is Sum_{k >= 0} floor((b(k) + b(k+1) + b(k+2))/2) * 2^k.
A342709 (program): 12-gonal (dodecagonal) square numbers.
A342710 (program): Solutions x to the Pell-Fermat equation x^2 - 5*y^2 = 4.
A342711 (program): Partial sums of A000267.
A342712 (program): Partial sums of A248333.
A342719 (program): Array read by ascending antidiagonals: T(k, n) is the sum of the consecutive positive integers from 1 to (n - 1)*k placed along the perimeter of an n-th order perimeter-magic k-gon.
A342728 (program): a(n) is the least number k such that A066323(k) = n.
A342730 (program): a(n) = floor((frac(e*n) + 1) * prime(n+1)).
A342737 (program): Number of wedged n-spheres in the homotopy type of the neighborhood complex of Kneser graph KG_{3,n}.
A342739 (program): Length of n-th word in the ordering A341334 of all binary words.
A342740 (program): Positions in A341334 of words that end with 0.
A342741 (program): Positions of words in A341334 that end with 1.
A342742 (program): Positions of words in A341334 such that first digit = 0 and last digit = 0.
A342743 (program): Positions of words in A341334 such that first digit = 0 and last digit = 1.
A342744 (program): Positions of words in A341334 such that first digit = 1 and last digit = 0.
A342745 (program): Positions of words in A341334 such that first digit = 1 and last digit = 1.
A342748 (program): a(n) = sum of digits in the n-th word in A341334.
A342751 (program): Positions in A341334 of words in which #0’s - #1’s is odd.
A342752 (program): Positions in A341334 of words in which #0’s - #1’s is even.
A342757 (program): Array read by ascending antidiagonals: T(k, n) is the minimum value of the magic constant in a perimeter-magic k-gon of order n.
A342758 (program): Array read by ascending antidiagonals: T(k, n) is the maximum value of the magic constant in a perimeter-magic k-gon of order n.
A342761 (program): Fold a square sheet of paper alternately vertically to the left and horizontally downwards; after each fold, draw a line along each inward crease; after n folds, the resulting graph has a(n) edges.
A342762 (program): Fold a square sheet of paper alternately vertically to the left and horizontally downwards; after each fold, draw a line along each inward crease; after n folds, the resulting graph has a(n) connected components.
A342766 (program): a(1) = 1, for any n > 1, a(n) = A342765(a(n-1), n).
A342768 (program): a(n) = A342767(n, n).
A342769 (program): Pairwise listing of the partitions of 2k into two parts, (s,t), with 0 < s <= t ordered by increasing values of s and where k = 1,2,… .
A342774 (program): Length of n-th word in the ordering A342753 of all binary words.
A342778 (program): Positions of words in A342753 in which the last digit is 0.
A342779 (program): Positions of words in A342753 in which the last digit is 1.
A342782 (program): Positions of words in A342753 having 1st digit 0 and last digit 0.
A342783 (program): Positions of words in A342753 having 1st digit 0 and last digit 1.
A342784 (program): Positions of words in A342753 having 1st digit 1 and last digit 0.
A342785 (program): Positions of words in A342753 having 1st digit 1 and last digit 1.
A342788 (program): a(n) = sum of the digits of n-th word in A342753.
A342791 (program): Positions in A342753 of words in which #0’s - #1’s is odd.
A342792 (program): Positions in A342753 of words in which #0’s - #1’s is even.
A342799 (program): Numbers m such that there are more 1s than 2s in {K(1), .., K(m)}, where K = A000002 (Kolakoski sequence).
A342802 (program): Replace 2^k with (-3)^k in binary expansion of n.
A342819 (program): Table read by ascending antidiagonals: T(k, n) is the number of distinct values of the magic constant in a perimeter-magic k-gon of order n.
A342826 (program): Numbers k such that d(1)^0 + d(2)^1 + … + d(p)^(p-1) = d(1)^(p-1) + d(2)^(p-2) + … + d(p)^0, where d(i), i=1..p, are the digits of k.
A342828 (program): a(n) = Sum_{d|n} (-1)^(n/d+1) * d^(n-d).
A342831 (program): a(n) is the smallest positive integer k such that the n-dimensional cube [0,k]^n contains at least as many internal lattice points as external lattice points.
A342850 (program): Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 4) missing three edges, where all three removed edges are incident to different vertices in the 3-point set and none of the removed edges are incident to the same vertex in the other set.
A342851 (program): Remove duplicates in the decimal digit-reversal of n.
A342856 (program): Factorial numbers n that are sqrt(n)-smooth.
A342871 (program): a(n) = Sum_{k=1..n} floor(n^(1/k)), n >= 1.
A342872 (program): Distance to nearest product of 3 consecutive numbers (three-dimensional promic number, A007531).
A342873 (program): Numbers whose distance to the nearest cube equals the distance to the nearest product of 3 consecutive integers (three-dimensional oblong).
A342877 (program): a(n) = 1 if the average distance between consecutive first n primes is greater than that of the first n-1 primes, otherwise a(n) = 0, for n > 2.
A342878 (program): Array read by antidiagonals: T(n,k) = the length of the longest word over [1,…,n] having the property that there are no two disjoint occurrences of the same length-k word.
A342892 (program): a(n) is the complement of the bit two places to the left of the least significant “1” in the binary expansion of n.
A342903 (program): a(n) is the smallest number that is the sum of n positive squares in two ways.
A342905 (program): Array read by antidiagonals: T(n,k) = product of all distinct primes dividing n*k (n>=1, k>=1).
A342906 (program): a(n) = 2^(2*n-2) - Catalan(n).
A342912 (program): a(n) = [x^n] (1 - 2*x - sqrt((1 - 3*x)/(1 + x)))/(2*x^3).
A342913 (program): Pairwise listing of the partitions of 2k into two parts, (s,t), with 0 < t <= s ordered by decreasing values of s and where k = 1,2,… .
A342914 (program): Number of grid points covered by a truncated triangle drawn on the hexagonal lattice with the short sides having length n and the long sides length 2*n.
A342915 (program): a(n) = gcd(1+n, A001615(n)), where A001615 is Dedekind psi, n * Product_{p|n, p prime} (1 + 1/p).
A342916 (program): a(n) = (1+n) / gcd(1+n, A001615(n)), where A001615 is Dedekind psi, n * Product_{p|n, p prime} (1 + 1/p).
A342917 (program): a(n) = A001615(n) / gcd(1+n, A001615(n)), where A001615 is Dedekind psi, n * Product_{p|n, p prime} (1 + 1/p).
A342918 (program): a(n) = (1+n) / A143771(n).
A342919 (program): a(n) = A003415(n) / gcd(A001615(n), A003415(n)), where A001615 is Dedekind psi, and A003415 is the arithmetic derivative of n.
A342920 (program): a(n) = A342002(A108951(n)).
A342921 (program): a(n) = A003415(A019565(n)).
A342925 (program): a(n) = A003415(sigma(n)), where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n.
A342926 (program): a(n) = A003415(sigma(n)) - n, where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n.
A342939 (program): a(n) is the Skolem number of the triangular grid graph T_n.
A342940 (program): Triangle read by rows: T(n, k) is the Skolem number of the parallelogram graph P_{n, k}, with 1 < k <= n.
A342956 (program): a(n) = A001222(A001414(n)).
A342959 (program): Number of 1’s within a sample word of length 10^n of the infinite Fibonacci word A003842 where n is the sequence index.
A342975 (program): Cubes composed of digits {0, 1, 3}.
A342977 (program): Decimal expansion of (Pi - 2) / 4.
A342982 (program): Triangle read by rows: T(n,k) is the number of tree-rooted planar maps with n edges and k+1 faces, n >= 0, k = 0..n.
A342983 (program): Number of tree-rooted planar maps with n+1 vertices and n+1 faces.
A342991 (program): Left(0)/right(1) turning sequence needed to traverse the Stern-Brocot tree (A007305, A047679) from the root down to e (A001113).
A342994 (program): a(n) = (1000^n - 1)*(220/333).
A343005 (program): a(n) is the number of dihedral symmetries D_{2m} (m >= 3) that configurations of n non-overlapping equal circles can possess.
A343007 (program): Relative position of the average value between two consecutive partial sums of the Leibniz formula for Pi.
A343008 (program): a(n) = F(n+5) * F(n+2) - 12 * (-1)^n where F(n) = A000045(n) are the Fibonacci numbers.
A343009 (program): a(n) = (n^(2n)-1)/(n^2-1) for n > 1, a(1) = 1.
A343010 (program): Integers k for which there exist three consecutive Fibonacci numbers a, b, and c such that a*b*c = k*(a+b+c).
A343028 (program): a(n) = floor(11*n / 3).
A343029 (program): Number of 1-bits in the binary expansion of n which have an even number of 0-bits at less significant bit positions.
A343030 (program): Number of 1-bits in the binary expansion of n which have an odd number of 0-bits at less significant bit positions.
A343034 (program): Positive numbers m such that m^2 with last digit z deleted is still a perfect square k^2, and z divides m-k.
A343037 (program): Triangle T(n,k), n >= 2, 1 <= k <= n-1, read by rows, where T(n,k) is the difference between smallest square >= binomial(n,k) and binomial(n,k).
A343039 (program): a(1) = 1, for n > 1, a(n) is the smallest positive integer for which a(n-1) + n + a(n) is a square.
A343041 (program): a(0) = 0 and for any n > 0, a(n) = A343040(a(n-1), n).
A343045 (program): a(0) = 0 and for any n > 0, a(n) = A343044(a(n-1), n).
A343048 (program): a(n) is the least number whose sum of digits in primorial base equals n.
A343060 (program): Decimal expansion of tan(Pi/16).
A343062 (program): Decimal expansion of tan(Pi/24).
A343068 (program): Multiplicative with a(p^e) = e*a(p-1).
A343069 (program): Decimal expansion of 2*(1+5*sqrt(2))/7.
A343070 (program): a(1) = 1, for n > 1, a(n) is the smallest positive integer for which a(n-1) + n + a(n) is a prime.
A343080 (program): a(n) is the smallest number that is the sum of n positive squares in three ways.
A343089 (program): Number of nonseparable rooted toroidal maps with n edges.
A343093 (program): Number of rooted toroidal maps with n edges and no isthmuses.
A343107 (program): Numbers having exactly 1 divisor of the form 8*k + 1, that is, numbers with no divisor of the form 8*k + 1 other than 1.
A343108 (program): Numbers having no divisor of the form 8*k + 3.
A343109 (program): Numbers having no divisor of the form 8*k + 5.
A343110 (program): Numbers having no divisor of the form 8*k + 7.
A343111 (program): Numbers having exactly 2 divisors of the form 8*k + 1, that is, numbers with exactly 1 divisor of the form 8*k + 1 other than 1.
A343112 (program): Numbers having exactly 1 divisor of the form 8*k + 3.
A343113 (program): Numbers having exactly 1 divisor of the form 8*k + 5.
A343114 (program): a(n) = Sum_{i=1..n} gcd(n^i,i).
A343116 (program): a(n) is the Pisano period of prime(n)^2.
A343117 (program): a(n) is the absolute difference between the Pisano periods of prime(n)^2 and prime(n).
A343118 (program): Length of the longest sequence of equidistant primes among the first n primes.
A343122 (program): Consider the longest arithmetic progressions of primes from among the first n primes; a(n) is the smallest constant difference of these arithmetic progressions.
A343124 (program): Total number of partitions of k*n into 3 parts for k = 1..n.
A343125 (program): Triangle T(k, n) = (n+3)*(k-n) - 4, k >= 2, 1 <= n <= k-1, read by rows.
A343131 (program): For m >= 1, the m-digit number k = d_m||…||d_2||d_1 is a term if it is divisible by f_m(k) that is the sum of the m elementary symmetric polynomials in m variables e_i(k): f_m(k) = Sum_{i=1..m} e_i(d_1, …, d_m).
A343148 (program): Numbers k such that A083266(k) is prime.
A343173 (program): First differences of paper-folding sequence A014577.
A343174 (program): Partial sums of paper-folding sequence A014577.
A343175 (program): a(0)=2; for n > 0, a(n) = 2^(2*n-1) + 2^n + 1.
A343176 (program): a(0)=3; for n > 0, a(n) = 2^(2*n) + 3*2^(n-1) + 1.
A343177 (program): a(0)=4; if n >0 is even then a(n) = 2^(n/2+1)+3, otherwise a(n) = 3*(2^((n-1)/2)+1).
A343180 (program): Trajectory of 1 under the morphism 1 -> 12, 2 -> 32, 3 -> 14, 4 -> 34.
A343199 (program): Decimal expansion of 6+2*sqrt(3).
A343204 (program): Numerators of coefficients in expansion of Product_{k>=1} (1 + x^k)^(1/2).
A343206 (program): Numerators of Daehee numbers.
A343218 (program): Numbers k such that A003415(sigma(k)) > k.
A343219 (program): a(n) = 1 if A003415(sigma(k)) > k, otherwise 0.
A343223 (program): a(n) = gcd(A003415(n), A003415(sigma(n))-n), where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n.
A343224 (program): a(n) = sigma(n) - A003415(n), where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n.
A343226 (program): a(n) = gcd(sigma(n), n+A003415(n)), where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n.
A343227 (program): a(n) = sigma(n) / gcd(sigma(n), n+A003415(n)), where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n.
A343228 (program): A binary encoding of the digits “+1” in balanced ternary representation of n.
A343229 (program): A binary encoding of the digits “-1” in balanced ternary representation of n.
A343230 (program): A binary encoding of the digits “0” in balanced ternary representation of n.
A343231 (program): A binary encoding of the nonzero digits in balanced ternary representation of n.
A343233 (program): Triangle read by rows: Riordan triangle T = (1 - x*c(x), x), with the generating function c of A000108 (Catalan).
A343234 (program): Triangle T read by rows: lower triangular Riordan matrix of the Toeplitz type with first column A067687.
A343235 (program): Decimal expansion of sqrt(3)/Pi - 1/2.
A343237 (program): Triangle T obtained from the array A(n, k) = (k+1)^(n+1) - k^(n+1), n, k >= 0, by reading antidiagonals upwards.
A343241 (program): Primes congruent to 2 or 8 modulo 15.
A343249 (program): a(n) is the least k0 <= n such that v_2(n), the 2-adic order of n, can be obtained by the formula: v_2(n) = log_2(n / L_2(k0, n)), where L_2(k0, n) is the lowest common denominator of the elements of the set S_2(k0, n) = {(1/n)*binomial(n, k), with 0 < k <= k0 such that k is not divisible by 2} or 0 if no such k0 exists.
A343250 (program): a(n) is the least k0 <= n such that v_3(n), the 3-adic order of n, can be obtained by the formula: v_3(n) = log_3(n / L_3(k0, n)), where L_3(k0, n) is the lowest common denominator of the elements of the set S_3(k0, n) = {(1/n)*binomial(n, k), with 0 < k <= k0 such that k is not divisible by 3} or 0 if no such k0 exists.
A343251 (program): a(n) is the least k0 <= n such that v_5(n), the 5-adic order of n, can be obtained by the formula: v_5(n) = log_5(n / L_5(k0, n)), where L_5(k0, n) is the lowest common denominator of the elements of the set S_5(k0, n) = {(1/n)*binomial(n, k), with 0 < k <= k0 such that k is not divisible by 5} or 0 if no such k0 exists.
A343252 (program): a(n) is the least k0 <= n such that v_7(n), the 7-adic order of n, can be obtained by the formula: v_7(n) = log_7(n / L_7(k0, n)), where L_7(k0, n) is the lowest common denominator of the elements of the set S_7(k0, n) = {(1/n)*binomial(n, k), with 0 < k <= k0 such that k is not divisible by 7} or 0 if no such k0 exists.
A343253 (program): a(n) is the least k0 <= n such that v_11(n), the 11-adic order of n, can be obtained by the formula: v_11(n) = log_11(n / L_11(k0, n)), where L_11(k0, n) is the lowest common denominator of the elements of the set S_11(k0, n) = {(1/n)*binomial(n, k), with 0 < k <= k0 such that k is not divisible by 11} or 0 if no such k0 exists.
A343259 (program): a(n) = 2 * T(n,n/2) where T(n,x) is a Chebyshev polynomial of the first kind.
A343260 (program): a(n) = 2 * T(n,(n+1)/2) where T(n,x) is a Chebyshev polynomial of the first kind.
A343261 (program): a(n) = 2 * T(n,(n+2)/2) where T(n,x) is a Chebyshev polynomial of the first kind.
A343265 (program): a(n) is the number of ways n can be reached starting from 0 and using only two operations: adding one or, once n > 1, squaring.
A343274 (program): a(n) = Sum_{d|n} d^d * sopf(d).
A343275 (program): a(n) = |2*n - 10^length(n)|.
A343276 (program): a(n) = n! * [x^n] -x*(x + 1)*exp(x)/(x - 1)^3.
A343279 (program): a(n) = Stirling2(n, floor(n/2)).
A343280 (program): a(n) is the number of steps for the n-th vertex of the Collatz tree A088975 to reach a vertex t == 0 (mod 3).
A343291 (program): a(n) = (n-2)*2^(n-1) + n + 2.
A343292 (program): Number of distinct results produced when generating a graphical image of each row of the multiplication table modulo n.
A343299 (program): a(n) = n + A000120(a(n-1)) - a(n-1), with n > 1, a(1) = 1, where A000120(x) is the binary weight of x.
A343300 (program): a(n) is p1^1 + p2^2 + … + pk^k where {p1,p2,…,pk} are the distinct prime factors in ascending order in the prime factorization of n.
A343311 (program): Numbers of the form x + y + z with distinct positive integers x,y,z such that (x+y+z) | x*y*z.
A343317 (program): a(n) is the least k >= 0 such that A343316(n, k) = n.
A343318 (program): a(n) = (2^n + 1)^3.
A343370 (program): a(1) = 1; a(n) = Sum_{d|n, d < n} (-1)^d * a(d).
A343371 (program): a(n) = 1 + Sum_{d|n, d < n} a(d - 1).
A343372 (program): Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 4) missing three edges, where exactly two removed edges are incident to the same vertex in the 3-point set and exactly two removed edges are incident to the same vertex in the other set.
A343386 (program): Number of odd Motzkin n-paths, i.e., Motzkin n-paths with an odd number of up steps.
A343392 (program): Decimal expansion of 2*Pi*sqrt(2).
A343394 (program): Sum of indices of n’s distinct prime factors below n.
A343395 (program): a(n) = Sum_{i=1..n} gcd(n^(n-i),n-i).
A343407 (program): Number of proper divisors of n that are triangular numbers.
A343408 (program): Sum of proper divisors of n that are triangular numbers.
A343425 (program): a(n) = Sum_{k=1..n} mu(k) * n^(n - k).
A343429 (program): G.f.: 1 + 1^2*x/(1 + 2^2*x/(1 + 3^2*x/(1 + 4^2*x/(1 + 5^2*x/(1 + …))))).
A343430 (program): Part of n composed of prime factors of the form 3k-1.
A343431 (program): Part of n composed of prime factors of the form 6k-1.
A343442 (program): If n = Product (p_j^k_j) then a(n) = Product (p_j + 2), with a(1) = 1.
A343443 (program): If n = Product (p_j^k_j) then a(n) = Product (k_j + 2), with a(1) = 1.
A343445 (program): Coefficients of the series S(p, q) for which (-sqrt(p))*S converges to the largest real root of x^3 - p*x + q for 0 < p and 0 < q < 2*(p/3)^(3/2).
A343446 (program): Coefficients of the series S(p, q) for which -(p^(1/3))*S converges to the largest real root of x^4 - p*x + q, where 0 < p and 0 < q < 3*(p/4)^(4/3).
A343447 (program): Smallest m such that alternating integer 101…101 = A094028(m) is a multiple of A045572(n), (i.e., integers coprime with 10).
A343461 (program): a(n) is the maximal number of congruent n-gons that can be arranged around a vertex without overlapping.
A343465 (program): a(n) = -(1/n) * Sum_{d|n} phi(n/d) * (-3)^d.
A343466 (program): a(n) = -(1/n) * Sum_{d|n} phi(n/d) * (-4)^d.
A343467 (program): a(n) = -(1/n) * Sum_{d|n} phi(n/d) * (-5)^d.
A343490 (program): a(n) = Sum_{k=1..n} 4^(gcd(k, n) - 1).
A343492 (program): a(n) = Sum_{k=1..n} 5^(gcd(k, n) - 1).
A343493 (program): a(n) = 1 - Sum_{d|n, d < n} a(d - 1).
A343497 (program): a(n) = Sum_{k=1..n} gcd(k, n)^3.
A343498 (program): a(n) = Sum_{k=1..n} gcd(k, n)^4.
A343499 (program): a(n) = Sum_{k=1..n} gcd(k, n)^5.
A343500 (program): Positions of 2’s in A003324.
A343501 (program): Positions of 4’s in A003324.
A343508 (program): a(n) = Sum_{k=1..n} gcd(k, n)^6.
A343509 (program): a(n) = Sum_{k=1..n} gcd(k, n)^7.
A343510 (program): Square array T(n,k), n >= 1, k >= 1, read by antidiagonals, where T(n,k) = Sum_{j=1..n} gcd(j, n)^k.
A343513 (program): a(n) = Sum_{k=1..n} (k/gcd(n, k))^3.
A343514 (program): a(n) = Sum_{k=1..n} (k/gcd(n, k))^4.
A343515 (program): a(n) is the number of real solutions to the equation sin(x) = x/n.
A343517 (program): a(n) = Sum_{1 <= x_1 <= x_2 <= … <= x_n <= n} gcd(x_1, x_2, … , x_n, n).
A343518 (program): a(n) = Sum_{1 <= x_1 <= x_2 <= x_3 <= x_4 <= n} gcd(x_1, x_2, x_3 , x_4, n).
A343519 (program): a(n) = Sum_{1 <= x_1 <= x_2 <= x_3 <= x_4 <= x_5 <= n} gcd(x_1, x_2, x_3 , x_4, x_5, n).
A343520 (program): a(n) = Sum_{1 <= x_1 <= x_2 <= x_3 <= x_4 <= x_5 <= x_6 <= n} gcd(x_1, x_2, x_3 , x_4, x_5, x_6, n).
A343521 (program): a(n) = Sum_{1 <= x_1 <= x_2 <= x_3 <= x_4 <= x_5 <= x_6 <= x_7 <= n} gcd(x_1, x_2, x_3 , x_4, x_5, x_6, x_7, n).
A343523 (program): a(0) = 1; a(n) = 2 * Sum_{k=1..n} binomial(n,k) * a(k-1).
A343525 (program): If n = Product (p_j^k_j) then a(n) = Product (2*p_j^k_j + 1), with a(1) = 1.
A343526 (program): Number of divisors of n^7.
A343539 (program): a(n) = (2*n+1)*Lucas(2*n+1).
A343541 (program): For n > 1, a(n) is the largest base b <= prime(n)-1 such that the digits of prime(n)-1 in base b contain the digit b-1.
A343543 (program): a(n) = n*Lucas(2*n).
A343544 (program): a(n) = n * Sum_{d|n} binomial(d+2,3)/d.
A343545 (program): a(n) = n * Sum_{d|n} binomial(d+3,4)/d.
A343546 (program): a(n) = n * Sum_{d|n} binomial(d+4,5)/d.
A343547 (program): a(n) = n * Sum_{d|n} binomial(d+n-2,n-1)/d.
A343548 (program): a(n) = Sum_{d|n} binomial(d+n-1,n).
A343549 (program): a(n) = n * Sum_{d|n} binomial(d+n-1,n)/d.
A343553 (program): a(n) = Sum_{1 <= x_1 <= x_2 <= … <= x_n = n} gcd(x_1, x_2, … , x_n).
A343560 (program): a(n) = (n-1)*(4*n+1).
A343561 (program): 2nd row of A341867: a(n) = (n^2+15*n+32)*2^(n-3).
A343567 (program): a(n) = Sum_{d|n} (n/d)^(n/d) * binomial(d+n-2,n-1).
A343568 (program): a(n) = Sum_{d|n} (n/d)^(n/d) * binomial(d+n-1,n).
A343569 (program): If n = Product (p_j^k_j) then a(n) = Product (2*(p_j^k_j + 1)), with a(1) = 1.
A343570 (program): If n = Product (p_j^k_j) then a(n) = Product (p_j^k_j + 3), with a(1) = 1.
A343572 (program): a(n) = ceiling((16^n)*Sum_{k=0..n+1} (4/(8k+1)-2/(8k+4)-1/(8k+5)-1/(8k+6))/16^k).
A343573 (program): a(n) = Sum_{d|n} d^d * binomial(d+n/d-2, d-1).
A343574 (program): a(n) = Sum_{d|n} d^d * binomial(d+n/d-1, d).
A343576 (program): Number of permutations of [n] without fixed points and all cycles equal length.
A343578 (program): a(n) = 32*n^2 - 40*n + 10.
A343580 (program): a(n) = abs(A021009(n, floor(n/2))).
A343581 (program): a(n) = binomial(n, floor(n/2))*FallingFactorial(n - 1, n - floor(n/2)).
A343582 (program): a(n) = (-1)^n*n!*[x^n] exp(-3*x)/(1 - 2*x).
A343583 (program): a(n) = (1/2)*Li_{-n-1}(1/2) - Li_{-n}(1/2), where Li_{n}(x) is the polylogarithm function.
A343584 (program): a(n) = Sum_{j=0..n}(-1)^(n-j)*binomial(n, j)*A028246(n+1, j+1).
A343585 (program): a(n) = A081411(n) mod prime(n+1).
A343586 (program): a(n) = the sum of all the multiples of 2 or 5 less than or equal to 10^n.
A343599 (program): T(n,k) is the coordination number of the (n+1)-dimensional cubic lattice for radius k; triangle read by rows, n>=0, 0<=k<=n.
A343607 (program): Minimal number of colors required for an edge-coloring of the complete graph K_n with no monochromatic triangle.
A343608 (program): a(n) = [n/5]*[n/5 - 1]*(3n - 10[n/5 + 1])/6, where [.] = floor: upper bound for minimum number of monochromatic triangles in a 3-edge-colored complete graph K_n.
A343609 (program): a(n) = floor(n/9).
A343621 (program): Numbers k such that the largest Dyck path of the symmetric representation of sigma(k) does not touch the largest Dyck path of the symmetric representation of sigma(k+1).
A343638 (program): a(n) = (Sum of decimal digits of 3*n) / 3.
A343639 (program): a(n) = (Sum of digits of 9*n) / 9.
A343652 (program): Number of maximal pairwise coprime sets of divisors of n.
A343653 (program): Number of non-singleton pairwise coprime nonempty sets of divisors > 1 of n.
A343654 (program): Number of pairwise coprime sets of divisors > 1 of n.
A343655 (program): Number of pairwise coprime sets of divisors of n, where a singleton is not considered pairwise coprime unless it is {1}.
A343656 (program): Array read by antidiagonals where A(n,k) is the number of divisors of n^k.
A343657 (program): Sum of number of divisors of x^y for each x >= 1, y >= 0, x + y = n.
A343660 (program): Number of maximal pairwise coprime sets of at least two divisors > 1 of n.
A343661 (program): Sum of numbers of y-multisets of divisors of x for each x >= 1, y >= 0, x + y = n.
A343670 (program): a(n) is the least semiprime congruent to 1 (mod n-th semiprime).
A343672 (program): a(0) = 1; a(n) = 2 * n * a(n-1) + Sum_{k=0..n-1} binomial(n,k) * a(k).
A343673 (program): a(0) = 1; a(n) = 3 * n * a(n-1) + Sum_{k=0..n-1} binomial(n,k) * a(k).
A343674 (program): a(0) = 1; a(n) = 4 * n * a(n-1) + Sum_{k=0..n-1} binomial(n,k) * a(k).
A343685 (program): a(0) = 1; a(n) = 2 * n * a(n-1) + Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k).
A343686 (program): a(0) = 1; a(n) = 3 * n * a(n-1) + Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k).
A343687 (program): a(0) = 1; a(n) = 4 * n * a(n-1) + Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k).
A343688 (program): a(1)=1, a(2)=0, a(n) = (4*n-2)*a(n-1) + a(n-2), n > 2.
A343689 (program): a(1)=0, a(2)=1, a(n) = (4*n-2)*a(n-1) + a(n-2), n > 2.
A343694 (program): a(n) is the number of men’s preference profiles in the stable marriage problem with n men and n women, such that all men prefer different women as their first choices.
A343707 (program): a(n) = 1 + 2 * Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k).
A343709 (program): a(n) = 1 + 3 * Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k).
A343710 (program): a(n) = 1 + 4 * Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k).
A343720 (program): Triangle read by rows: T(n,k) = k^2 mod n for k = 0..n-1, n >= 1.
A343732 (program): Numbers k at which tau(k^k) is a prime power, where tau is the number-of-divisors function A000005.
A343745 (program): Decimal expansion of 12*sqrt(25+10*sqrt(5))/(15+7*sqrt(5)).
A343752 (program): a(1) = 1; for n > 1, a(n) = n if a(n-1) is divisible by n, otherwise a(n) = a(n-1)+n.
A343754 (program): a(n) = 0, and for any n > 0, a(n+1) = a(n) - A065363(n) + 1.
A343758 (program): Total area of all p X r rectangles, where n = p + r, p <= r, p is prime and r is a positive integer.
A343759 (program): Total area of all p X r rectangles where n = p + r, p < r, p is prime and r is a positive integer.
A343766 (program): Lexicographically earliest sequence of distinct integers such that a(0) = 0 and the balanced ternary expansions of two consecutive terms differ by a single digit, as far to the right as possible.
A343773 (program): Excess of the number of even Motzkin n-paths (A107587) over the odd ones (A343386).
A343785 (program): a(n) is completely multiplicative with a(p^e) = (-1)^e if p == 2 (mod 3) and a(p^e) = 1 otherwise.
A343794 (program): Numbers k > 0 such that 630*k + 315 is not an abundant number (A005101).
A343803 (program): a(n) = Sum_{k=1..n} k * (number of divisors of n <= k).
A343808 (program): Partial sums of A062074.
A343810 (program): Numbers that contain only the digits 0,4,8. Permutable multiples of 4: numbers k such that every permutation of the digits of k is a multiple of 4.
A343823 (program): Numbers k > 10 such that every permutation of the digits of k is congruent to 3 (mod 4).
A343824 (program): Sum of the elements in all pairs (d1, d2) of divisors of n such that d1<=d2, d1|n, d2|n, and d1 + d2 <= n.
A343830 (program): a(n) = numerator of (1/e) * Sum_{a_1>=1, a_2>=1, … , a_n>=1} a_1 * a_2 * … * a_n / (a_1 + a_2 + … + a_n)!.
A343832 (program): a(n) = Sum_{k=0..n} k! * binomial(n,k) * binomial(2*n+1,k).
A343840 (program): a(n) = Sum_{k=0..n}(-1)^(n-k)*binomial(n, k)*|A021009(n, k)|.
A343842 (program): Series expansion of 1/sqrt(8*x^2 + 1), even powers only.
A343843 (program): a(n) = Sum_{k=0..n} (-1)^k*binomial(n, k)*A000831(k).
A343846 (program): a(n) = binomial(2*n, n)*2^n*|Euler(n, 1/2) - Euler(n, 0)|.
A343847 (program): T(n, k) = (n - k)! * [x^(n-k)] exp(k*x/(1 - x))/(1 - x). Triangle read by rows, T(n, k) for 0 <= k <= n.
A343848 (program): a(n) = Sum_{k = 0..n} (n - k)! LaguerreL(n - k, -k).
A343849 (program): a(n) = Sum_{k = 0..n} n! * LaguerreL(n, -k).
A343850 (program): Integer part of the area of an irregular hexagon, formed by the regular overlap of two regular pentagons each of side length n.
A343859 (program): Partial sums of the primes excluding 3.
A343863 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = (n!)^k * Sum_{j=1..n} (1/j!)^k.
A343877 (program): Number of pairs (d1, d2) of divisors of n such that d1<d2, d1|n, d2|n, and d1 + d2 <= n.
A343879 (program): Number of pairs (d1, d2) of divisors of n such that d1<d2, d1|n, d2|n, d1|d2 and d1 + d2 <= n.
A343885 (program): a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-4), with a(1) = a(2) = a(3) = a(4) = 1.
A343896 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * k! * binomial(n,k) * binomial(2*n+1,k).
A343898 (program): a(n) = Sum_{k=0..n} (k!)^3 * binomial(n,k).
A343899 (program): a(n) = Sum_{k=0..n} (k!)^k * binomial(n,k).
A343900 (program): a(n) = Sum_{k=0..n} (k!)^(k+1) * binomial(n,k).
A343906 (program): Decimal expansion of 6*sqrt(6).
A343908 (program): a(n) is the least prime == 4 (mod prime(n)).
A343910 (program): a(n) = mu(phi(n)), where mu is the Möbius function and phi is the Euler totient function.
A343911 (program): a(n) = Omega(phi(n)), where Omega is the number of prime factors of n with multiplicity and phi is the Euler totient function.
A343912 (program): a(n) = n - phi(n - phi(n)), where phi is the Euler totient function.
A343914 (program): Riesel problem in base 3: a(n) is the smallest k >= 0 such that (2*n)*3^k-1 is prime, or -1 if no such k exists.
A343923 (program): If n = Product (p_j^k_j) then a(n) = Sum (abs(p_j-k_j)) (a(1) = 0 by convention).
A343928 (program): a(n) = Sum_{k=0..n} (k!)^n * binomial(n,k).
A343929 (program): a(n) = Sum_{k=0..n} (k!)^(n+1) * binomial(n,k).
A343932 (program): a(n) = (Sum_{k=1..n} k^k) mod n.
A343933 (program): a(n) = (Sum_{k=1..n} (-k)^k) mod n.
A343935 (program): Number of ways to choose a multiset of n divisors of n.
A343936 (program): Number of ways to choose a multiset of n divisors of n - 1.
A343938 (program): Twice the number of prime factors of n minus the sum of prime indices of n, both counted with multiplicity.
A343939 (program): Number of n-chains of divisors of n.
A343942 (program): Number of even-length strict integer partitions of 2n+1.
A343943 (program): Number of distinct possible alternating sums of permutations of the multiset of prime factors of n.
A343947 (program): Surface area to volume ratio of a right prism with unit height and whose base is a regular n-gon with side length 1 (rounded to the nearest integer).
A343948 (program): Decimal expansion of -(1 + (5/9)^(1/3)*((9+4*sqrt(6))^(1/3) - (4*sqrt(6)-9)^(1/3)))/4 (negated).
A343949 (program): Shortest distance from curve start to end along the segments of dragon curve expansion level n, and which is the diameter of the curve as a graph.
A343953 (program): Square array T(n,k), n>=1, k>=0, read by antidiagonals, where row n is the expansion of x*(1+x^n)/((1-x)^2*(1-x^n)).
A343963 (program): a(0) = 0, and for any n > 0, the binary expansion of n has n digits and starts with the binary expansion of n, say of w digits, and in case n > w, the remaining binary digits in a(n) are those of a(n-w).
A343964 (program): Decimal expansion of 18 + 2*sqrt(3).
A343965 (program): Decimal expansion of 4 + 10*sqrt(2)/3.
A343966 (program): Decimal expansion of (4/3)*(4*sqrt(2)-5).
A343974 (program): Even numbers k such that the two sets of primes in the Goldbach representation of k and k+2 as the sum of two odd primes do not intersect.
A343975 (program): a(0) = 1; a(n) = 3 * Sum_{k=1..n} binomial(n,k) * a(k-1).
A343984 (program): a(n) = number of n-digit singular subwords of the Thue-Morse word A010060; see Comments.
A343985 (program): a(n) = A343984(n)/2.
A343994 (program): Number of nodes in graph BC(n,2) when the internal nodes are counted with multiplicity.
A343996 (program): a(n) = A011772(n) if that number is odd, otherwise A011772(n)+1.
A343997 (program): a(n) = A011772(n) if that number is even, otherwise A011772(n)+1.
A343998 (program): a(n) = A343997(n)/2.
A343999 (program): a(n) = A011772(n) mod 2, where A011772(n) is the smallest number m such that m(m+1)/2 is divisible by n.
A344000 (program): Indices k such that A011772(k) is even.
A344001 (program): Indices k such that A011772(k) is odd.
A344002 (program): Erroneous version of A077868 (if initial 0 is ignored).
A344003 (program): Erroneous version of A050228 (if initial 0 is ignored).
A344004 (program): Number of ordered subsequences of {1,…,n} containing at least three elements and such that the first differences contain only odd numbers.
A344005 (program): a(n) = smallest positive m such that n divides the oblong number m*(m+1).
A344006 (program): a(n) = m*(m+1)/n, where A344005(n) is the smallest number m such that n divides m*(m+1).
A344015 (program): 2-adic valuation of A344014(n).
A344019 (program): A tight upper bound on the order of a finite subgroup of the collineation group of the free projective plane F_n.
A344024 (program): a(n) = A003415(A001615(n)).
A344026 (program): Arithmetic derivative applied to the Doudna sequence: a(n) = A003415(A005940(1+n)).
A344028 (program): a(n) = A069359(A005940(1+n)).
A344037 (program): E.g.f.: exp(-2*x) / (2 - exp(x)).
A344041 (program): Decimal expansion of Sum_{k>=1} F(k)/(k*2^k), where F(k) is the k-th Fibonacci number (A000045).
A344042 (program): a(n) = n * Sum_{d|n} sigma(d)^2 / d.
A344043 (program): a(n) = n * Sum_{d|n} sigma(d)^3 / d.
A344044 (program): a(n) = Sum_{d|n} sigma(d)^3.
A344047 (program): a(n) = Sum_{d|n} sigma(d)^d.
A344048 (program): T(n, k) = n! * [x^n] exp(k * x/(1 - x))/(1 - x). Triangle read by rows, T(n, k) for 0 <= k <= n.
A344049 (program): a(n) = KummerU(-2*n, 1, -n).
A344050 (program): a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*|Lah(n, k)|. Inverse binomial convolution of the unsigned Lah numbers A271703.
A344051 (program): a(n) = Sum_{k=0..n} binomial(n, k)*|Lah(n, k)|. Binomial convolution of the unsigned Lah numbers A271703.
A344052 (program): a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*E1(n, k).
A344053 (program): a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*Stirling2(n, k)*k!.
A344054 (program): a(n) = Sum_{k = 0..n} E1(n, k)*k^2, where E1 are the Eulerian numbers A173018.
A344055 (program): a(n) = 2^n * n! * x^n.
A344057 (program): a(n) = (2*n)! / CatalanNumber(n - 1) for n >= 1 and a(0) = 1.
A344069 (program): Decimal expansion of sqrt(13)/3.
A344081 (program): a(n) = Sum_{d|n} tau(d)^d, where tau(n) is the number of divisors of n.
A344082 (program): a(n) = n * Sum_{d|n} tau(d)^3 / d, where tau(n) is the number of divisors of n.
A344106 (program): a(n) = n! * LaguerreL(n, -n+1).
A344107 (program): a(n) = n! * LaguerreL(n, -n+2).
A344109 (program): a(n) = (5*2^n + 7*(-1)^n)/3.
A344110 (program): Triangle read by rows: T(n,k) = 2^(n*k), n >= 0, 0 <= k <= n.
A344111 (program): Decimal expansion of 4 + sqrt(3).
A344112 (program): Triangle read by rows: T(n,k) is the number of relations from an n-element set to a k-element set that are not functions.
A344113 (program): a(n) = 2^(n^2) - n^n.
A344114 (program): a(n) = 2^(n^2) - n!.
A344120 (program): For n >= 0, let N = 243 + n*343, let v(x) be the maximum power of 7 dividing x, and let p(N) be the partition function A000041(N). If v(p(N)) >= v(24*N-1) then a(n)=1, otherwise a(n)=0.
A344121 (program): a(n) is the multiplicative inverse of 24 (mod 7^n).
A344128 (program): a(n) = Sum_{k=1..n} k * floor(n/k^2).
A344131 (program): a(n+1) = (8*n^2+8*n+3)*a(n) - 16*n^4*a(n-1), with a(0)=0, a(1)=1.
A344132 (program): a(n) = Sum_{i|n, j|n, k|n} gcd(i,j,k).
A344134 (program): a(n) = Sum_{i|n, j|n, k|n} lcm(i,j,k).
A344135 (program): a(n) = Sum_{i|n, j|n, k|n} i*j*k/lcm(i,j,k).
A344136 (program): Number of linear intervals in the Tamari lattices.
A344137 (program): Sum of the squarefree divisors of n whose square does not divide n.
A344150 (program): Length of the n-th word in A342910.
A344154 (program): Numbers k such that the k-th word in A342910 ends with 0.
A344155 (program): Numbers k such that the k-th word in A342910 ends with 1.
A344158 (program): Numbers k such that the k-th word in A342910 starts with 0 and ends with 0.
A344159 (program): Numbers k such that the k-th word in A342910 starts with 0 and ends with 1.
A344160 (program): Numbers k such that the k-th word in A342910 starts with 1 and ends with 0.
A344161 (program): Numbers k such that the k-th word in A342910 starts with 1 and ends with 1.
A344164 (program): a(n) = sum of the digits of n-th word in A342910.
A344167 (program): Positions in A342910 of words in which #0’s - #1’s is odd.
A344168 (program): Positions in A342910 of words where #0’s - #1’s is even.
A344171 (program): Decimal expansion of 12*sqrt(5).
A344172 (program): Decimal expansion of 4*sqrt(5 + 2*sqrt(5)).
A344178 (program): Difference between the arithmetic derivative of n and the cototient of n: a(n) = A003415(n) - A051953(n).
A344180 (program): Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j) for all i, j >= 0, where f(n) = 0 if n is a Fibbinary number (A003714), otherwise f(n) = n.
A344181 (program): Numbers such that repeated division by their largest factorial divisor (as long as such a divisor larger than one exists) eventually yields 1.
A344191 (program): a(n) = Catalan(n) * (n^2 + 2) / (n + 2).
A344194 (program): a(n) = Sum_{k=1..n} tau(gcd(k,n))^gcd(k,n), where tau(n) is the number of divisors of n.
A344212 (program): Decimal expansion of 1 + 1/sqrt(5).
A344215 (program): a(n) = n*(3^(n-1) - 2^(n-1)).
A344216 (program): a(n) = n!*((n+1)/2 + 2*Sum_{k=2..n-1}(n-k)/(k+1)).
A344219 (program): Number of cyclic subgroups of the group (C_n)^5, where C_n is the cyclic group of order n.
A344220 (program): a(n) is the least k >= 0 such that n XOR k is a binary palindrome (where XOR denotes the bitwise XOR operator).
A344221 (program): a(n) = Sum_{k=1..n} tau(gcd(k,n)^3), where tau(n) is the number of divisors of n.
A344222 (program): a(n) = Sum_{k=1..n} tau(gcd(k,n)^4), where tau(n) is the number of divisors of n.
A344223 (program): a(n) = Sum_{k=1..n} tau(gcd(k,n)^n), where tau(n) is the number of divisors of n.
A344224 (program): a(n) = Sum_{k=1..n} tau(gcd(k,n)^gcd(k,n)), where tau(n) is the number of divisors of n.
A344226 (program): a(n) = Sum_{d|n} n^omega(d) / d.
A344227 (program): Sprague-Grundy value for the Node-Kayles game played on the n-queens graph.
A344228 (program): a(n) = binomial(2*n,n)*(2*n+1)/2+n*binomial(2*n-2,n)+(n-1)*binomial(2*n-2,n+1).
A344229 (program): a(n) = n*a(n-1) + n^signum(n mod 4), a(0) = 1.
A344235 (program): Triangle T from the array A(k, n) giving the sums of k+1 consecutive squares starting with n^2, read as upwards antidiagonals, for k >= 0 and n >= 0.
A344236 (program): Number of n-step walks from a universal vertex to the other on the diamond graph.
A344259 (program): For any number n with binary expansion (b(1), …, b(k)), the binary expansion of a(n) is (b(1), …, b(ceiling(k/2))).
A344260 (program): a(n) is the number of relations from an n-element set into a set of at most n elements.
A344261 (program): Number of n-step walks from one of the vertices with degree 3 to itself on the four-vertex diamond graph.
A344262 (program): a(0)=1; for n>0, a(n) = a(n-1)*n+1 if n is even, (a(n-1)+1)*n otherwise.
A344276 (program): Number of halving and tripling steps to reach 3 in the ‘3x+3’ problem, or -1 if 3 is never reached.
A344291 (program): Numbers whose sum of prime indices is at least twice their number of prime indices (counted with multiplicity).
A344296 (program): Numbers with at least as many prime factors (counted with multiplicity) as half their sum of prime indices.
A344299 (program): Expansion of Sum_{k>=1} (-1)^(k+1) * x^(k^2) / (1 - x^(k^2)).
A344300 (program): Expansion of Sum_{k>=1} (-1)^(k+1) * k^2 * x^(k^2) / (1 - x^(k^2)).
A344302 (program): Number of cyclic subgroups of the group (C_n)^6, where C_n is the cyclic group of order n.
A344303 (program): Number of cyclic subgroups of the group (C_n)^7, where C_n is the cyclic group of order n.
A344304 (program): Number of cyclic subgroups of the group (C_n)^8, where C_n is the cyclic group of order n.
A344305 (program): Number of cyclic subgroups of the group (C_n)^9, where C_n is the cyclic group of order n.
A344306 (program): Number of cyclic subgroups of the group (C_n)^10, where C_n is the cyclic group of order n.
A344308 (program): Numbers k such that A205791(k) = k+1.
A344317 (program): a(n) = n*a(n-1) + n^(1+n mod 2), a(0) = 1.
A344318 (program): Number of partitions of n into consecutive parts not divisible by 3.
A344326 (program): Dirichlet g.f.: zeta(s)^2/zeta(2*s-1).
A344327 (program): Number of divisors of n^4.
A344328 (program): Number of divisors of n^5.
A344329 (program): Number of divisors of n^6.
A344335 (program): Number of divisors of n^8.
A344336 (program): Number of divisors of n^9.
A344337 (program): a(n) = 9^omega(n), where omega(n) is the number of distinct primes dividing n.
A344341 (program): Gray-code Niven numbers: numbers divisible by the number of 1’s in their binary reflected Gray code (A005811).
A344345 (program): Digitally balanced numbers in Gray code: numbers whose binary reflected Gray code has the same number of 0’s as 1’s.
A344346 (program): Numbers k which have an odd number of trailing zeros in their binary reflected Gray code A014550(k).
A344348 (program): a(n) = floor(frac(e * n) * n).
A344349 (program): Number of primes along the main antidiagonal of the n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows.
A344350 (program): a(n) = Sum_{k=1..n} mu(n*k-k-1)^2, where mu is the Möbius function.
A344351 (program): Number of squarefree numbers along the main diagonal of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows.
A344362 (program): Decimal expansion of (5^(1/4) + 5^(-1/4))/2.
A344363 (program): Decimal expansion of (5^(1/4) + 5^(3/4))/2.
A344370 (program): Dirichlet g.f.: Product_{k>=2} (1 + k^(1-s)).
A344371 (program): a(n) = Sum_{k=1..n} (-1)^(n-k) gcd(k,n).
A344372 (program): a(n) = Sum_{k=1..2n} (-1)^k gcd(k,2n).
A344373 (program): a(n) = Sum_{k=1..n-1} (-1)^k gcd(k, n).
A344374 (program): a(n) is the number of squarefree numbers appearing in the 1st column of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows.
A344381 (program): Triangle read by rows: T(n,k) = (n+2) * (Sum_{i=k..n} i!) / ((k+2) * k!) for 0 <= k <= n with T(i,j) = 0 if j < 0 or i < j.
A344382 (program): Decimal expansion of sqrt(29)/5.
A344386 (program): Decimal expansion of sqrt(53)/7.
A344387 (program): Decimal expansion of sqrt(17)/4.
A344389 (program): a(n) is the number of nonnegative numbers < 10^n with all digits distinct.
A344391 (program): T(n, k) = binomial(n - k, k) * factorial(k), for n >= 0 and 0 <= k <= floor(n/2). Triangle read by rows.
A344392 (program): T(n, k) = k!*Stirling2(n - k, k), for n >= 0 and 0 <= k <= floor(n/2). Triangle read by rows.
A344393 (program): T(n, k) = Eulerian1(n - k, k), for n >= 0 and 0 <= k <= floor(n/2). Triangle read by rows.
A344394 (program): a(n) = binomial(n, n/2 - 1/4 + (-1)^n/4)*hypergeom([-n/4 - 1/8 + (-1)^n/8, -n/4 + 3/8 + (-1)^n/8], [n/2 + 7/4 + (-1)^n/4], 4).
A344395 (program): a(n) = binomial(4*n - 1, 2*n - 1)*hypergeom([-n, -n + 1/2], [2*n + 1], 4).
A344396 (program): a(n) = binomial(2*n + 1, n)*hypergeom([-(n + 1)/2, -n/2], [n + 2], 4).
A344397 (program): a(n) = Stirling2(n, floor(n/2)) * floor(n/2)!.
A344399 (program): a(n) = 4^n*binomial(n - 1/2, -1/2)*(n^2 + 1).
A344400 (program): a(n) = [x^n] 6*(8*x^3 + 3*x + 1) / (1 - 4*x)^(7/2).
A344402 (program): a(n) = denominator(R(n,3)), where R(n,d) = (Product_{j prime to d)} Pochhammer(j/d, n)) / n!.
A344403 (program): a(n) = Sum_{d|n} d * floor(n/d^2).
A344404 (program): a(n) = Sum_{d|n} floor(n/d^2).
A344405 (program): a(n) = Sum_{d|n} (n/d) * floor(n/d^2).
A344410 (program): a(n) = (3*n^2 - 1) * (3*n^2 - 2) * (3*n^3 - 3*n + 1)/2.
A344411 (program): Sum of the prime numbers in the interval (2n, 3n].
A344413 (program): Numbers n whose sum of prime indices A056239(n) is even and is at least twice the number of prime factors A001222(n).
A344417 (program): Number of palindromic factorizations of n.
A344418 (program): a(n) = n*a(n-1) + n^(1+n mod 2), a(0) = 0.
A344419 (program): a(n) = n*a(n-1) + n^(n mod 2), a(0) = 0.
A344420 (program): a(n) = floor(n/11).
A344423 (program): a(n) = 10^(2*n+2) + 111*10^n + 1.
A344425 (program): Decimal expansion of sqrt(85)/9.
A344426 (program): Decimal expansion of sqrt(26)/5.
A344428 (program): Decimal expansion of exp(-2/5).
A344430 (program): a(n) = Sum_{k=1..n} mu(k) * k^k.
A344431 (program): a(n) = Sum_{k=1..n} mu(k) * n^(k - 1).
A344432 (program): a(n) = Sum_{k=1..n} mu(k) * 2^(n - k).
A344433 (program): a(n) = Sum_{k=1..n} mu(k) * k^(n - k).
A344434 (program): a(n) = Sum_{d|n} sigma_d(d), where sigma_k(n) is the sum of the k-th powers of the divisors of n.
A344439 (program): a(n) = n - A206369(n).
A344440 (program): a(n) = n + A061020(n).
A344441 (program): a(n) = A061020(n) + abs(A061020(n)).
A344442 (program): a(n) = A332844(n) - n.
A344444 (program): Completely additive with a(2) = 12, a(3) = 19; for prime p > 3, a(p) = ceiling((a(p-1) + a(p+1))/2).
A344457 (program): a(n) = Sum_{d|n} d * Omega(d).
A344458 (program): a(n) = Sum_{d|n} d^omega(d).
A344459 (program): a(n) = Sum_{d|n} d^Omega(d).
A344460 (program): a(n) = Sum_{d|n} d * floor(sqrt(d)).
A344461 (program): a(n) = Sum_{d|n} d^gcd(d,n/d).
A344464 (program): a(n) = Sum_{d|n} d^p(d), where p is the number of partitions of n.
A344465 (program): a(n) = Sum_{d|n} d^abs(mu(d)).
A344469 (program): T(n, k) = [x^k] x^n * n! * [t^n] x*(1 + t)/(x*exp(-t) - t). Triangle read by rows, T(n, k) for 0 <= k <= n.
A344478 (program): Number of unitary prime divisors p of n such that n/p is squarefree.
A344480 (program): a(n) = Sum_{d|n} d * sigma_d(d), where sigma_k(n) is the sum of the k-th powers of the divisors of n.
A344482 (program): Primes, each occurring twice, such that a(C(n)) = a(4*n-C(n)) = prime(n), where C is the Connell sequence (A001614).
A344483 (program): a(n) = n^2 + sigma(n) - n*d(n).
A344485 (program): a(n) = Sum_{d|n} (n-d) * phi(n/d).
A344489 (program): a(n) = 1 + Sum_{k=0..n-2} binomial(n-1,k) * a(k).
A344490 (program): a(n) = 1 + Sum_{k=0..n-3} binomial(n-2,k) * a(k).
A344491 (program): a(n) = 1 + Sum_{k=0..n-4} binomial(n-3,k) * a(k).
A344492 (program): a(n) = 1 + Sum_{k=0..n-5} binomial(n-4,k) * a(k).
A344493 (program): a(n) = 1 + Sum_{k=0..n-6} binomial(n-5,k) * a(k).
A344495 (program): a(0)=1; for n>0 a(n)=(a(n-1) + n) * n if n is odd, a(n-1)*n + n otherwise.
A344496 (program): a(0)=0; for n > 0, a(n) = a(n-1)*n + n if n is odd, (a(n-1) + n)*n otherwise.
A344500 (program): a(n) = Sum_{k=0..n} binomial(n, k)*CT(n, k) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*CT(n, k), where CT(n, k) is the Catalan triangle A053121.
A344501 (program): a(n) = Sum_{k=0..n} binomial(n, k)*HT(n, k) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*HT(n, k), where HT(n, k) is the Hermite triangle A099174.
A344502 (program): a(n) = Sum_{k=0..n} binomial(n, k)^2 * hypergeom([(k-n)/2, (k-n+1)/2], [k+2], 4).
A344503 (program): a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)^2*hypergeom([(k-n)/2, (k-n+1)/2], [k+2], 4).
A344504 (program): a(n) = [x^n] ((x - 1)/sqrt(4/(x + 1) - 3) + x + 1)/(2*x*(3*x - 1)).
A344506 (program): a(n) = [x^n] 2 / (1 - 7*x + sqrt(1 - 2*x - 3*x^2)).
A344507 (program): a(n) = [x^n] 2/(3*x + sqrt((1 - 3*x)*(x + 1)) + 1).
A344508 (program): a(n) = Sum_{k=1..n} k * lcm(k,n).
A344509 (program): a(n) = (1/n) * Sum_{k=1..n} k * lcm(k,n).
A344510 (program): a(n) = Sum_{k=1..n} k * gcd(k,n).
A344511 (program): a(n) = Sum_{k >= 0} sign(d_k) * 2^k for any number n with decimal expansion Sum_{k >= 0} d_k * 10^k.
A344514 (program): a(n) = Sum_{k=1..n} floor(n/k^2)^k.
A344517 (program): Minimum diameter of 4-regular circulant graphs of order n.
A344520 (program): Decimal expansion of 2*(1+sqrt(10))/3.
A344521 (program): a(n) = Sum_{1 <= i <= j <= k <= n} gcd(i,j,k).
A344522 (program): a(n) = Sum_{1 <= i, j, k <= n} gcd(i,j,k).
A344523 (program): a(n) = Sum_{1 <= i, j, k, l <= n} gcd(i,j,k,l).
A344526 (program): a(n) = Sum_{k=1..n} k^3 * phi(k).
A344543 (program): Lexicographically earliest sequence S of distinct positive terms such that the product of the last k digits of S is even, k being the rightmost digit of a(n).
A344551 (program): a(n) = Sum_{k=1..n} k^floor((n-k)/k).
A344552 (program): a(n) = Sum_{k=1..n} floor(k*(n-k)/n).
A344553 (program): Number of lattice paths from (0,0) to (2n-1,n) using steps E=(1,0), N=(0,1), and D=(1,1) which stay weakly above the line through (0,0) and (2n-1,n).
A344554 (program): Decimal expansion of 2*(1+sqrt(26))/5.
A344557 (program): Triangle read by rows, T(n, k) = 2^(n - k)*M(n, k, 1/2, 1/2), where M(n, k, x, y) is a generalized Motzkin recurrence. T(n, k) for 0 <= k <= n.
A344558 (program): Row sums of A344557.
A344559 (program): a(n) = (1/6) * 2^(-n) * n! * [x^n] Exp(2*x, 1)*(Exp(2*x, 3) - 1), where Exp(x, m) = Sum_{k>=0} (x^k / k!)^m.
A344560 (program): a(n) = hypergeom([-n/3, (1 - n)/3, (2 - n)/3], [1, 1], -27).
A344563 (program): T(n, k) = binomial(n - 1, k - 1) * binomial(n, k) * 2^k, T(0, 0) = 1. Triangle read by rows, T(n, k) for 0 <= k <= n.
A344564 (program): a(n) = [x^n] -3/(2*x - 1)^5.
A344565 (program): Triangle read by rows, for 0 <= k <= n: T(n, k) = binomial(n, k) * binomial(binomial(n + 3, 2), 2).
A344566 (program): T(n, k) = (-1)^(n - k)*binomial(n - 1, k - 1)*hypergeom([-(n - k)/2, -(n - k - 1)/2], [1 - n], 4). Triangle read by rows, T(n, k) for 0 <= k <= n.
A344568 (program): Decimal expansion of 2*(1+sqrt(82))/9.
A344569 (program): Decimal expansion of 2*(1+sqrt(290))/17.
A344572 (program): a(n) = Sum_{d|n} Omega(d!).
A344573 (program): a(n) = Sum_{d|n} phi(d!).
A344574 (program): Number of ordered pairs (i,j) with 0 < i < j < n such that gcd(i,j,n) > 1.
A344575 (program): a(n) = Sum_{d|n} d^abs(mu(n/d)).
A344576 (program): a(n) = f(n,n) where f(0,n) = f(n,0) = Fibonacci(n) and f(m,n) = f(m-1,n) + f(m,n-1) + f(m-1,n-1).
A344578 (program): a(n) = Sum_{d|n} d * sopf(d).
A344579 (program): a(n) = Sum_{d|n} d^sopf(d).
A344580 (program): Numbers k such that A101203(k) is prime.
A344584 (program): Difference between the inverse Möbius transform of the arithmetic derivative of n and the sum of the proper divisors of n: a(n) = A319684(n) - A001065(n).
A344586 (program): Numbers k for which A003415(k) >= A001065(k), where A003415 gives the arithmetic derivative, and A001065 is the sum of proper divisors.
A344587 (program): a(n) = 2*A003961(n) - sigma(A003961(n)).
A344596 (program): a(n) = Sum_{k=1..n} mu(k) * (floor(n/k)^3 - floor((n-1)/k)^3).
A344598 (program): a(n) = Sum_{k=1..n} phi(k) * (floor(n/k)^2 - floor((n-1)/k)^2).
A344599 (program): a(n) = Sum_{k=1..n} phi(k) * (floor(n/k)^3 - floor((n-1)/k)^3).
A344600 (program): a(n) = Sum_{k=1..n} phi(k) * (floor(n/k)^4 - floor((n-1)/k)^4).
A344602 (program): Integers whose Hamming weight is triangular.
A344607 (program): Number of integer partitions of n with reverse-alternating sum >= 0.
A344608 (program): Number of integer partitions of n with reverse-alternating sum < 0.
A344609 (program): Numbers whose alternating sum of prime indices is >= 0.
A344611 (program): Number of integer partitions of 2n with reverse-alternating sum >= 0.
A344616 (program): Alternating sum of the integer partition with Heinz number n.
A344617 (program): Sign of the alternating sum of the prime indices of n.
A344618 (program): Reverse-alternating sums of standard compositions (A066099). Alternating sums of the compositions ranked by A228351.
A344619 (program): The a(n)-th composition in standard order (A066099) has alternating sum 0.
A344622 (program): a(n) = n*(n+1)/2 - sigma(n) + d(n).
A344623 (program): Pseudo-involution companion for the Fibonacci generating function.
A344624 (program): a(n) = Sum_{k=1..n} k^c(k), where c(n) is the characteristic function of squares.
A344646 (program): Array read by antidiagonals T(n,k) = ((n+k+1)^2 - (n+k+1) mod 2)/4 + min(n,k) for n and k >= 0.
A344650 (program): Number of strict odd-length integer partitions of 2n.
A344658 (program): a(n) = a^a - b^b + c^c - … -+ d^d where the decimal expansion of n is abc…d.
A344674 (program): a(n) is the maximum value such that there is an n X n binary orthogonal matrix with every row having at least a(n) ones.
A344675 (program): a(n) = Sum_{k=1..n} floor(n^3/k^3).
A344679 (program): Number of 2-matchings of the n-th centered square grid graph.
A344683 (program): Dirichlet convolution of the Euler totient function with itself, applied twice.
A344684 (program): Sum of two consecutive products of Fibonacci and Pell numbers: F(n)*P(n) + F(n+1)*P(n+1).
A344685 (program): Triangle T(n, k) obtained from the array N1(a, b) = a^2 + a*b - b^2, for a >= 0 and b >= 0, read by upwards antidiagonals.
A344686 (program): Triangle T(n, k) obtained from the array N2(a, b) = a^2 - a*b - b^2, for a >= 0 and b >= 0, read by upwards antidiagonals.
A344687 (program): a(n) is the lowest nonnegative exponent k such that n!^k is the product of the divisors of n!.
A344690 (program): a(n) is the number of multisets of size n consisting of permutations of n elements.
A344695 (program): a(n) = gcd(sigma(n), psi(n)), where sigma is the sum of divisors function, A000203, and psi is the Dedekind psi function, A001615.
A344696 (program): a(n) = sigma(n) / gcd(sigma(n), A001615(n)).
A344697 (program): a(n) = A001615(n) / gcd(sigma(n), A001615(n)).
A344698 (program): a(n) = A344696(A108951(n)).
A344699 (program): a(n) = A344697(A108951(n)).
A344704 (program): a(n) = gcd(A001615(n)-n, sigma(n)-(A001615(n)+n)).
A344705 (program): a(n) = n + A001615(n) - sigma(n), where A001615 is the Dedekind psi-function, and sigma(n) gives the sum of divisors of n; difference between psi and the sum of proper divisors.
A344713 (program): a(n) is the number of iterations needed for n to reach 0 under the mapping x -> A055212(x).
A344717 (program): a(n) = (3n - 9/2 - 1/n + 6/(n+1))*binomial(2n-2,n-1).
A344718 (program): Divide the positive integers into subsets of lengths given by successive primes. a(n) is the sum of primes contained in the n-th subset.
A344720 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/k)^2.
A344721 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/k)^3.
A344722 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/k)^4.
A344723 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/k)^5.
A344724 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/k)^n.
A344725 (program): Square array T(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where T(n,k) = Sum_{j=1..n} floor(n/j)^k.
A344735 (program): a(0) = 1; a(n) = 4 * Sum_{k=1..n} binomial(n,k) * a(k-1).
A344742 (program): Numbers whose prime factors have a permutation with no consecutive monotone triple, i.e., no triple (…, x, y, z, …) such that either x <= y <= z or x >= y >= z.
A344743 (program): Number of integer partitions of 2n with reverse-alternating sum < 0.
A344747 (program): a(n) = (1/6)*(3^n + (-2)^n - 1).
A344753 (program): a(n) = sigma(n) + psi(n) - 2n = Sum_{d|n, d<n} d+(mu(n/d)^2 * d), where mu is Möbius mu-function.
A344756 (program): a(n) = A003415(n) / gcd(A003415(n), A069359(n)).
A344757 (program): a(n) = A069359(n) / gcd(A003415(n), A069359(n)).
A344763 (program): a(n) = n - A011772(n).
A344764 (program): a(n) = gcd(n, A011772(n)).
A344765 (program): a(n) = sigma(n) - A011772(n).
A344766 (program): a(n) = gcd(sigma(n), A011772(n)).
A344769 (program): a(n) = A005187(n) - A011772(n).
A344777 (program): a(n) = Sum_{d|n} (-1)^(n/d-1) * binomial(d+n/d-1, d).
A344784 (program): Decimal expansion of the sum of the reciprocals of the prime factors of Fermat numbers (A023394).
A344785 (program): Decimal expansion of the sum of the reciprocals of the elite primes (A102742).
A344787 (program): a(n) = n * Sum_{d|n} sigma_d(d) / d, where sigma_k(n) is the sum of the k-th powers of the divisors of n.
A344791 (program): a(n) is the number of 2-point antichains in the poset D_{2n+1} of type D, whose elements are compositions of 2n+1.
A344805 (program): Numbers that are the sum of six second powers in one or more ways.
A344809 (program): Numbers that are the sum of six squares in five or more ways.
A344814 (program): a(n) = Sum_{k=1..n} floor(n/k) * 3^(k-1).
A344815 (program): a(n) = Sum_{k=1..n} floor(n/k) * 4^(k-1).
A344816 (program): a(n) = Sum_{k=1..n} floor(n/k) * 5^(k-1).
A344817 (program): a(n) = Sum_{k=1..n} floor(n/k) * (-2)^(k-1).
A344818 (program): a(n) = Sum_{k=1..n} floor(n/k) * (-3)^(k-1).
A344819 (program): a(n) = Sum_{k=1..n} floor(n/k) * (-4)^(k-1).
A344820 (program): a(n) = Sum_{k=1..n} floor(n/k) * (-n)^(k-1).
A344840 (program): a(0) = 1; a(n) = 5 * Sum_{k=1..n} binomial(n,k) * a(k-1).
A344851 (program): a(n) = (n^2) mod (2^A070939(n)).
A344852 (program): Number of rooted binary trees with n leaves with minimal Symmetry Nodes Index (SNI) or, equivalently, with the maximal number of symmetry nodes.
A344853 (program): a(n) = n minus (sum of digits of n in base 3).
A344854 (program): The number of equilateral triangles with vertices from the vertices of the n-dimensional hypercube.
A344856 (program): Bitwise XOR of prime(n) and n^2.
A344858 (program): a(n) = floor(exp(cos(n))).
A344863 (program): a(n) = mu(sigma(n)).
A344864 (program): a(n) = mu(d(n)).
A344866 (program): Number of polygons formed when every pair of vertices of a regular (2n-1)-gon are joined by an infinite line.
A344867 (program): a(n) = n * Sum_{d|n} floor(sqrt(d)) / d.
A344872 (program): Semiprimes of the form 3m+2.
A344874 (program): a(n) = A047994(n) - A011772(n).
A344875 (program): Multiplicative with a(2^e) = 2^(1+e) - 1, and a(p^e) = p^e - 1 for odd primes p.
A344876 (program): a(n) = A344875(n) - A011772(n).
A344877 (program): a(n) = gcd(n, A344875(n)), where A344875 is multiplicative with a(2^e) = 2^(1+e) - 1, and a(p^e) = p^e -1 for odd primes p.
A344886 (program): a(n) is the smallest triangular number that is a multiple of the product of the members of the n-th pair of twin primes.
A344887 (program): a(n) is the least base k >= 2 that the base-k digits of n are nonincreasing.
A344892 (program): Loxton-van der Poorten sequence: base-4 representation contains only -1, 0, +1, converted to ordinary base-4 digits 0,1,2,3.
A344902 (program): Number of open tours by a biased rook on a specific f(n) X 1 board, where f(n) = A070941(n) and cells are colored white or black according to the binary representation of 2n.
A344907 (program): Number of polygon edges formed when every pair of vertices of a regular (2n-1)-gon are joined by an infinite line.
A344908 (program): Sum of the distinct odd-indexed prime divisors, p_{2k-1}, of n.
A344913 (program): Table read by rows, T(n, k) (for 0 <= k <= n) = (-2)^(n - k)*k!*Stirling2(n, k).
A344918 (program): a(n) = denominator(4^(n + 1)*zeta(-n, 1/4)).
A344919 (program): a(n) = n^n - n*(n + 1) / 2.
A344920 (program): The Worpitzky transform of the squares.
A344931 (program): Sum of the distinct even-indexed prime divisors, p_{2k}, of n.
A344935 (program): a(0)=1; for n > 0, a(n) = n*(a(n-1) + i^(n-1)) if n is odd, n*a(n-1) + i^n otherwise, where i = sqrt(-1).
A344947 (program): Number of open tours by a biased rook on a specific A070941(n) X 1 board, which ends on a black cell, where cells are colored white or black according to the binary representation of 2n.
A344953 (program): Positions of words in A341258 that end with 1.
A344956 (program): Positions of words in A341258 starting with 0 and ending with 0.
A344957 (program): Positions of words in A341258 starting with 0 and ending with 1.
A344958 (program): Positions of words in A344953 starting with 1 and ending with 0.
A344959 (program): Positions of words in A344953 starting with 1 and ending with 1.
A344969 (program): a(n) = gcd(A011772(n), A344875(n)).
A344970 (program): a(n) = A011772(n) / gcd(A011772(n), A344875(n)).
A344971 (program): a(n) = A344875(n) / gcd(A011772(n), A344875(n)).
A344972 (program): a(n) = floor(A344875(n) / A011772(n)).
A344974 (program): Numbers k such that A011772(k) divides A344875(k).
A344980 (program): Numbers k such that A011772(k) does not divide A344875(k).
A344992 (program): a(n) = Sum_{1 <= i <= j <= k <= m <= n} gcd(i,j,k,m).
A344996 (program): a(n) = A048250(n) * A051709(n).
A344997 (program): a(n) = A173557(n) * A344753(n).
A344998 (program): a(n) = A342001(n) * A344753(n).
A344999 (program): a(n) = A048250(n) * A345001(n).
A345000 (program): a(n) = gcd(A003415(n), A003415(A276086(n))), where A003415(n) is the arithmetic derivative of n, and A276086(n) gives the prime product form of primorial base expansion of n.
A345001 (program): a(n) = sigma(n) + n’ - 2n, where n’ is the arithmetic derivative of n (A003415) and sigma is the sum of divisors (A000203).
A345013 (program): Triangle read by rows, related to clusters of type D.
A345016 (program): Positive even integers with an odd number of Goldbach partitions.
A345017 (program): Positive even integers with an even number of Goldbach partitions.
A345018 (program): For each n, append to the sequence n^2 consecutive integers, starting from n.
A345019 (program): Numbers whose last digit is refactorable.
A345021 (program): a(n) is the result of replacing 2’s by 0’s in the hereditary base-2 expansion of n.
A345022 (program): Smallest number divisible by all numbers 1 through n+1 except n, or 0 if impossible.
A345028 (program): a(n) = Sum_{k=1..n} 2^(floor(n/k) - 1).
A345029 (program): a(n) = Sum_{k=1..n} 3^(floor(n/k) - 1).
A345030 (program): a(n) = Sum_{k=1..n} n^(floor(n/k) - 1).
A345031 (program): a(n) = 6*a(n-1) - 7*a(n-2) - 2*a(n-3) for n >= 3, with a(0) = a(1) = 0, a(2) = 1.
A345034 (program): a(n) = Sum_{k=1..n} (-2)^(floor(n/k) - 1).
A345035 (program): a(n) = Sum_{k=1..n} (-3)^(floor(n/k) - 1).
A345036 (program): a(n) = Sum_{k=1..n} (-n)^(floor(n/k) - 1).
A345037 (program): a(n) = Sum_{k=1..n} (-k)^(floor(n/k) - 1).
A345039 (program): Number of partitions of n into two composite parts that share a nontrivial divisor.
A345046 (program): If n = Product p(k)^e(k) then a(n) = LCM (p(k)-1)^e(k).
A345048 (program): a(n) = A342001(n) * A051709(n).
A345049 (program): a(n) = A173557(n) * A345001(n).
A345052 (program): a(n) = A003557(n) * A048250(n) * A173557(n).
A345059 (program): a(n) = A129283(n) / gcd(sigma(n), A129283(n)), where A129283(n) is the sum of n and its arithmetic derivative.
A345068 (program): a(n) = Sum_{d|n, d>1} d^floor(1/omega(d)).
A345069 (program): Sums of two consecutive even-indexed primes.
A345070 (program): Averages of two consecutive even-indexed primes.
A345071 (program): Sums of two consecutive odd-indexed primes.
A345073 (program): a(n) is the least integer k such that e * (n!)^(1/n) < n + k.
A345075 (program): E.g.f.: exp( x*(1 + 2*x) / (1 - x - x^2) ).
A345077 (program): a(0) = 1; a(n) = 6 * Sum_{k=1..n} binomial(n,k) * a(k-1).
A345078 (program): a(0) = 1; a(n) = 7 * Sum_{k=1..n} binomial(n,k) * a(k-1).
A345079 (program): Consider the coefficients in the expansion of the n-th cyclotomic polynomial. a(n) is the difference between the extremes.
A345081 (program): a(0) = 1; a(n) = 8 * Sum_{k=1..n} binomial(n,k) * a(k-1).
A345082 (program): Number of elements of order n in R/Z X Z/2Z.
A345089 (program): Averages of two consecutive odd-indexed odd primes.
A345090 (program): a(n) = Sum_{k=1..n} k^floor(1/gcd(k,2*n-k)).
A345091 (program): a(n) = Sum_{k=1..n} k^floor(1/gcd(n,k)).
A345094 (program): a(n) = Sum_{k=1..n} floor(n/k)^(floor(n/k) - 1).
A345098 (program): a(n) = Sum_{k=1..n} floor(n/k)^floor(n/k).
A345100 (program): a(n) = Sum_{k=1..n} k^floor(n/k).
A345102 (program): a(n) = 1 + 3 * Sum_{k=0..n-1} binomial(n,k) * a(k) * a(n-k-1).
A345103 (program): a(n) = 1 + 4 * Sum_{k=0..n-1} binomial(n,k) * a(k) * a(n-k-1).
A345106 (program): a(n) = Sum_{k=1..n} k^(n - floor(n/k)).
A345107 (program): a(n) = Sum_{k=1..n} (-k)^(n - floor(n/k)).
A345108 (program): a(n) = Sum_{k=1..n} 2^(n - floor(n/k)).
A345109 (program): a(n) = Sum_{k=1..n} (-2)^(n - floor(n/k)).
A345110 (program): a(n) is n rotated one place to the left or, equivalently, n with the most significant digit moved to the least significant place, omitting leading zeros.
A345111 (program): a(n) = n + A345110(n).
A345116 (program): Irregular triangle T(n,k) read by rows in which row n has length the n-th triangular number A000217(n) and every column k lists the positive integers A000027, n >= 1, k >= 1.
A345117 (program): a(n) is the index (in Z/nZ) of the first already visited element in the process of moving around Z/nZ, starting at 0 with stride 1 and increasing stride by 1 after each step.
A345118 (program): a(n) is the sum of the lengths of all the segments used to draw a square of side n representing a basketweave pattern where all the multiple strands are of unit width, the horizontal ones appearing as 1 X 3 rectangles, while the vertical ones as unit area squares.
A345127 (program): Total sum of the distinct prime factors of s*t, for all positive integer pairs (s,t) such that s + t = n.
A345128 (program): Number of squarefree products s*t from all positive integer pairs (s,t), such that s + t = n, s <= t.
A345132 (program): Number of (n+2) X (n+2) symmetric matrices with nonnegative integer entries, trace 0, with n rows that sum to 2, and 2 rows that sum to 1.
A345135 (program): Number of ordered rooted binary trees with n leaves and with minimal Sackin tree balance index.
A345137 (program): a(1) = a(2) = 1; a(n+2) = Sum_{d|n, d < n} a(d).
A345138 (program): a(1) = 1, a(2) = 0; a(n+2) = Sum_{d|n, d < n} a(d).
A345139 (program): a(1) = 1; a(n) = a(n-1) + Sum_{d|n, d < n} a(d).
A345141 (program): a(1) = 1, a(2) = 0; a(n+2) = Sum_{d|n} a(d).
A345160 (program): a(n) = Product_{k=1..n} sigma_3(k).
A345161 (program): If n = Product (p_j^k_j) then a(n) = max (nextprime(p_j) - p_j), where nextprime = A151800.
A345172 (program): Numbers whose multiset of prime factors has an alternating permutation.
A345176 (program): a(n) = Sum_{k=1..n} floor(n/k)^k.
A345182 (program): a(1) = 1, a(2) = 0; a(n) = Sum_{d|n, d < n} a(d).
A345211 (program): Numbers with the same number of odd / even, refactorable divisors.
A345212 (program): Numbers with equal numbers of prime and semiprime divisors.
A345219 (program): Number of divisors of n with an odd number of primes not exceeding them.
A345220 (program): Number of divisors of n with an even number of primes not exceeding them.
A345221 (program): Number of divisors of n with an even sum of divisors.
A345222 (program): Number of divisors of n with a prime number of divisors.
A345253 (program): Maximal Fibonacci tree: Arrangement of the positive integers as labels of a complete binary tree.
A345254 (program): Dispersion of A004754, a rectangular array T(n,k) read by downward antidiagonals.
A345261 (program): a(n) = Sum_{d|n} d * rad(d).
A345263 (program): a(n) = Sum_{d|n} d^rad(d).
A345264 (program): a(n) = Sum_{d|n} rad(d) * mu(n/d)^2.
A345266 (program): a(n) = Sum_{p|n, p prime} gcd(p,n/p).
A345269 (program): a(n) = Sum_{d|n} (n/d)^(phi(n/d) - 1).
A345277 (program): Sums of 3 consecutive even-indexed primes.
A345280 (program): a(n) = Sum_{p|n} nextprime(p), where nextprime(n) is the smallest prime > n.
A345284 (program): a(n) = Sum_{p|n} (p #).
A345290 (program): a(n) is obtained by replacing 2^k in binary expansion of n with Fibonacci(-k-2).
A345298 (program): a(n) = Sum_{p|n, p prime} tau(p #).
A345302 (program): a(n) = Sum_{p|n} lcm(p,n/p).
A345303 (program): a(n) = Sum_{p|n, p prime} p * gcd(p,n/p).
A345304 (program): a(n) = Sum_{p|n, p prime} p * lcm(p,n/p).
A345305 (program): a(n) = n * Sum_{p|n, p prime} gcd(p,n/p) / p.
A345306 (program): a(n) = n * Sum_{p|n, p prime} lcm(p,n/p) / p.
A345315 (program): a(n) = Sum_{d|n} d^[Omega(d) = 2], where [ ] is the Iverson bracket.
A345320 (program): Sum of the divisors of n whose square does not divide n.
A345321 (program): Sum of the divisors of n whose cube does not divide n.
A345339 (program): a(n) = 18*n + 20.
A345340 (program): The number of squares with vertices from the vertices of the n-dimensional hypercube.
A345345 (program): a(n) = Sum_{d^2|n} omega(n/d^2).
A345347 (program): Find the largest k with F(k) <= n, where F(k) is the k-th Fibonacci number. a(n) = F(k+2) + n.
A345350 (program): Even triangular numbers such that the next integer is nonprime.
A345354 (program): a(n) = Sum_{p|n, p prime} omega(n/p).
A345360 (program): a(n) = n^n*n - n.
A345365 (program): a(n) = (2*n)!*Pi^(-2*n)*PolyLog(2*n, 1)*Clausen(2*n - 1)/2, where Clausen(n) = A160014(n, 1).
A345366 (program): a(n) = (p*q+1) mod (p+q) where p=prime(n) and q=prime(n+1).
A345367 (program): a(n) = Sum_{k=0..n} binomial(4*k,k) / (3*k + 1).
A345368 (program): a(n) = Sum_{k=0..n} binomial(5*k,k) / (4*k + 1).
A345371 (program): Number of squarefree divisors of n whose square does not divide n.
A345373 (program): Sum of the divisor complements of the unitary prime divisors of n.
A345374 (program): Number of unitary prime divisors of n whose prime index is odd.
A345376 (program): Number of Companion Pell numbers m <= n.
A345377 (program): Number of terms m <= n, where m is a term in A006190.
A345378 (program): Number of terms m <= n, where m is a term in A006497.
A345379 (program): Number of terms m <= n, where m is a term in the bisection of Lucas numbers (A005248).
A345380 (program): Number of Jacobsthal-Lucas numbers m <= n.
A345381 (program): Numbers with exactly 2 semiprime divisors.
A345382 (program): Numbers with exactly 3 semiprime divisors.
A345401 (program): a(n) is the unique odd number h such that BCR(h*2^m-1) = 2n (except for BCR(0) = 1) where BCR is bit complement and reverse per A036044.
A345414 (program): a(n) = n^a(n-1) mod 100; a(0) = 0.
A345419 (program): Row 2 of array in A345417.
A345443 (program): a(n) = smallest m such that for every red-blue edge-coloring of the graph K_{m,m} there exists either a red 4-cycle or a blue K_{1,n}.
A345444 (program): a(n) = A344005(2*n+1).
A345445 (program): a(n) = n^n - (n+1)!/2.
A345447 (program): Numbers of the form i+j+2*i*j and 2+i+j+2*i*j for i,j >= 1.
A345448 (program): Number of tilings of a 2 X n rectangle with dominoes and long L-shaped 4-minoes.
A345449 (program): Decimal expansion of Gascheau’s value, which is defined as the smaller solution of 27*x*(1 - x) = 1.
A345451 (program): Sum of the unitary divisors of n whose square does not divide n.
A345452 (program): Positive integers with an even number of prime factors (counting repetitions) that sum to an even number.
A345455 (program): a(n) = Sum_{k=0..n} binomial(5*n+1,5*k).
A345456 (program): a(n) = Sum_{k=0..n} binomial(5*n+2,5*k).
A345457 (program): a(n) = Sum_{k=0..n} binomial(5*n+3,5*k).
A345458 (program): a(n) = Sum_{k=0..n} binomial(5*n+4,5*k).
A345462 (program): Triangle T(n,k) (n >= 1, 0 <= k <= n-1) read by rows: number of distinct permutations after k steps of the “first transposition” algorithm.
A345465 (program): a(n) = Sum_{d|n} (d!)^d.
A345466 (program): a(n) = Product_{k=1..n} binomial(n, floor(n/k)).
A345468 (program): a(n) is the least number k such that k^2+4*n is prime.
A345478 (program): Numbers that are the sum of seven squares in one or more ways.
A345480 (program): Numbers that are the sum of seven squares in three or more ways.
A345482 (program): Numbers that are the sum of seven squares in five or more ways.
A345483 (program): Numbers that are the sum of seven squares in six or more ways.
A345487 (program): Numbers that are the sum of seven squares in ten or more ways.
A345488 (program): Numbers that are the sum of eight squares in one or more ways.
A345489 (program): Numbers that are the sum of eight squares in two or more ways.
A345490 (program): Numbers that are the sum of eight squares in three or more ways.
A345492 (program): Numbers that are the sum of eight squares in five or more ways.
A345493 (program): Numbers that are the sum of eight squares in six or more ways.
A345494 (program): Numbers that are the sum of eight squares in seven or more ways.
A345495 (program): Numbers that are the sum of eight squares in eight or more ways.
A345496 (program): Numbers that are the sum of eight squares in nine or more ways.
A345497 (program): Numbers that are the sum of eight squares in ten or more ways.
A345498 (program): Numbers that are the sum of nine squares in one or more ways.
A345499 (program): Numbers that are the sum of nine squares in two or more ways.
A345500 (program): Numbers that are the sum of nine squares in three or more ways.
A345501 (program): Numbers that are the sum of nine squares in four or more ways.
A345502 (program): Numbers that are the sum of nine squares in five or more ways.
A345503 (program): Numbers that are the sum of nine squares in six or more ways.
A345504 (program): Numbers that are the sum of nine squares in seven or more ways.
A345505 (program): Numbers that are the sum of nine squares in eight or more ways.
A345508 (program): Numbers that are the sum of ten squares in one or more ways.
A345509 (program): Numbers that are the sum of ten squares in two or more ways.
A345510 (program): Numbers that are the sum of ten squares in three or more ways.
A345531 (program): Smallest prime power greater than the n-th prime.
A345632 (program): Sum of terms of even index in the binomial decomposition of n^(n-1).
A345633 (program): Sum of terms of odd index in the binomial decomposition of n^(n-1).
A345647 (program): Square array read by downward antidiagonals: A(n, k) = number of primes in the interval [n+1, n+k], n >= 1, k > 1.
A345652 (program): Expansion of the e.g.f. exp(-1 + (x + 1)*exp(-x)).
A345655 (program): a(n) is the number of permutations w of [n] with no w(i)+1 == w(i+1) (mod n) that are not simply cyclic permutations of the numbers 1 to n in backwards order.
A345668 (program): Last prime minus distance to last prime.
A345681 (program): a(0) = 0; for n >= 1, a(n) = A004185(a(n-1)+n).
A345685 (program): a(n) is the smallest cardinality of all covering sets associated with Riesel number A101036(n).
A345701 (program): a(n) = 3*n^3 - 1.
A345702 (program): Numbers that can be written as 2*a^2 - 1 and 3*b^3 - 1.
A345708 (program): a(n) is the least positive number starting an interval of consecutive integers whose product of elements is n.
A345727 (program): a(n) = (prime(n)+1) * prime(n+1).
A345735 (program): A prime-generating quasipolynomial: a(n) = 6*floor(n^2/4) + 17.
A345741 (program): a(n) = n + (n - 1) * d(n).
A345743 (program): a(n) = Sum_{k=1..n} n^abs(mu(k)).
A345745 (program): a(n) = Sum_{k=1..n} n^(1 - mu(k)^2).
A345754 (program): Number of 2 X 2 matrices over Z_n whose permanent equals their determinant.
A345867 (program): Total number of 0’s in the binary expansions of the first n primes.
A345876 (program): a(n) = Sum_{k=0..n} binomial(2*n, n-k) * k^n.
A345877 (program): a(1) = 1, a(n) = a(n-1)/2 if a(n-1) is even, otherwise a(n) = n - a(n-1).
A345886 (program): a(1) = 1, a(n) = a(n-1)/3 if a(n-1) is divisible by 3, otherwise a(n) = n - a(n-1).
A345887 (program): Number of tilings of an n-cell circular array with rectangular tiles of any size, and where the number of possible colors of a tile is given by the largest cell covered.
A345888 (program): a(n) = n + (n - 1) * pi(n).
A345889 (program): Number of tilings of an n-cell circular array with rectangular tiles of any size, and where the number of possible colors of a tile is given by the smallest cell covered.
A345890 (program): a(n) = n + (n - 1) * (n - pi(n)).
A345891 (program): a(n) = n + (n - 1) * phi(n).
A345892 (program): a(n) = n + (n - 1) * (n - phi(n)).
A345897 (program): a(n) = 2*n^4/3 - 4*n^3/3 + 11*n^2/6 - 13*n/6 + 1.
A345902 (program): a(0) = 1; for n >= 1, a(n) = A004185(a(n-1)*n).
A345908 (program): Traces of the matrices (A345197) counting integer compositions by length and alternating sum.
A345909 (program): Numbers k such that the k-th composition in standard order (row k of A066099) has alternating sum 1.
A345910 (program): Numbers k such that the k-th composition in standard order (row k of A066099) has alternating sum -1.
A345911 (program): Numbers k such that the k-th composition in standard order (row k of A066099) has reverse-alternating sum 1.
A345912 (program): Numbers k such that the k-th composition in standard order (row k of A066099) has reverse-alternating sum -1.
A345913 (program): Numbers k such that the k-th composition in standard order (row k of A066099) has alternating sum >= 0.
A345914 (program): Numbers k such that the k-th composition in standard order (row k of A066099) has reverse-alternating sum >= 0.
A345915 (program): Numbers k such that the k-th composition in standard order (row k of A066099) has alternating sum <= 0.
A345916 (program): Numbers k such that the k-th composition in standard order (row k of A066099) has reverse-alternating sum <= 0.
A345917 (program): Numbers k such that the k-th composition in standard order (row k of A066099) has alternating sum > 0.
A345918 (program): Numbers k such that the k-th composition in standard order (row k of A066099) has reverse-alternating sum > 0.
A345919 (program): Numbers k such that the k-th composition in standard order (row k of A066099) has alternating sum < 0.
A345920 (program): Numbers k such that the k-th composition in standard order (row k of A066099) has reverse-alternating sum < 0.
A345921 (program): Numbers k such that the k-th composition in standard order (row k of A066099) has alternating sum != 0.
A345922 (program): Numbers k such that the k-th composition in standard order (row k of A066099) has reverse-alternating sum 2.
A345923 (program): Numbers k such that the k-th composition in standard order (row k of A066099) has reverse-alternating sum -2.
A345924 (program): Numbers k such that the k-th composition in standard order (row k of A066099) has alternating sum -2.
A345925 (program): Numbers k such that the k-th composition in standard order (row k of A066099) has alternating sum 2.
A345927 (program): Alternating sum of the binary expansion of n (row n of A030190). Replace 2^k with (-1)^(A070939(n)-k) in the binary expansion of n (compare to the definition of A065359).
A345930 (program): a(n) = A344756(A276086(n)).
A345931 (program): a(n) = gcd(n, A002034(n)), where A002034(n) gives the smallest positive integer k such that n divides k!.
A345932 (program): a(n) = A002034(n) / gcd(n, A002034(n)), where A002034(n) gives the smallest positive integer k such that n divides k!.
A345933 (program): a(n) = n / gcd(n, A002034(n)), where A002034(n) gives the smallest positive integer k such that n divides k!.
A345937 (program): a(n) = gcd(n-1, uphi(n)), where uphi is unitary totient (or unitary phi) function, A047994.
A345938 (program): a(n) = uphi(n) / gcd(n-1, uphi(n)), where uphi is unitary totient (or unitary phi) function, A047994.
A345939 (program): a(n) = (n-1) / gcd(n-1, uphi(n)), where uphi is unitary totient (or unitary phi) function, A047994.
A345940 (program): Factorial of the largest prime factor of n, read modulo n: a(n) = A006530(n)! mod n.
A345941 (program): a(n) = gcd(n, A329044(n)).
A345942 (program): a(n) = n / gcd(n, A329044(n)).
A345943 (program): a(n) = A329044(n) / gcd(n, A329044(n)).
A345947 (program): a(n) = gcd(A153151(n), A344875(n)).
A345948 (program): a(n) = A344875(n) / gcd(A153151(n), A344875(n)).
A345949 (program): a(n) = A153151(n) / gcd(A153151(n), A344875(n)).
A345951 (program): a(n) = 1 if A002034(n), the smallest positive integer k such that n divides k!, is larger than A006530(n), the greatest prime factor of n, otherwise 0.
A345952 (program): a(n) = 1 if the largest prime power divisor of n (A034699) is greater than the largest prime divisor of n (A006530).
A345953 (program): Number of ways to tile a 2 X n strip with squares and P-shaped pentominos.
A345954 (program): a(n) is the number of ternary strings of length n with at least three 0’s.
A345957 (program): Number of divisors of n with exactly half as many prime factors as n, counting multiplicity.
A345963 (program): a(n) = (q^2-q+1)/3 where q = 2^(2*n+1) = A004171(n).
A345965 (program): a(1) = 1; for n>1, a(n) = phi(n) + a(n/p) where p is the least prime divisor of n.
A345978 (program): Third coordinate of the points of a counterclockwise spiral on an hexagonal grid in a symmetric redundant hexagonal coordinate system.
A345979 (program): a(n) = integral spum of an n-cycle.
A345980 (program): a(n) = spum of a path P_n.
A345981 (program): a(n) = integral spum of a path P_n.
A345983 (program): Partial sums of A344005.
A345984 (program): Partial sums of A011772.
A345988 (program): Smallest oblong number m*(m+1) that is divisible by n.
A345989 (program): Smallest tetrahedral number m*(m+1)*(m+2)/6 that is divisible by n.
A345990 (program): Smallest m such that n divides m*(m+1)*(m+2).
A345991 (program): Smallest number of the form m*(m+1)*(m+2) that is divisible by n.
A345992 (program): Let m = A344005(n) = smallest m such that n divides m*(m+1); a(n) = gcd(n,m).
A345993 (program): Let m = A344005(n) = smallest m such that n divides m*(m+1); a(n) = gcd(n,m+1).
A345998 (program): a(n) = m/gcd(m,n), where m = A344005(n).
A345999 (program): a(n) = (m+1)/gcd(m+1,n), where m = A344005(n).
A346002 (program): Distance 2 lexicode over the alphabet {0,1,2}, with the codewords written in base 10.
A346004 (program): If n even then n otherwise ((n+1)/2)^2.
A346014 (program): Numbers whose average number of distinct prime factors of their divisors is an integer.
A346017 (program): a(n) is the least number k such that the average number of distinct prime factors of the divisors of k is equal to n.
A346034 (program): a(1) = 1, a(2) = 0; a(n+2) = Sum_{d|n} mu(n/d) * a(d).
A346035 (program): a(1) = 1; if a(n) is not divisible by 3, a(n+1) = 4*a(n) + 1, otherwise a(n+1) = a(n)/3.
A346041 (program): Numbers with exactly 1 semiprime divisor.
A346042 (program): Decimal expansion of Sum_{k>=0} 2^floor(k/2)/(k!^2).
A346050 (program): G.f. A(x) satisfies: A(x) = x + x^2 + x^3 * A(x/(1 - x)) / (1 - x).
A346051 (program): G.f. A(x) satisfies: A(x) = 1 + x^2 + x^3 * A(x/(1 - x)) / (1 - x).
A346052 (program): G.f. A(x) satisfies: A(x) = 1 + x + x^3 * A(x/(1 - x)) / (1 - x).
A346053 (program): G.f. A(x) satisfies: A(x) = 1 - x * A(x/(1 - x)) / (1 - x)^3.
A346054 (program): Number of ways to tile a 3 X n strip with dominoes and L-shaped 5-minoes.
A346059 (program): G.f. A(x) satisfies: A(x) = 1 - x * A(x/(1 - x)) / (1 - x)^4.
A346065 (program): a(n) = Sum_{k=0..n} binomial(6*k,k) / (5*k + 1).
A346070 (program): Symbolic code for the corner turns in the Lévy dragon curve.
A346073 (program): a(n) = 1 + Sum_{k=0..n-4} a(k) * a(n-k-4).
A346074 (program): a(n) = 1 + Sum_{k=0..n-5} a(k) * a(n-k-5).
A346078 (program): G.f. A(x) satisfies: A(x) = 1 + x - x^2 * A(x/(1 - x)) / (1 - x).
A346079 (program): G.f. A(x) satisfies: A(x) = x - x^2 * A(x/(1 - x)) / (1 - x).
A346087 (program): a(n) = min(A071178(n), A329348(n)).
A346090 (program): Numbers k such that k and A346098(k) are relatively prime; positions of ones in A346099, positions of zeros in A346100.
A346091 (program): a(n) = A328571(A108951(n)).
A346093 (program): a(n) = A276085(A328571(A108951(n))).
A346095 (program): a(n) = gcd(A324886(n), A064989(A324886(n))).
A346096 (program): Numerator of the primorial deflation of A276086(A108951(n)): a(n) = A319626(A324886(n)).
A346097 (program): Denominator of the primorial deflation of A276086(A108951(n)): a(n) = A319627(A324886(n)).
A346098 (program): a(n) = A064989(A346096(n) = A064989(A319626(A324886(n))).
A346099 (program): a(n) = gcd(n, A346098(n)).
A346100 (program): a(n) = A100995(gcd(n, A064989(A319626(A324886(n))))).
A346105 (program): a(n) = A276085(A108951(n)).
A346108 (program): a(n) = A276085(A108951(A346096(n))), where A346096(n) gives the numerator of the primorial deflation of A276086(A108951(n)).
A346112 (program): Size of the smallest regular polygon chain for a regular polygon with n sides.
A346117 (program): a(1) = a(2) = 1; a(n+2) = 1 + Sum_{d|n} a(d).
A346118 (program): a(1) = 1; a(n+1) = 1 + Sum_{d|n} mu(n/d) * a(d).
A346122 (program): n times the n-th digit of the decimal expansion of Pi.
A346131 (program): Numbers m such that no self-avoiding walk that can make turns from the set +-Pi/11, +-3*Pi/11, +-5*Pi/11, +-7*Pi/11, +-9*Pi/11, of length m + 1 fits into the smallest circle that can enclose a walk of length m.
A346139 (program): Numbers k that require fewer than k steps to reach 1 under the 3x+1 map.
A346145 (program): Primes of the form k^2 + 25.
A346151 (program): a(n) is the smallest integer k > 0 such that 1 - tanh(k) < 10^(-n).
A346152 (program): a(n) is the least prime divisor p_j of n such that if n = Product_{i=1..k} p_i^e_i and p_1 < p_2 < … < p_k, then Product_{i=1..j-1} p_i^e_i <= sqrt(n) < Product_{i=j..k} p_i^e_i. a(1) = 1.
A346153 (program): a(n) = A346152(n!).
A346155 (program): Partial sums of A007978.
A346174 (program): Inverse binomial transform of A317614.
A346178 (program): Expansion of (1-2*x)/(1-10*x).
A346180 (program): a(n) = prime(n) + n if n is prime, a(n) = prime(n) otherwise.
A346181 (program): a(n) = Sum_{k=0..n} binomial(n,k) * k^n * (k+1)^(n-1), with a(0)=1.
A346183 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial((k+1)^2, n).
A346184 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(k^2, n).
A346185 (program): a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n-1,k)^3 * a(k).
A346190 (program): Decimal expansion of Sum_{k>=0} 1/(2^(2^(2*k+1)) - 1).
A346191 (program): Decimal expansion of Sum_{k>=0} 1/(2^(2^(2*k)) - 1).
A346196 (program): a(n) = Sum_{d|n} (d!)^n.
A346197 (program): a(n) is the minimum number of pebbles such that any assignment of those pebbles on K_5 is a next-player winning game in the two-player impartial (n+1,n) pebbling game.
A346200 (program): a(n) = Sum_{k=0..n} (binomial(n+k,k) * binomial(n,k))^k.
A346202 (program): a(n) = L(n)^2, where L is Liouville’s function.
A346208 (program): E.g.f.: exp(-3*x) / (2 - exp(x)).
A346213 (program): Number of iterations of A000688 needed to reach 1 starting at n (n is counted).
A346224 (program): a(n) = (n!)^2 * Sum_{k=0..floor(n/2)} 1 / ((n-2*k)! * 4^k * k!).
A346232 (program): Maximum number of squares in a square grid whose interiors can be touched by a (possibly skew) line segment of length n.
A346234 (program): Dirichlet inverse of A003961, where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1).
A346244 (program): a(n) = n - A342001(n).
A346258 (program): E.g.f.: exp(x) / (1 - 3 * x)^(1/3).
A346291 (program): a(0) = 1; a(n) = (1/n) * Sum_{k=2..n} (binomial(n,k) * k!)^2 * a(n-k) / k.
A346295 (program): a(n) = Sum_{k=0..n} (2^k + 1) * (2^k + 2) / 2.
A346296 (program): a(0) = 1; thereafter a(n) = 2*a(n-1) + 1, with digits rearranged into nondecreasing order.
A346299 (program): Positions of words in A076478 in which #0’s < #1’s.
A346300 (program): Positions of words in A076478 in which #0’s > #1’s.
A346301 (program): Positions of words in A076478 such that first digit = last digit.
A346302 (program): Positions of words in A076478 such that first digit != last digit.
A346303 (program): Positions of words in A076478 that start with 0 and end with 0.
A346304 (program): Positions of words in A076478 that start with 1 and end with 0.
A346305 (program): Positions of words in A076478 that start with 1 and end with 1.
A346306 (program): Position in A076478 of the binary complement of the n-th word in A076478.
A346307 (program): Number of runs in the n-th word in A076478.
A346309 (program): Positions of words in A076478 such that #0’s - #1’s is odd.
A346310 (program): Positions of words in A076478 such that #0’s - #1’s is even.
A346311 (program): Maximum number of edges a single edge crosses in a drawing of the complete graph K_n where every vertex lies on the outer face.
A346317 (program): Number of permutations of [n] having two cycles of the form (c1, c2, …, c_m) where c1 = min_{i>=1} c_i and c_j = min_{i>=j} c_i or c_j = max_{i>=j} c_i.
A346370 (program): Upper bound for the number of solutions of the TRINTUM cube puzzle n X 1 X 1 (cuboid formed by 4n + 2 parts) different by the set of parts, which are distinguished by the amount of surface area they contribute to the assembled cuboid.
A346374 (program): a(n) = f(n,n) where f(0,n) = f(n,0) = n! and f(m,n) = f(m-1,n) + f(m,n-1) + f(m-1,n-1).
A346375 (program): a(n) = Sum_{k=0..n} (2^k + 2) * (2^k + 3) / 2.
A346376 (program): a(n) = n^4 + 14*n^3 + 63*n^2 + 98*n + 28.
A346377 (program): a(n) is the number of solutions k to A075254(k) = n.
A346380 (program): Complement of A187430 in A000108.
A346388 (program): a(n) is the number of proper divisors of A053742(n) ending with 5.
A346394 (program): Expansion of e.g.f. -log(1 - x) * exp(2*x).
A346395 (program): Expanison of e.g.f. -log(1 - x) * exp(3*x).
A346396 (program): Expansion of e.g.f. -log(1 - x) * exp(4*x).
A346397 (program): Expansion of e.g.f. -log(1 - x) * exp(-2*x).
A346398 (program): Expansion of e.g.f. -log(1 - x) * exp(-3*x).
A346401 (program): a(n) is the minimum number of pebbles such that any assignment of those pebbles on a complete graph with n vertices is a next-player winning game in the two-player impartial (3, 2) pebbling game.
A346403 (program): a(1)=1; for n>1, a(n) gives the sum of the exponents in the different ways to write n as n = x^y, 2 <= x, 1 <= y.
A346405 (program): a(n) = (n!)^2 * Sum_{k=0..n-1} 1 / ((n-k)^2 * k!).
A346409 (program): a(n) = (n!)^2 * Sum_{k=0..n-1} (-1)^k / ((n-k)^2 * k!).
A346410 (program): a(n) = (n!)^2 * Sum_{k=0..n-1} 1 / ((n-k) * k!)^2.
A346411 (program): a(n) = (n!)^2 * Sum_{k=0..n-1} (-1)^k / ((n-k) * k!)^2.
A346422 (program): a(n) = (1 + A014081(n))*a(A053645(n)) for n > 0 with a(0) = 1.
A346425 (program): a(n) is the greatest number k such that k! <= prime(n).
A346432 (program): a(0) = 1; a(n) = n! * Sum_{k=0..n-1} (n-k+1) * a(k) / k!.
A346434 (program): Triangle read by rows of numbers with n 1’s and n 0’s in their representation in base of Fibonacci numbers (A210619), written as those 1’s and 0’s.
A346440 (program): Decimal expansion of the constant Sum_{k>=0} (-1)^k/(4*k)!.
A346441 (program): Decimal expansion of the constant Sum_{k>=0} (-1)^k/(3*k)!.
A346448 (program): Number of nontrivial disconnected induced K_{1,3}-saturated graphs on n vertices.
A346455 (program): a(n) is the smallest number k such that Sum_{j=1..k} (-1)^omega(j) = n, where omega(j) is the number of distinct primes dividing j.
A346458 (program): Numbers with hexadecimal representation A, AB, ABC, …, ABCDEFA, ABCDEFAB, …
A346459 (program): Triangle read by rows: T(n,k) = 0 if all positive integers can be colored with two colors without any positive integer x being the same color as n*x or k*x; otherwise, T(n,k) = 1 (for 2 <= k <= n).
A346461 (program): a(n) = 2^A042965(n+1).
A346463 (program): a(n) = 6 * GaussBinomial(2*n, 2, 2) / denominator(Bernoulli(2*n, 1)).
A346469 (program): a(n) = A340070(A276086(n)).
A346470 (program): a(n) = psi(A276086(n)), where psi is Dedekind psi function A001615, and A276086 is the prime product form of primorial base expansion of n.
A346471 (program): a(n) = A344695(A276086(n)), where A344695(x) = gcd(psi(x), sigma(x)), and A276086 gives the prime product form of primorial base expansion of n.
A346472 (program): a(n) = A011772(A276086(n)).
A346474 (program): a(n) = A342414(A276086(n)).
A346475 (program): a(n) = A342919(A276086(n)).
A346494 (program): Heptagonal numbers (A000566) with prime indices (A000040).
A346502 (program): a(n) = 3n - (sum of digits of 3n in base 3).
A346503 (program): G.f. A(x) satisfies: A(x) = 1 + x^3 * A(x)^2 / (1 - x).
A346513 (program): a(n) = Fibonacci(n+1)^3 - Fibonacci(n)^3.
A346514 (program): a(n) = n^4 + 28*n^3 + 252*n^2 + 784*n + 448.
A346515 (program): a(n) = n*(n+2)*(n+4)*(n+6)*(n+8)*(n+10)*(n+12)*(n+14).
A346522 (program): a(n) is the smallest number such that there are precisely n squares between a(n) and 2*a(n) inclusive.
A346535 (program): Numbers obtained by adding the first k repdigits that consist of the same digit, for some number k.
A346550 (program): Expansion of Sum_{k>=0} k! * x^k * (1 + x)^(k+1).
A346558 (program): a(n) = Sum_{d|n} phi(n/d) * (2^d - 1).
A346563 (program): a(n) = n + A007978(n).
A346572 (program): Decimal expansion of 2 - 7 * Pi^3 / 216.
A346573 (program): Decimal expansion of 2 - Pi/3.
A346597 (program): Partial sums of A019554.
A346608 (program): Indices k such that A047994(k) != A344005(k).
A346612 (program): Moebius transform of A019554.
A346613 (program): Inverse Moebius transform of A019554.
A346614 (program): Inverse Moebius transform of A011772.
A346616 (program): Inverse Moebius transform of A344005.
A346618 (program): Triangle read by rows: T(n,k) = 1 iff 2 divides binomial(n,k) but 4 does not (0 <= k <= n).
A346620 (program): Partial sums of A007774.
A346621 (program): a(n) = Sum_{ x <= n : omega(x) = 2 } x.
A346622 (program): a(n) = card{ x <= n : x odd and omega(x) = 2 }.
A346626 (program): G.f. A(x) satisfies: A(x) = (1 + x * A(x)^3) / (1 - x).
A346627 (program): G.f. A(x) satisfies: A(x) = 1 / (1 + x) + x * A(x)^3.
A346628 (program): G.f. A(x) satisfies: A(x) = 1 / (1 + x) + x * (1 + x) * A(x)^3.
A346629 (program): Number of n-digit positive integers that are the product of two integers ending with 2.
A346633 (program): Sum of even-indexed parts (even bisection) of the n-th composition in standard order.
A346634 (program): Number of strict odd-length integer partitions of 2n + 1.
A346635 (program): Numbers whose division (or multiplication) by their greatest prime factor yields a perfect square. Numbers k such that k*A006530(k) is a perfect square.
A346636 (program): a(n) is the number of quadruples (a_1, a_2, a_3, a_4) having all terms in {1,…,n} such that there exists a quadrilateral with these side lengths.
A346637 (program): a(n) is the number of quintuples (a_1,a_2,a_3,a_4,a_5) having all terms in {1,…,n} such that there exists a pentagon with these side-lengths.
A346638 (program): a(n) is the number of 6-tuples (a_1,a_2,a_3,a_4,a_5,a_6) having all terms in {1,…,n} such that there exists a hexagon with these side-lengths.
A346641 (program): Numbers k with at least one partition into two parts (s,t), s<=t such that t | s*k but no proper divisor of k has this property.
A346642 (program): a(n) = Sum_{j=1..n} Sum_{i=1..j} j^3*i^3.
A346646 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(4*k,k) / (3*k + 1).
A346647 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(5*k,k) / (4*k + 1).
A346648 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(6*k,k) / (5*k + 1).
A346649 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(7*k,k) / (6*k + 1).
A346650 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(8*k,k) / (7*k + 1).
A346651 (program): a(n) is the number of divisors of A139245(n) ending with 2.
A346654 (program): a(n) = Bell(2*n,n).
A346655 (program): a(n) = Bell(3*n,n).
A346657 (program): Numbers that are not divisible by the product of their nonzero digits.
A346663 (program): The number of nonreal roots of Sum_{k=0..n} prime(k+1)*x^k.
A346664 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(4*k,k) / (3*k + 1).
A346665 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(5*k,k) / (4*k + 1).
A346666 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(6*k,k) / (5*k + 1).
A346667 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(7*k,k) / (6*k + 1).
A346668 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(8*k,k) / (7*k + 1).
A346671 (program): a(n) = Sum_{k=0..n} binomial(7*k,k) / (6*k + 1).
A346672 (program): a(n) = Sum_{k=0..n} binomial(8*k,k) / (7*k + 1).
A346675 (program): First differences of A088176.
A346680 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(4*k,k) / (3*k + 1).
A346681 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(5*k,k) / (4*k + 1).
A346682 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(6*k,k) / (5*k + 1).
A346683 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(7*k,k) / (6*k + 1).
A346684 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(8*k,k) / (7*k + 1).
A346688 (program): Replace 4^k with (-1)^k in base-4 expansion of n.
A346689 (program): Replace 5^k with (-1)^k in base-5 expansion of n.
A346690 (program): Replace 6^k with (-1)^k in base-6 expansion of n.
A346691 (program): Replace 7^k with (-1)^k in base-7 expansion of n.
A346692 (program): a(n) = phi(n) - phi(n-phi(n)), a(1) = 1.
A346693 (program): Minimum integer length of a segment that touches the interior of n squares on a unit square grid.
A346695 (program): Numbers with more divisors than digits in their binary representation.
A346697 (program): Sum of the odd-indexed parts (odd bisection) of the multiset of prime indices of n.
A346698 (program): Sum of the even-indexed parts (even bisection) of the multiset of prime indices of n.
A346699 (program): Sum of the odd bisection (odd-indexed parts) of the integer partition with Heinz number n.
A346700 (program): Sum of the even bisection (even-indexed parts) of the integer partition with Heinz number n.
A346701 (program): Heinz number of the odd bisection (odd-indexed parts) of the integer partition with Heinz number n.
A346703 (program): Product of primes at odd positions in the weakly increasing list (with multiplicity) of prime factors of n.
A346704 (program): Product of primes at even positions in the weakly increasing list (with multiplicity) of prime factors of n.
A346719 (program): a(n) is the number of positive Euler permutations of order 2*n. Bisection (even indices) of A347601.
A346720 (program): a(n) is the number of negative Euler permutations of order 2*n. Bisection (even indices) of A347602.
A346731 (program): Replace 8^k with (-1)^k in base-8 expansion of n.
A346732 (program): Replace 9^k with (-1)^k in base-9 expansion of n.
A346738 (program): E.g.f.: exp(exp(x) - 3*x - 1).
A346739 (program): E.g.f.: exp(exp(x) - 4*x - 1).
A346740 (program): E.g.f.: exp(exp(x) - 5*x - 1).
A346747 (program): E.g.f.: exp( (x * exp(x) + sinh(x)) / 2 ).
A346758 (program): a(n) = Sum_{d|n} mu(n/d) * floor(d^2/4).
A346759 (program): a(n) = Sum_{d|n} floor(d^2/4).
A346762 (program): G.f. A(x) satisfies: A(x) = 1 / (1 - 2*x) + x * (1 - 2*x) * A(x)^3.
A346763 (program): G.f. A(x) satisfies: A(x) = 1 / (1 - 3*x) + x * (1 - 3*x) * A(x)^3.
A346770 (program): Expansion of g.f. Product_{k>=1} (1 - x^k)^phi(k), where phi() is the Euler totient function (A000010).
A346771 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - x)) / (1 - x^2).
A346773 (program): a(n) = Sum_{d|n} möbius(d)^n.
A346781 (program): a(n) is the numerator of the sum of the first n terms of 1 - 1/3 - 1/5 + 1/7 + 1/9 - 1/11 - 1/13 + … .
A346792 (program): G.f.: 1 / (1 + x + Sum_{k>=2} prime(k-1) * x^k).
A346794 (program): Primes p such that the largest Dyck path of the symmetric representation of sigma(p) does not touch the largest Dyck path of the symmetric representation of sigma(p+1).
A346796 (program): Number of equivalence classes of triangles in an n-dimensional hypercube, equivalent up to translation of difference vectors corresponding to edges.
A346803 (program): Numbers that are the sum of nine squares in ten or more ways.
A346804 (program): Numbers that are the sum of ten squares in five or more ways.
A346805 (program): Numbers that are the sum of ten squares in six or more ways.
A346806 (program): Numbers that are the sum of ten squares in seven or more ways.
A346807 (program): Numbers that are the sum of ten squares in eight or more ways.
A346808 (program): Numbers that are the sum of ten squares in ten or more ways.
A346811 (program): Square array read by antidiagonals upwards in which T(n, k) is the number of essentially different relations from the first proportional segment theorem for n lines, k parallel and n-k intersecting in a common point.
A346813 (program): Number of partitions of the (n+3)-multiset {0,0,0,1,2,…,n} into distinct multisets.
A346822 (program): Number of partitions of the (n+2)-multiset {0,…,0,1,2} with n 0’s into distinct multisets.
A346838 (program): a(n) = (PolyLog(-n, -i) - exp(i*Pi*n)*PolyLog(-n, i)) * i / exp(i*Pi*n/2).
A346839 (program): Decimal expansion of Sum_{n>=0} A346838(n) / n!.
A346845 (program): E.g.f.: log(1 + x) / (1 - x)^3.
A346846 (program): E.g.f.: log(1 + x) / (1 - x)^4.
A346847 (program): E.g.f.: log(1 + x) / (1 - x)^5.
A346865 (program): Sum of divisors of the n-th hexagonal number.
A346866 (program): Sum of divisors of the n-th second hexagonal number.
A346867 (program): Sum of divisors of the numbers that have middle divisors.
A346868 (program): Sum of divisors of the numbers with no middle divisors.
A346869 (program): Sum of all divisors, except the smallest and the largest of every number, of the first n odd numbers.
A346870 (program): Sum of all divisors, except the smallest and the largest of every number, of the first n positive even numbers.
A346877 (program): Sum of the divisors, except the largest, of the n-th odd number.
A346878 (program): Sum of the divisors, except the largest, of the n-th positive even number.
A346879 (program): Sum of the divisors, except the smallest and the largest, of the n-th odd number.
A346880 (program): Sum of the divisors, except the smallest and the largest, of the n-th positive even number.
A346888 (program): Expansion of e.g.f. 1 / (1 - x^2 * exp(x) / 2).
A346896 (program): Expansion of e.g.f.: (1-12*x)^(-11/12).
A346908 (program): Decimal expansion of 2 - Pi / (2*sqrt(2)).
A346909 (program): Continued fraction expansion of the constant whose decimal expansion is A269707.
A346912 (program): a(0) = 1; a(n) = a(n-1) + a(floor(n/2)) + 1.
A346932 (program): Decimal expansion of 7 * Pi^4 / 729.
A346933 (program): Decimal expansion of 2 * Pi^2 / 27.
A346943 (program): a(n) = a(n-1) + n*(n+1)*a(n-2) with a(0)=1, a(1)=1.
A346949 (program): Value of the permanent of the matrix [1-zeta^{j-k}]_{1<=j,k<=2n}, where zeta is any primitive 2n-th root of unity.
A346958 (program): a(n) is the minimal number of cubes required to make a void of volume n.
A346960 (program): a(0) = 0, a(1) = 1; a(n) = n * (n+1) * a(n-1) + a(n-2).
A346965 (program): a(n) is the number of ascending subsequences in reducing n to 1 using the Collatz reduction, or -1 if n refutes the Collatz conjecture.
A346982 (program): E.g.f.: 1 / (4 - 3 * exp(x))^(1/3).
A346983 (program): E.g.f.: 1 / (5 - 4 * exp(x))^(1/4).
A346984 (program): E.g.f.: 1 / (6 - 5 * exp(x))^(1/5).
A346985 (program): E.g.f.: 1 / (7 - 6 * exp(x))^(1/6).
A347001 (program): Expansion of e.g.f. exp( log(1 - x)^2 / 2 ).
A347011 (program): Euler transform of j-> ceiling(2^(j-2)).
A347012 (program): E.g.f.: exp(x) / (1 - 4 * x)^(1/4).
A347013 (program): E.g.f.: exp(x) / (1 - 5 * x)^(1/5).
A347014 (program): E.g.f.: exp(x) / (1 - 6 * x)^(1/6).
A347017 (program): a(n) = floor(2^(n-1)) - binomial(n,3) + binomial(n,2) - n + 1.
A347026 (program): Irregular triangle read by rows in which row n lists the first n odd numbers, followed by the first n odd numbers in decreasing order.
A347027 (program): a(1) = 1; a(n) = a(n-1) + 2 * a(floor(n/2)).
A347028 (program): a(1) = 1; a(n+1) = -Sum_{k=1..n} a(floor(n/k)).
A347030 (program): a(n) = 1 + Sum_{k=2..n} (-1)^k * a(floor(n/k)).
A347031 (program): a(n) = 1 - Sum_{k=2..n} (-1)^k * a(floor(n/k)).
A347036 (program): Number of Motzkin paths of length n avoiding UHHD.
A347047 (program): Smallest squarefree semiprime whose prime indices sum to n.
A347051 (program): a(0) = 1, a(1) = 2; a(n) = n * (n+1) * a(n-1) + a(n-2).
A347056 (program): Triangle read by rows: T(n,k) = (n+1)*(n+2)*(k+3)*binomial(n,k)/6, 0 <= k <= n.
A347061 (program): Determinant of the (2n+1) X (2n+1) matrix with the (j,k)-entry (tan(Pi*(j-k)/(2n+1)))^2 (j,k = 0..2n).
A347071 (program): E.g.f.: exp(x) * (sec(x) - tan(x)) / (1 - x).
A347072 (program): E.g.f.: -log(1 - x) * (sec(x) + tan(x)).
A347088 (program): a(n) = A055155(n) - d(n), where A055155(n) = Sum_{d|n} gcd(d, n/d) and d(n) gives the number of divisors of n.
A347089 (program): a(n) = gcd(A055155(n), d(n)), where A055155(n) = Sum_{d|n} gcd(d, n/d) and d(n) gives the number of divisors of n.
A347092 (program): Dirichlet inverse of A322577, which is the convolution of Dedekind psi with Euler phi.
A347100 (program): a(n) = phi(A003961(n)) - phi(n), where A003961 is the prime shift towards larger primes, and phi is Euler totient function.
A347101 (program): Fully multiplicative with a(prime(k)) = A001223(k), where A001223 gives the distance from the k-th prime to the (k+1)-th prime.
A347102 (program): Totally additive with a(prime(k)) = A001223(k), where A001223 gives the distance from the k-th prime to the next larger prime.
A347104 (program): Dirichlet g.f.: primezeta(s-1) * zeta(s-1) / zeta(s).
A347106 (program): Number of derangements of [n] having an even number of 2-cycles.
A347107 (program): a(n) = Sum_{1 <= i < j <= n} j^3*i^3.
A347112 (program): a(n) = concat(prime(n+1),n) mod prime(n).
A347121 (program): a(n) = A347136(n) - 2*n.
A347122 (program): Möbius transform of A347121.
A347124 (program): Möbius transform of A341528, n * sigma(A003961(n)).
A347126 (program): a(n) = A347129(A276086(n)).
A347127 (program): a(n) = A327251(n) / A003557(n).
A347128 (program): a(n) = A018804(n) / A003557(n), where A018804 is Pillai’s arithmetical function.
A347129 (program): a(n) = A347130(n) / A003557(n), where A347130 is the Dirichlet convolution of the identity function with the arithmetic derivative of n.
A347130 (program): a(n) = Sum_{d|n} d * A003415(n/d), where A003415 is the arithmetic derivative.
A347131 (program): a(n) = Sum_{d|n} phi(n/d) * A003415(d), where A003415 is the arithmetic derivative and phi is Euler totient function
A347134 (program): a(n) = Sum_{d|n} phi(n/d) * A069359(d), where phi is Euler totient function.
A347136 (program): a(n) = Sum_{d|n} d * A003961(n/d), where A003961 shifts the prime factorization of its argument one step towards larger primes.
A347137 (program): a(n) = Sum_{d|n} phi(d) * A003961(n/d), where A003961 shifts the prime factorization of its argument one step towards larger primes, and phi is Euler totient function.
A347142 (program): Sum of 4th powers of divisors of n that are < sqrt(n).
A347143 (program): Sum of 4th powers of divisors of n that are <= sqrt(n).
A347146 (program): a(n) = Sum_{d|n} (d^d)’, where ‘ is the arithmetic derivative.
A347149 (program): Dirichlet g.f.: Product_{primes p} (1 + 3/p^s).
A347152 (program): Decimal expansion of 7 * Pi / 2.
A347153 (program): Sum of all divisors, except the largest of every number, of the first n odd numbers.
A347154 (program): Sum of all divisors, except the largest of every number, of the first n positive even numbers.
A347155 (program): Sum of divisors of nontriangular numbers.
A347156 (program): Sum of squares of distinct prime divisors of n that are < sqrt(n).
A347157 (program): Sum of cubes of distinct prime divisors of n that are < sqrt(n).
A347158 (program): Sum of 4th powers of distinct prime divisors of n that are < sqrt(n).
A347159 (program): Sum of cubes of distinct prime divisors of n that are <= sqrt(n).
A347160 (program): Sum of 4th powers of distinct prime divisors of n that are <= sqrt(n).
A347161 (program): Sum of squares of odd divisors of n that are < sqrt(n).
A347162 (program): Sum of cubes of odd divisors of n that are < sqrt(n).
A347167 (program): Numbers k such that phi(binomial(k,2)) is a power of 2.
A347171 (program): Triangle read by rows where T(n,k) is the sum of Golay-Rudin-Shapiro terms GRS(j) (A020985) for j in the range 0 <= j < 2^n and having binary weight wt(j) = A000120(j) = k.
A347172 (program): Sum of 4th powers of odd divisors of n that are < sqrt(n).
A347173 (program): Sum of squares of odd divisors of n that are <= sqrt(n).
A347174 (program): Sum of cubes of odd divisors of n that are <= sqrt(n).
A347175 (program): Sum of 4th powers of odd divisors of n that are <= sqrt(n).
A347176 (program): G.f.: Sum_{k>=1} (-1)^(k+1) * k * x^(k^2) / (1 - x^(k^2)).
A347178 (program): Decimal expansion of imaginary part of (i + (i + (i + (i + …)^(1/3))^(1/3))^(1/3))^(1/3), where i is the imaginary unit.
A347191 (program): Number of divisors of n^2-1.
A347194 (program): Numbers such that the two adjacent integers are a prime and the square of another prime.
A347197 (program): Decimal expansion of arccosh(phi) where phi is the golden ratio (1 + sqrt(5))/2.
A347199 (program): Decimal expansion of sin(1) * sinh(1).
A347202 (program): Numbers whose number of odd divisors is not equal to 2.
A347233 (program): Möbius transform of A126760.
A347235 (program): Dirichlet convolution of Euler phi with A342001, where A342001(n) = A003415(n) / A003557(n).
A347246 (program): a(n) = 1 if the greatest prime factor of A000593(n) [sum of odd divisors of n] is at least as large as the greatest prime factor of n itself, otherwise a(n) = 0.
A347248 (program): Numbers k such that the greatest prime factor of A000593(k) [the sum of odd divisors of k] is less than the greatest prime factor of k itself.
A347262 (program): Positive integers that are not the numbers k for which the symmetric representation of sigma(k) has two parts, each of width one.
A347264 (program): Largest value in the 3x+1 sequence starting at n, divided by 4.
A347266 (program): a(n) is the number whose binary representation is the concatenation of terms in the n-th row of A237048.
A347267 (program): a(n) is the first term of the n-th 3x+1 sequence that shares infinitely many 1’s with the 3x+1 sequence that starts at 1.
A347268 (program): a(n) is the first term of the n-th 3x+1 sequence that shares infinitely many 1’s with the 3x+1 sequence that starts at 2.
A347269 (program): a(n) is the first term of the n-th 3x+1 sequence that shares infinitely many 1’s with the 3x+1 sequence that starts at 4.
A347270 (program): Square array T(n,k) in which row n lists the 3x+1 sequence starting at n, read by antidiagonals upwards, with n >= 1 and k >= 0.
A347272 (program): Main diagonal of the square array A347270.
A347273 (program): Number of positive widths in the symmetric representation of sigma(n).
A347274 (program): a(n) = Sum_{j=1..n} j*n^(n+1-j).
A347275 (program): a(n) is the number of nonnegative ordered pairs (a,b) satisfying (a+b <= n) and (a*b <= n).
A347283 (program): Square array read by antidiagonals upwards in which row n lists the parity of the 3x+1 sequence starting in n, with n >= 1 and k >= 0.
A347286 (program): a(n) is n minus the number of odd divisors of n.
A347289 (program): Number of independent sets in the binomial tree of order n.
A347290 (program): Arnoux-Rauzy word sigma_0 x sigma_2 x sigma_1. Fixed point of the morphism 0-> 0201020, 1->1020, 2->201020 starting from a(1)=0.
A347291 (program): Multiplicative function defined by a(p) = 2 and a(p^k) = p^(k-1) for k >= 2.
A347293 (program): Triangle read by rows: T(n, k) = Sum_{i=1..n} gcd(1 + (i-1) * (k-1),n) for 1 <= k <= n.
A347297 (program): a(1) = 1; for n >= 1, if a(n) is even then a(n+1) = a(n) / 2, otherwise, say a(n) is the k-th odd term in the sequence, a(n+1) = a(n) + k.
A347302 (program): a(n) = 3^n - lcm{1..n}, with a(0) = 0.
A347303 (program): a(n) = 3^(n-1) - lcm{1..n}.
A347319 (program): a(n) = (2*n+1)*(n^3-2*n^2+n+1).
A347325 (program): Solution to the spectator-first Tantalizer problem.
A347329 (program): Decimal expansion of Pi^4/105.
A347341 (program): Decimal expansion of (Pi^2-3)/12.
A347342 (program): a(n) = prime(n) mod floor(prime(n) / n).
A347345 (program): Decimal expansion of 1 / 1^1 + 1 / (1^1 * 2^2) + 1 / (1^1 * 2^2 * 3^3) + 1 / (1^1 * 2^2 * 3^3 * 4^4) + …
A347350 (program): Sequence obtained by writing the first 4 integers and skipping 1, then writing the next 5 integers and skipping 2, then writing the next 6 and skipping 3, etc.
A347352 (program): Decimal expansion of 1 / 1^1 - 1 / (1^1 * 2^2) + 1 / (1^1 * 2^2 * 3^3) - 1 / (1^1 * 2^2 * 3^3 * 4^4) + …
A347360 (program): Numbers that can be represented as the sum of squares of 3 numbers and also equal to twice the sum of their joint products.
A347361 (program): Number of widths that are zero in the symmetric representation of sigma(n).
A347365 (program): a(n) = n * (2-(-1)^n), or zero together with first differences of even triangular numbers halved (A074378).
A347385 (program): Dedekind psi function applied to the odd part of n: a(n) = A001615(A000265(n)).
A347386 (program): Number of iterations of A347385 (Dedekind psi function applied to the odd part of n) needed to reach a power of 2.
A347397 (program): a(n) = Sum_{k=1..n} k^k * floor(n/k^k).
A347398 (program): Expansion of g.f. Sum_{k>=1} k^k * x^(k^k)/(1 - x^(k^k)).
A347399 (program): a(n) = A347398(n^n).
A347400 (program): Lexicographically earliest sequence of distinct terms > 0 such that concatenating n to a(n) forms a palindrome in base 10.
A347405 (program): a(n) = Sum_{d|n} 2^(tau(d) - 1).
A347409 (program): Longest run of halving steps in the trajectory from n to 1 in the Collatz map (or 3x+1 problem), or -1 if no such trajectory exists.
A347411 (program): Sqrt(3)+1-adic expansion of 4, in balanced ternary alphabet.
A347412 (program): Sqrt(3)+1-adic expansion of 4, in binary alphabet
A347415 (program): a(n) = Sum_{k=1..n} floor((n/k)^k).
A347420 (program): Number of partitions of [n] where the first k elements are marked (0 <= k <= n) and at least k blocks contain their own index.
A347425 (program): a(n) = Bernoulli(2*n) * (2*n+1)! if 2*n+1 is a prime, otherwise a(n) = Bernoulli(2*n) * (2*n)!.
A347429 (program): a(n) is the alternating sum of the n-th row of A047920.
A347433 (program): Irregular triangle read by rows: T(n,k) is the difference between the total arch lengths of a semi-meander multiplied by its number of exterior arches and total arch lengths of the semi-meanders with n + 1 top arches generated by the exterior arch splitting algorithm on the given semi-meander.
A347448 (program): Number of integer partitions of n with alternating product > 1.
A347450 (program): Numbers whose multiset of prime indices has alternating product <= 1.
A347465 (program): Numbers whose multiset of prime indices has alternating product > 1.
A347476 (program): Numbers which give a prime number when 0’s and 1’s are interchanged in their binary representation.
A347477 (program): Number of total dominating sets in the complement graph of the n-cycle.
A347478 (program): Number of total dominating sets in the n-alkane graph.
A347481 (program): Number of total dominating sets in the n-dipyramidal graph.
A347493 (program): a(0) = 1, a(1) = 0, a(2) = a(3) = 1; thereafter, a(n) = a(n-1) + a(n-2) + a(n-4).
A347501 (program): Number of dominating sets in the n-alkane graph.
A347502 (program): Number of dominating sets in the n-cycle complement graph.
A347503 (program): Number of dominating sets in the n-dipyramidal graph.
A347512 (program): Number of minimal dominating sets in the n-book graph.
A347513 (program): Number of minimal dominating sets in the n-cycle complement graph.
A347516 (program): Number of divisors of n that are at most n^(1/3).
A347517 (program): Partial sums of A347516.
A347523 (program): Characteristic function of nonpowers of 2.
A347525 (program): Number of minimum dominating sets in the n-Andrásfai graph.
A347526 (program): Number of divisors of n that are at most n^(1/4).
A347528 (program): Total number of layers of width 1 of all symmetric representations of sigma() with subparts of all positive integers <= n.
A347530 (program): Primes of the form (p^2 + 9)/2 where p is prime.
A347532 (program): a(n) is the sum of the nonpowers of 2 in the 3x+1 sequence that starts at n.
A347535 (program): Number of minimum dominating sets in the complete bipartite graph K_n,n.
A347536 (program): Number of minimum dominating sets in the complete tripartite graph K_n,n,n.
A347550 (program): Number of partitions of n into at most 2 distinct prime parts.
A347552 (program): Number of partitions of n into at most 2 prime parts.
A347553 (program): Number of minimum dominating sets in the n-cycle complement graph.
A347581 (program): The Barnyard sequence: a(n) is the minimum number of unit length line segments required to enclose areas of 1 through n on a square grid.
A347586 (program): Number of partitions of n into at most 4 distinct parts.
A347587 (program): Number of partitions of n into at most 5 distinct parts.
A347596 (program): Alternating row sums of A346837.
A347597 (program): a(n) = Permanent(T(2*n + 1)) where T(n) is the tangent matrix defined in A346831. Bisection of A347598 (odd indices).
A347611 (program): a(n) is the n-th n-factorial number: a(n) = n!_n.
A347614 (program): a(n) = Sum_{k=1..n} n^Omega(k).
A347616 (program): a(n) = Sum_{k=1..n} k^Omega(k).
A347622 (program): Number of partitions of n into at most 2 prime parts (counting 1 as a prime).
A347629 (program): Number of minimum dominating sets in the n-pan graph (for n > 2).
A347633 (program): Number of minimum dominating sets in the path graph P_n.
A347643 (program): Number of partitions of n into at most 2 prime powers (including 1).
A347648 (program): Number of partitions of n into at most 2 squarefree parts.
A347665 (program): E.g.f.: exp( exp(x) * (1 + x + x^2 / 2) - 1 ).
A347667 (program): Triangle read by rows: T(n,k) = Sum_{j=0..k} binomial(n,j) * j! (0 <= k <= n).
A347671 (program): a(n) = n^n mod 100.
A347677 (program): Number of Baxter matrices of size 3 X n that contain n+2 1’s.
A347694 (program): Largest k <= 2*n such that k is a prime or twice a prime.
A347696 (program): Length of longest sequence of directed edges in the graph G (see Comments) that starts at node n.
A347697 (program): a(n) = max_{k <= n} A347696(k).
A347699 (program): Triangle read by rows: For n >= 1, 0 <= k <= n-1, T(n,k) = 0 if k=0, otherwise the number of inequivalent k X (n-k) 0,1 matrices having at least one 1 in each column.
A347702 (program): Prime numbers that give a remainder of 1 when divided by the sum of their digits.
A347714 (program): Number of compositions (ordered partitions) of n into at most 2 cubes.
A347717 (program): Number of states of the minimal deterministic finite automaton that accepts ternary strings that represent numbers that are divisible by n.
A347725 (program): Number of irredundant sets in the (2n-1)-triangular snake graph (for n > 1).
A347730 (program): Number of compositions (ordered partitions) of n into at most 2 triangular numbers.
A347731 (program): Number of compositions (ordered partitions) of n into at most 3 triangular numbers.
A347737 (program): Zero together with the partial sums of A238005.
A347739 (program): Number of compositions (ordered partitions) of n into at most 2 prime parts.
A347744 (program): Number of compositions (ordered partitions) of n into at most 2 prime parts (counting 1 as a prime).
A347762 (program): Number of compositions (ordered partitions) of n into at most 2 prime powers (including 1).
A347765 (program): a(n) is the concatenation of terms in the n-th row of triangle A237048.
A347777 (program): Number of compositions (ordered partitions) of n into at most 2 squarefree parts.
A347782 (program): Domination number of the n-tetrahedral (Johnson) graph.
A347788 (program): Number of compositions (ordered partitions) of n into at most 2 nonprime parts.
A347789 (program): a(n) is the number of times that only 2 pegs have disks on them during the optimal solution to a Towers of Hanoi problem with n disks.
A347792 (program): Beatty sequence for 2^(2/3).
A347823 (program): Triangle read by rows: T(n,k) = (n+k+1)*binomial(n,k), 0 <= k <= n.
A347826 (program): Numbers k with at least one odd semiprime divisor < k.
A347834 (program): An array A of the positive odd numbers, read by antidiagonals upwards, giving the present triangle T.
A347836 (program): a(n) = 8*(n + floor(n/3)) - 3; second column of A347834.
A347837 (program): a(n) = 32*(n + floor(n/3)) - 11; third column of A347834.
A347838 (program): Positive numbers that are congruent to 2, 5, or 11 modulo 12.
A347839 (program): An array of the positive integers congruent to 2 modulo 3 (A016789), read by antidiagonals upwards, giving the present triangle.
A347840 (program): A surjective map of the positive numbers congruent to 5 modulo 8 (A004770) to the positive numbers congruent to 1, 3, or 7 modulo 8 (A047529).
A347861 (program): a(n) = A000032(n)*A000032(n+1) mod A000032(n+2).
A347870 (program): a(n) = A003415(sigma(n)) mod 2, where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n.
A347871 (program): a(n) = (n+A003415(sigma(n))) mod 2, where A003415 gives the arithmetic derivative of its argument.
A347872 (program): Numbers k such that k and A003415(sigma(k)) have the same parity.
A347873 (program): Numbers k such that k and A003415(sigma(k)) are of different parity.
A347877 (program): Numbers k for which A003415(sigma(k)) is odd.
A347878 (program): Numbers k for which A003415(sigma(k)) is even.
A347880 (program): Numbers k such that A342926(k) is a multiple of 3.
A347885 (program): Odd numbers k such that sigma(k^2) has an odd number of prime factors when counted with multiplicity.
A347886 (program): Odd numbers k such that sigma(k^2) has an even number of prime factors when counted with multiplicity.
A347902 (program): a(n) = a(n-1) + a(n-3) + a(n-4) with initial values a(0) = 8, a(1)=5, a(2) = 13, a(3) = 30.
A347909 (program): Decimal expansion of Integral_{x=0..1} exp(-x^2) dx.
A347910 (program): Decimal expansion of Integral_{x=0..1} exp(x^2) dx.
A347912 (program): a(n) = Sum_{k=1..n} k - floor(sqrt(k)+1/2) * floor(sqrt(k-1)).
A347922 (program): Number of minimal total dominating sets in the n X n rook complement graph.
A347941 (program): For sets of n random points in the real plane, a(n) is an upper bound for the minimal number of nearest neighbors.
A347945 (program): To get {a(n)}, start with the nonnegative integers sequence f() and, for each y>=0, shift the f(y) to position f(2y) and reset indices.
A347950 (program): Characteristic function of numbers that have middle divisors.
A347952 (program): Decimal expansion of exp(1) * (gamma - Ei(-1)).
A347958 (program): Inverse Möbius transform of A345000.
A347964 (program): Greatest common divisor of A003415 (arithmetic derivative) and A003961 (prime shift towards larger primes).
A347976 (program): Triangle T(n,k) read by rows: the rows list volumes of rank 2 Schubert matroid polytopes.
A347981 (program): Irregular triangle T(n, k) read by rows in which row n lists the number of parts in the symmetric representation of sigma for n = 2^m * q, 2^(m-1) * q, … , q, with m >= 0, q odd, 1 <= k <= m + 1.
A347992 (program): a(n) = Sum_{d|n} (-1)^(tau(d) - 1).
A347993 (program): a(n) = n! * Sum_{k=1..n} (-1)^(k+1) * n^(n-k) / (n-k)!.
A347994 (program): a(n) = n! * Sum_{k=1..n-1} (-1)^(k+1) * n^(n-k-2) / (n-k-1)!.
A348005 (program): Positive even integers with an even number of even divisors.
A348006 (program): Largest increment in the trajectory from n to 1 in the Collatz map (or 3x+1 problem), or -1 if no such trajectory exists.
A348011 (program): a(n) = phi(n^2) * Sum_{d|n} 2^omega(d) / d.
A348012 (program): Invert transform of A037952.
A348015 (program): Number of periodic n X n matrices over GF(2).
A348018 (program): a(n) is the index of A064549(n) = n * Product_{p prime|n} p in the sequence of powerful numbers (A001694).
A348027 (program): Dirichlet convolution of Euler phi with A324198.
A348028 (program): Greatest common divisor of A003415 (arithmetic derivative) and sigma, the sum of divisors function.
A348029 (program): a(n) = A003959(n) - sigma(n), where A003959 is multiplicative with a(p^e) = (p+1)^e and sigma is the sum of divisors.
A348030 (program): a(n) = A003968(n) - n, where A003968 is multiplicative with a(p^e) = p*(p+1)^(e-1).
A348036 (program): a(n) = gcd(n, A003968(n)), where A003968 is multiplicative with a(p^e) = p*(p+1)^(e-1).
A348037 (program): a(n) = n / gcd(n, A003968(n)), where A003968 is multiplicative with a(p^e) = p*(p+1)^(e-1).
A348038 (program): a(n) = A003968(n) / gcd(n, A003968(n)), where A003968 is multiplicative with a(p^e) = p*(p+1)^(e-1).
A348044 (program): The nearest common ancestor of n and n^2 in the Doudna tree (A005940).
A348047 (program): a(n) = gcd(sigma(n), A003959(n)), where A003959 is multiplicative with a(p^e) = (p+1)^e and sigma is the sum of divisors function.
A348048 (program): a(n) = sigma(n) / gcd(sigma(n), A003959(n)), where A003959 is multiplicative with a(p^e) = (p+1)^e and sigma is the sum of divisors function.
A348049 (program): a(n) = A003959(n) / gcd(sigma(n), A003959(n)), where A003959 is multiplicative with a(p^e) = (p+1)^e and sigma is the sum of divisors function.
A348060 (program): a(n) = Sum_{k=1..n, gcd(n,k) = 1} (k-1) / gcd(n,k-1).
A348061 (program): a(n) = Sum_{k=1..n, gcd(n,k) = 1} n / gcd(n,k-1).
A348063 (program): Coefficient of x^2 in expansion of n!* Sum_{k=0..n} binomial(x,k).
A348094 (program): If the Collatz trajectory of n reaches 1, say after k steps, and there is an integer m > n such that T^i(m) and T^i(n) have the same parity for i = 0..k (where T^i denotes the i-th iterate of the Collatz map A006370), then a(n) is the least such m, otherwise a(n) is -1.
A348097 (program): Numbers having equally many unitary and nonunitary prime divisors.
A348110 (program): Number of positive integers <= n that have middle divisors.
A348112 (program): a(n) = t(n)*a(n-1) + a(n-2) for n>1 where t(n) is the Prouhet-Thue-Morse sequence A106400 with a(0)=0 and a(1)=1.
A348124 (program): Number of compositions of n where the smallest part is smaller than the number of parts.
A348131 (program): a(n) is the numerator of the relativistic sum of n velocities of 1/n, in units where the speed of light is 1.
A348132 (program): a(n) is the denominator of the relativistic sum of n velocities of 1/n, in units where the speed of light is 1.
A348140 (program): a(n) is the numerator of tan(n * arctan(1/n)).
A348141 (program): a(n) is the denominator of tan(n * arctan(1/n)).
A348145 (program): a(n) = Sum_{d|n} (n-d) * d!.
A348149 (program): Variation of the Barnyard sequence A347581: a(n) is the minimum number of unit length line segments required to enclose areas of 1 through n on a square grid when the number of segments is minimized as each area of incrementing size, starting at 1, is added.
A348156 (program): S_3-primes: let S_3 = {1,4,7,…,3i+1,…}; then an S_3-prime is in S_3 but is not divisible by any elements of S_3 except for itself and 1.
A348161 (program): Number of factorizations of (n,n) into one or two pairs (i,j) with i > 0, j > 0 (and if i=1 then j=1).
A348166 (program): a(n) = abs(A020338(n)-A338754(n))
A348175 (program): Irregular table T(n,k) read by rows: T(n,k) = T(n-1,k/2) when k is even and 3*T(n-1,(k-1)/2) + 2^(n-1) when k is odd. T(0,0) = 0 and 0 <= k <= 2^n-1.
A348182 (program): a(1) = 1; for n >= 2, a(n) = 1 + a(A057022(n)).
A348189 (program): Pseudo-involutory Riordan companion of 1 + 2*x*M(x), where M(x) is the g.f. of A001006.
A348192 (program): a(0) = 0; for n >= 1, a(n) = 1 + a(n - GCD(n, digital sum(n)))
A348193 (program): (Number of primes == 3 mod 4 less than n^2) - (number of primes == 1 mod 4 less than n^2).
A348194 (program): a(n) = A077767(n) - A077766(n).
A348195 (program): Number of primes of the form 4k+3 < n^2.
A348196 (program): Number of primes of the form 4k+1 < n^2.
A348203 (program): a(n) = n - omega(n) + n * Sum_{p|n} 1/p.
A348219 (program): a(n) = tau(n) - omega(n) + n * Sum_{p|n} 1/p.
A348223 (program): a(n) = Sum_{d|n} (-1)^(sigma(d) - 1).
A348225 (program): a(n) = Sum_{d|n} binomial(n,d)^d.
A348227 (program): Coordination sequence for Wilkinson’s 123-circle packing with respect to a circle of radius 1.
A348228 (program): Partial sums of A348227.
A348229 (program): Coordination sequence for Wilkinson’s 123-circle packing with respect to a circle of radius 2.
A348230 (program): Partial sums of A348229.
A348231 (program): Coordination sequence for Wilkinson’s 123-circle packing with respect to a circle of radius 3.
A348232 (program): Partial sums of A348231.
A348253 (program): Indices of records in A348246.
A348257 (program): Number of ways we can write [n] as the union of 2 sets of sizes i, j which intersect in exactly 2 elements (2 < i,j < n; i = j allowed).
A348259 (program): Number of bases 1<b<n and coprime to n, such that b^n == b (mod n).
A348271 (program): a(n) is the sum of noninfinitary divisors of n.
A348278 (program): a(n) = Sum_{d|n} d^(d’).
A348279 (program): a(n) = Sum_{d|n} d*d’, where d’ is the arithmetic derivative of d (A003415).
A348280 (program): a(n) = Sum_{d|n} n^(d’).
A348281 (program): a(n) = Sum_{d|n} d’ * mu(d)^2.
A348282 (program): a(n) = Sum_{d|n, d>1} mu(d’)^2.
A348283 (program): Numbers k such that k’ | k.
A348284 (program): Numbers k such that k | k” where k” is the 2nd arithmetic derivative of k.
A348287 (program): Arrange nonzero digits of n in increasing order then append the zeros.
A348289 (program): a(n) = Sum_{k=0..floor(n/8)} binomial(n-4*k,4*k).
A348290 (program): a(n) = Sum_{k=0..floor(n/10)} binomial(n-5*k,5*k).
A348299 (program): Indices of 0 in A348295: numbers m such that Sum_{k=1..m} (-1)^(floor(k*(sqrt(2)-1))) = Sum_{k=1..m} (-1)^A097508(k) = 0.
A348301 (program): a(n) is the difference between the numerator and denominator of the (reduced) fraction Sum_{i = 1..n} 1/prime(i).
A348304 (program): a(n) = Sum_{d|n} d’’, where d’’ is the second arithmetic derivative of d (A068346).
A348308 (program): a(n) = Sum_{k=0..floor(n/6)} (-1)^k * binomial(n-3*k,3*k).
A348309 (program): a(n) = Sum_{k=0..floor(n/8)} (-1)^k * binomial(n-4*k,4*k).
A348311 (program): a(n) = n! * Sum_{k=1..n} (-1)^k * (k-2) / (k-1)!.
A348312 (program): a(n) = n! * Sum_{k=0..n-1} 3^k / k!.
A348314 (program): a(n) = n! * Sum_{k=0..n-1} 4^k / k!.
A348315 (program): a(n) = Sum_{k=0..n} binomial(n^2 - k,n*k).
A348324 (program): Number of compositions (ordered partitions) of n into two or more primes.
A348327 (program): Characteristic function of numbers that have no middle divisors.
A348331 (program): Lexicographically earliest sequence of positive integers such that for any n > 0, the sum of the indices k < n such that a(k) = a(n) is less than or equal to n.
A348336 (program): Number of positive integers <= n that have no middle divisors.
A348338 (program): a(n) is the number of distinct numbers of steps required for the last n digits of integers to repeat themselves by iterating the map m -> 2*m.
A348339 (program): a(n) is the number of distinct numbers of steps required for the last n digits of integers to repeat themselves by iterating the map m -> m^2.
A348341 (program): a(n) is the number of noninfinitary divisors of n.
A348349 (program): a(n) = Sum_{d|n} d^(tau(d) - 1).
A348350 (program): a(n) = Sum_{d|n} d^(sigma(d) - 1).
A348354 (program): The base-5 expansion of a(n) is obtained by replacing 1’s, 2’s, 3’s and 4’s by 3’s, 4’s, 1’s and 2’s, respectively, in the base-5 expansion of n.
A348357 (program): Square array T(n, k), n, k > 0, read by antidiagonal upwards; the k-th column contains, in ascending order, the integers m such that A348331(m) = k.
A348361 (program): a(n) = Sum_{k=1..n} k^(k’), where ‘ is the arithmetic derivative.
A348364 (program): Number of vertices on the axis of symmetry of the symmetric representation of sigma(n).
A348367 (program): a(n) = w(n + w(n)), where w(n) is the binary weight of n, A000120(n).
A348368 (program): Numbers k such that w(k + w(k)) < w(k), where w(k) is the binary weight of k, A000120(k).
A348375 (program): a(n) = Sum_{k=1..n} (n^k)’ where ‘ is the arithmetic derivative.
A348376 (program): a(n) = Sum_{k=1..n} n^(k’), where ‘ is the arithmetic derivative.
A348378 (program): Number of ways to reach n by starting with any positive integer, and repeatedly adding any positive integer or multiplying by any integer greater than 1.
A348382 (program): Number of compositions of n that are not a twin (x,x) but have adjacent equal parts.
A348388 (program): Irregular triangle read by rows: T(n, k) = floor((n-k)/k), for k = 1, 2, …, floor(n/2) and n >= 2.
A348391 (program): Row sums of irregular triangle A348390.
A348392 (program): Row sums of the irregular triangle A348389.
A348396 (program): Number of ways to reach n by starting with 1 and repeatedly adding any positive integer or multiplying by any integer greater than 1.
A348398 (program): a(n) = Sum_{d|n} sigma_n/d, where sigma_k is the sum of the k-th powers of the divisors of n.
A348401 (program): a(n) is the least m > 0 such that n = m! / k! for some k <= m.
A348405 (program): a(0) = 1, a(n) + a(n+1) = round(2^n/9), n >= 0.
A348406 (program): Number of vertices on the axis of symmetry of the symmetric representation of sigma(n) with subparts.
A348407 (program): a(n) = ((n+1)*3*2^(n+1) + 29*2^n + (-1)^n)/9.
A348410 (program): Number of nonnegative integer solutions to n = Sum_{i=1..n} (a_i + b_i), with b_i even.
A348416 (program): For n >= 1; a(n) = gcd(n,w(n)) where w(n) is the binary weight of n, A000120(n).
A348417 (program): Number of coprime squares modulo A081754(n): a(n) = A046073(A081754(n)).
A348419 (program): Triangular table read by rows: T(n,k) is the k-th entry of the main diagonal of the inverse Hilbert matrix of order n.
A348420 (program): a(n) = Product_{k=1..n} (p_k - 1)/2 where p_1, p_2, …, p_n are the first n primes congruent to 3 modulo 4.
A348421 (program): Primes p == 3 (mod 4) such that (p+3)/2 is not prime.
A348423 (program): Odd composite numbers k such that 2*k-3 is prime.
A348431 (program): a(n) = (n’)^(n’), where ‘ is the arithmetic derivative of n.
A348435 (program): Decimal expansion of (2/3)*e in Coulombs, two thirds of the elementary charge.
A348457 (program): a(n) = Sum_{s=0..n} (-1)^s * ( Sum_{k=0..s} binomial(n,k) )^3.
A348465 (program): a(n) = minimum L such that a ternary linear code of length L, dimension 6, and minimum distance n exists.
A348468 (program): Expansion of e.g.f. sqrt(exp(x)*(2-exp(x))).
A348471 (program): One half of the even numbers without middle divisors.
A348473 (program): a(n) = Sum_{k=1..A003056(n)} 2^(T(n,k)-1), where T(n,k) = k-th term in row n of A235791.
A348476 (program): Number of compositions of n into exactly n nonnegative parts such that all positive parts are odd.
A348482 (program): Triangle read by rows: T(n,k) = (Sum_{i=k..n} i!)/(k!) for 0 <= k <= n.
A348484 (program): Maximum number of squares on an n X n chessboard such that no two are two steps apart horizontally or vertically.
A348492 (program): Greatest common divisor of the arithmetic derivative (A003415) and Pillai’s arithmetical function (A018804).
A348493 (program): a(n) = A003415(n) / gcd(A003415(n), A018804(n)), where A003415 is the arithmetic derivative and A018804 is Pillai’s arithmetical function.
A348494 (program): a(n) = A348492(n) / A003557(n), where A348492 is the GCD of the arithmetic derivative (A003415) and Pillai’s arithmetical function (A018804).
A348495 (program): a(n) = gcd(A018804(n), A347130(n)), where A347130 is the Dirichlet convolution of the identity function with the arithmetic derivative of n (A003415), and A018804 is Pillai’s arithmetical function.
A348497 (program): a(n) = gcd(A003415(n), A347130(n)), where A003415 is the arithmetic derivative and A347130 is its Dirichlet convolution with the identity function.
A348498 (program): a(n) = gcd(A003415(n), A347130(n)) / A003557(n), where A003415 is the arithmetic derivative and A347130 is its Dirichlet convolution with the identity function.
A348499 (program): Numbers k such that A003968(k) is a multiple of k, where A003968 is multiplicative with a(p^e) = p*(p+1)^(e-1).
A348500 (program): a(n) = A348494(A276086(n)).
A348502 (program): a(n) = A348498(A276086(n)).
A348503 (program): a(n) = gcd(sigma(n), usigma(n)), where sigma is the sum of divisors function, A000203, and usigma is the unitary sigma, A034448.
A348504 (program): a(n) = sigma(n) / gcd(sigma(n), usigma(n)), where sigma is the sum of divisors function, A000203, and usigma is the unitary sigma, A034448.
A348505 (program): a(n) = usigma(n) / gcd(sigma(n), usigma(n)), where sigma is the sum of divisors function, A000203, and usigma is the unitary sigma, A034448.
A348506 (program): Numbers k such that sigma(k) is a multiple of usigma(k), where sigma is the sum of divisors function, A000203, and usigma is the unitary sigma, A034448.
A348507 (program): a(n) = A003959(n) - n, where A003959 is multiplicative with a(p^e) = (p+1)^e.
A348508 (program): a(n) = A003959(n) - 2*n, where A003959 is multiplicative with a(p^e) = (p+1)^e.
A348509 (program): a(n) is the numerator of the harmonic mean of the divisors of A003961(n).
A348510 (program): a(n) = A099377(n) - n, where A099377(n) is the numerator of the harmonic mean of the divisors of n.
A348512 (program): a(n) = A003959(sigma(n)), where A003959 is multiplicative with a(p^e) = (p+1)^e and sigma is the sum of divisors function.
A348513 (program): Möbius transform of A048146, the sum of non-unitary divisors of n.
A348515 (program): a(n) = Sum_{d|n, d <= sqrt(n)} (-1)^(n/d + 1).
A348529 (program): Number of compositions (ordered partitions) of n into two or more triangular numbers.
A348536 (program): Number of partitions of n into 3 parts that divide n.
A348537 (program): Number of partitions of n into 3 parts whose largest part divides n.
A348539 (program): Triangle T(n, m) = binomial(n+2, m)*binomial(n+2, n-m), read by rows.
A348540 (program): Number of partitions of n into 3 parts whose smallest part divides the largest part.
A348542 (program): Number of partitions of n into 3 parts where at least one part is even.
A348543 (program): Number of partitions of n into 3 parts with at least 1 odd part.
A348556 (program): Binary expansion contains 4 adjacent 1’s.
A348573 (program): Decimal expansion of exp(-1) * (Ei(1) - gamma).
A348577 (program): Positive integers that are not the perimeter of any integer-sided right triangle.
A348580 (program): Expansion of e.g.f. exp(x) / (1 - sin(x)).
A348589 (program): a(n) = (10^n+2)^2 / 6.
A348590 (program): Number of endofunctions on [n] with exactly one isolated fixed point.
A348591 (program): a(n) = L(n)*L(n+1) mod F(n+2) where F=A000045 is the Fibonacci numbers and L = A000032 is the Lucas numbers.
A348592 (program): a(n) = F(n)*F(n+1) mod L(n+2) where F=A000045 is the Fibonacci numbers and L = A000032 is the Lucas numbers.
A348596 (program): a(n) = A068527(2*n+1).
A348597 (program): a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^k / (3*k)!.
A348607 (program): Decimal expansion of BesselJ(1,2).
A348608 (program): a(n) = Sum_{d|n, d <= sqrt(n)} (-1)^(d + n/d) * d.
A348612 (program): Numbers k such that the k-th composition in standard order is not an anti-run, i.e., has adjacent equal parts.
A348615 (program): Number of non-alternating permutations of {1…n}.
A348618 (program): a(n) = (1+(-1)^n)/2*4^n*(C((3*n)/2-1,n))+(1-(-1)^n)/2*((C((3*n-1)/2,n))*(C(3*n-1,(3*n-1)/2)))/(C(n-1,(n-1)/2)).
A348621 (program): The number of additions required to compute the permanent of general n X n matrices using Ryser’s formula without Gray code ordering.
A348622 (program): Triangular array read by rows: T(n,k) is the number of periodic n X n matrices over GF(2) having rank k, n>=0, 0<=k<=n.
A348623 (program): a(1) = 1; for n > 1 a(n) = a(n-1) + A001227(a(n-1)).
A348636 (program): Greedy Cantor’s Dust Partition.
A348642 (program): a(n) = Product_{k=1..A003056(n)} prime(k)^T(n,k), with row n of T = row n of A237591.
A348643 (program): a(n) = (16*n + 1)*(2592*n^2 + 288*n + 7).
A348644 (program): a(n) = (18*n + 1)*(24*n + 1)*(144*n + 11).
A348645 (program): a(n) = (12*n + 1)*(5184*n^2 + 540*n + 13).
A348646 (program): a(n) = (72*n + 5)*(1296*n^2 + 153*n + 4).
A348660 (program): a(n) = Sum_{d|n, d <= sqrt(n)} (-1)^(n/d + 1) * d.
A348662 (program): a(n) = Sum_{m=0..n} (-1)^m * ( Sum_{k=0..m} binomial(n,k) )^2.
A348665 (program): Number of partitions of n into 3 parts whose smallest and middle parts divide n.
A348670 (program): Decimal expansion of 10 - Pi^2.
A348675 (program): a(n) = Sum_{k=0..n-1} Omega(n^2-k^2).
A348676 (program): Triangle read by rows, T(n, k) = 2^(n - HammingWeight(k)), for 0 <= k <= n.
A348677 (program): a(n) is the difference between A262275(n) and the next lower prime.
A348684 (program): Triangle read by rows, T(n, k) = 2*n - HammingWeight(k), for 0 <= k <= n.
A348685 (program): Triangle read by rows, T(n, k) = 2^(2*n - HammingWeight(k)), for 0 <= k <= n.
A348687 (program): Triangle read by rows, T(n, k) = n - HammingWeight(k), for 0 <= k <= n.
A348688 (program): a(n) = sigma(n) + sigma(n+1) + sigma(n+2) - sigma(n+3), where sigma is the sum of divisors.
A348689 (program): a(n) = sigma(n) + sigma(n+1) - sigma(n+2), where sigma is the sum of divisors.
A348705 (program): a(n) is the total length of all line segments in the symmetric representation of sigma(n).
A348706 (program): Delete all 0’s from ternary expansion of n.
A348710 (program): In the binary expansion of n, decrease the length of each run of 1-bits by one.
A348717 (program): a(n) is the least k such that A003961^i(k) = n for some i >= 0 (where A003961^i denotes the i-th iterate of A003961).
A348720 (program): Decimal expansion of 4*cos(2*Pi/13)*cos(3*Pi/13).
A348721 (program): Decimal expansion of 4*cos(4*Pi/13)*cos(6*Pi/13).
A348722 (program): Decimal expansion of 4*cos(8*Pi/13)*cos(12*Pi/13).
A348723 (program): Decimal expansion of the positive root of Shanks’ simplest cubic associated with the prime p = 19.
A348724 (program): Decimal expansion of the absolute value of one of the negative roots of Shanks’ simplest cubic associated with the prime p = 19.
A348725 (program): Decimal expansion of the absolute value of one of the negative roots of Shanks’ simplest cubic associated with the prime p = 19.
A348726 (program): Decimal expansion of the positive root of Shanks’ simplest cubic associated with the prime p = 37.
A348727 (program): Decimal expansion of the absolute value of one of the negative roots of Shanks’ simplest cubic associated with the prime p = 37.
A348728 (program): Decimal expansion of the absolute value of one of the negative roots of Shanks’ simplest cubic associated with the prime p = 37.
A348732 (program): a(n) = A003959(n) - A034448(n), where A003959 is multiplicative with a(p^e) = (p+1)^e and A034448 (usigma) is multiplicative with a(p^e) = (p^e)+1.
A348733 (program): a(n) = gcd(A003959(n), A034448(n)), where A003959 is multiplicative with a(p^e) = (p+1)^e and A034448 (usigma) is multiplicative with a(p^e) = (p^e)+1.
A348734 (program): Numerator of Product((p+1)^e / ((p^e)+1)), when n = Product(p^e), with p primes, and e their exponents.
A348735 (program): Denominator of Product((p+1)^e / ((p^e)+1)), when n = Product(p^e), with p primes, and e their exponents.
A348736 (program): a(n) = n - A326042(n), where A326042(n) = A064989(sigma(A003961(n))).
A348737 (program): a(n) = 1 if A326042(k) < k, otherwise 0.
A348738 (program): Numbers k for which A326042(k) < k.
A348739 (program): Numbers k for which A326042(k) > k.
A348741 (program): Odd numbers k for which A161942(k) < k, where A161942 is the odd part of sigma.
A348757 (program): Decimal expansion of the area of a regular pentagram inscribed in a unit-radius circle.
A348759 (program): (43200/719)*{a(n)} are the times, measured in seconds from 00:00:00, at which the angle of the sector enclosing the three hands of an analog clock has a local minimum.
A348760 (program): For any nonnegative number n with binary expansion Sum_{k >= 0} b_k * 2^k, a(n) is the real part of f(n) = Sum_{k >= 0} ((-1)^Sum_{j = 0..k-1} b_j) * (1+i)^k (where i denotes the imaginary unit); sequence A348761 gives the imaginary part.
A348761 (program): For any nonnegative number n with binary expansion Sum_{k >= 0} b_k * 2^k, a(n) is the imaginary part of f(n) = Sum_{k >= 0} ((-1)^Sum_{j = 0..k-1} b_j) * (1+i)^k (where i denotes the imaginary unit); sequence A348760 gives the real part.
A348762 (program): a(n) = A000265((n-8)*(n+8)).
A348768 (program): Number of inequivalent solutions to the problem of the maximal number of squares that can be formed from n points in the plane (see A051602).
A348774 (program): A348773(2*n+1).
A348776 (program): The numbers >= 2 with 3 repeated.
A348783 (program): Let c(i) be the number of times the digit i appears in n, for 0 <= i <= 9; then a(n) is the concatenation of c(9) c(8) … c(1) c(0), with leading 0’s omitted.
A348793 (program): G.f. A(x) satisfies: A(x) = (1 + x * A(x)^3) / (1 - 2 * x).
A348794 (program): a(n) = number of 3-regular one-face rooted maps on orientable surfaces.
A348840 (program): Triangle T(n,h) read by rows: The number of Motzkin Paths of n>=2 steps that start with an Up step and touch the horizontal axis h>=1 times afterwards.
A348841 (program): Number of primes with even exponents >= 2 in the prime power factorization of n!, for n >= 1.
A348845 (program): Part two of the trisection of A017101: a(n) = 11 + 24*n.
A348852 (program): Numbers k such that the number of odd nonprimes <= k is equal to the number of primes <= k.
A348853 (program): Delete any least significant 0’s from the Zeckendorf representation of n, leaving its “odd” part.
A348854 (program): a(n) is the total length of all line segments in an octant of the symmetric representation of sigma(n).
A348856 (program): a(n) = Sum_{d|n} (Stirling2(n,d) mod 2).
A348864 (program): a(n) is the number of multiplications required to compute the permanent of general n X n matrices using trellis method with normalization.
A348874 (program): Decimal expansion of Sum_{k>=0} (-1)^k / (k!)^3.
A348893 (program): a(n) = 840*(2*n)!/((n + 4)!*n!).
A348898 (program): a(n) = 15120*(2*n)!/(n!*(n + 5)!); super ballot numbers, row 4 of A135573.
A348899 (program): a(n) = 332640*4^n*Gamma(n + 1/2)/(sqrt(Pi)*Gamma(n + 7)); super ballot numbers, row 5 of A135573.
A348901 (program): G.f. A(x) satisfies: A(x) = 1 / (1 + x - 2 * x * A(2*x)).
A348906 (program): Squares with a square number of 1’s in their binary expansion.
A348907 (program): If n is prime, a(n) = n, else a(n) = a(n-pi(n)), n >= 2; where pi is the prime counting function A000720.
A348908 (program): Decimal expansion of the positive real root of x^4 - 3*x - 6.
A348909 (program): Decimal expansion of the real root of x^3 + x^2 - 2*x - 4.
A348912 (program): G.f. A(x) satisfies: A(x) = (1 + 2 * x * A(x)^3) / (1 - x).
A348915 (program): a(n) = Sum_{d|n} d^(d mod 2).
A348919 (program): Sum of the middle parts of the partitions of k into 3 parts for all 0 <= k <= n.
A348928 (program): a(n) = gcd(n, A003958(n)), where A003958 is multiplicative with a(p^e) = (p-1)^e.
A348929 (program): a(n) = gcd(n, A003959(n)), where A003959 is multiplicative with a(p^e) = (p+1)^e.
A348930 (program): a(n) = A038502(sigma(n)), where A038502 is fully multiplicative with a(3) = 1, and a(p) = p for any other prime p.
A348932 (program): Numbers k congruent to 1 or 5 mod 6, for which A348930(k) > k.
A348937 (program): a(n) = A003961(n) - A003415(n), where A003961 shifts the prime factorization of n one step towards larger primes, and A003415 gives the arithmetic derivative of n.
A348940 (program): a(n) = gcd(n, A326042(n)), where A326042 is multiplicative function A064989(sigma(A003961(n))).
A348941 (program): a(n) = n / gcd(n, A326042(n)).
A348942 (program): a(n) = A326042(n) / gcd(n, A326042(n)).
A348944 (program): a(n) = (1/2) * (A003959(n)+A034448(n)), where A003959 is multiplicative with a(p^e) = (p+1)^e and A034448 (usigma) is multiplicative with a(p^e) = (p^e)+1.
A348945 (program): a(n) = A348944(n) - sigma(n), where A348944 is the arithmetic mean of A003959 and A034448, and sigma is the sum of divisors function.
A348946 (program): a(n) = gcd(sigma(n), A348944(n)), where A348944 is the arithmetic mean of A003959 and A034448, and sigma is the sum of divisors function.
A348947 (program): a(n) = A348944(n) / gcd(sigma(n), A348944(n)), where A348944 is the arithmetic mean of A003959 and A034448, and sigma is the sum of divisors function.
A348948 (program): a(n) = sigma(n) / gcd(sigma(n), A348944(n)), where A348944 is the arithmetic mean of A003959 and A034448, and sigma is the sum of divisors function.
A348949 (program): a(n) = A003959(A276086(n)), where A003959 is multiplicative with a(p^e) = (p+1)^e, and A276086 gives the prime product form of primorial base expansion of n.
A348950 (program): a(n) = A348507(A276086(n)), where A348507(n) = A003959(n) - n, A003959 is multiplicative with a(p^e) = (p+1)^e, and A276086 gives the prime product form of primorial base expansion of n.
A348951 (program): a(n) = Sum_{d|n, d < sqrt(n)} (-1)^(n/d).
A348952 (program): a(n) = -Sum_{d|n, d < sqrt(n)} (-1)^(d + n/d).
A348953 (program): a(n) = -Sum_{d|n, d < sqrt(n)} (-1)^(d + n/d) * d.
A348954 (program): a(n) = Sum_{d|n, d < sqrt(n)} (-1)^(n/d) * d.
A348957 (program): G.f. A(x) satisfies: A(x) = (1 + x * A(-x)) / (1 - x * A(x)).
A348960 (program): a(n) = floor(log_10(Pi*n!)).
A348968 (program): a(n) = gcd(n, A099377(n)), where A099377(n) is the numerator of the harmonic mean of the divisors of n.
A348969 (program): a(n) = n / gcd(n, A099377(n)).
A348970 (program): a(n) = A003959(n) - A129283(n), where A003959 is multiplicative with a(p^e) = (p+1)^e and A129283(n) is sum of n and its arithmetic derivative.
A348971 (program): a(n) = Product(p*(p+1)^(e-1)) - Product((p-1)*p^(e-1)), when n = Product(p^e), with p primes, and e their exponents.
A348972 (program): a(n) = gcd(A003959(n), A129283(n)), where A003959 is multiplicative with a(p^e) = (p+1)^e and A129283(n) is sum of n and its arithmetic derivative.
A348973 (program): Numerator of ratio A129283(n) / A003959(n), where A003959 is multiplicative with a(p^e) = (p+1)^e and A129283(n) is sum of n and its arithmetic derivative.
A348974 (program): Denominator of ratio A129283(n) / A003959(n), where A003959 is multiplicative with a(p^e) = (p+1)^e and A129283(n) is sum of n and its arithmetic derivative.
A348975 (program): a(n) = A003415(n) + A003958(n) - n, where A003415 is the arithmetic derivative and A003958 is fully multiplicative with a(p) = (p-1).
A348976 (program): Möbius transform of A129283, which is sum of n and its arithmetic derivative.
A348977 (program): a(n) = gcd(sigma(n), A332993(n)).
A348978 (program): Numerator of ratio A332993(n) / sigma(n).
A348979 (program): Denominator of ratio A332993(n) / sigma(n).
A348980 (program): a(n) = Sum_{d|n} d * A322582(n/d), where A322582(n) = n - A003958(n), and A003958 is fully multiplicative with a(p) = (p-1).
A348981 (program): a(n) = Sum_{d|n} phi(n/d) * A322582(d), where A322582(n) = n - A003958(n), and A003958 is fully multiplicative with a(p) = (p-1).
A348984 (program): a(n) = gcd(sigma(n), A325973(n)), where A325973 is the arithmetic mean of {sum of squarefree divisors} and {sum of unitary divisors}.
A348985 (program): Numerator of ratio sigma(n) / A325973(n), where A325973 is the arithmetic mean of {sum of squarefree divisors} and {sum of unitary divisors}.
A348986 (program): Denominator of ratio sigma(n) / A325973(n), where A325973 is the arithmetic mean of {sum of squarefree divisors} and {sum of unitary divisors}.
A348987 (program): a(n) = gcd(sigma(n), A332994(n)).
A348988 (program): Numerator of ratio A332994(n) / sigma(n).
A348989 (program): Denominator of ratio A332994(n) / sigma(n).
A348990 (program): a(n) = n / gcd(n, A003961(n)), where A003961(n) is fully multiplicative function with a(prime(k)) = prime(k+1).
A348991 (program): a(n) = A333791(A276086(n)).
A348992 (program): a(n) = A000265(sigma(n)) / gcd(sigma(n), A003961(n)), where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors function.
A348993 (program): a(n) = A064989(sigma(n) / gcd(sigma(n), A003961(n))), where A003961 shifts the prime factorization of n one step towards larger primes, while A064989 shifts it back towards smaller primes, and sigma is the sum of divisors function.
A348994 (program): a(n) = A003961(n) / gcd(n, A003961(n)), where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1).
A348996 (program): a(n) = usigma(A276086(n)), where usigma (A034448) is multiplicative with a(p^e) = (p^e)+1, and A276086 gives the prime product form of primorial base expansion of n.
A348997 (program): a(n) = A348733(A276086(n)), where A348733(n) = gcd(A003959(n), A034448(n)), and A276086 gives the prime product form of primorial base expansion of n.
A348998 (program): a(n) = A348928(A276086(n)), where A348928(n) = gcd(n, A003958(n)), and A003958 is multiplicative with a(p^e) = (p-1)^e, and A276086 gives the prime product form of primorial base expansion of n.
A348999 (program): a(n) = A348929(A276086(n)), where A348929(n) = gcd(n, A003959(n)), A003959 is multiplicative with a(p^e) = (p+1)^e, and A276086 gives the prime product form of primorial base expansion of n.
A349000 (program): a(n) = A323166(A276086(n)), where A323166(n) = gcd(n, usigma(n)), usigma (A034448) is multiplicative with a(p^e) = (p^e)+1, and A276086 gives the prime product form of primorial base expansion of n.
A349003 (program): Decimal expansion of lim_{n->infinity} E(2*n, n)/n^(2*n), where E(n, x) is the n-th Euler polynomial.
A349004 (program): Decimal expansion of lim_{n->infinity} B(2*n, n)/n^(2*n), where B(n, x) is the n-th Bernoulli polynomial.
A349005 (program): a(n) = Sum_{d|n, d^2>=n} 1+d+n/d.
A349015 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x) / (1 - x) - x * A(x)^2.
A349017 (program): G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x)))^3.
A349018 (program): G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x)))^4.
A349021 (program): G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^2)^4.
A349022 (program): G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^3)^4.
A349023 (program): G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^4)^2.
A349024 (program): G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^4)^3.
A349039 (program): Square array T(n, k) read by antidiagonals, n, k >= 0; T(n, k) = n^2 - n*k + k^2.
A349043 (program): Number of solutions to n = s + t such that 1 <= s <= t and s | 2*t.
A349047 (program): G.f. A(x) satisfies: A(x) = 1 / (1 - x + x^3 * A(x)).
A349048 (program): G.f. A(x) satisfies: A(x) = 1 / (1 - x + x^4 * A(x)).
A349049 (program): Number of prime factors (with multiplicity) of the denominator of the harmonic number H(n) = Sum_{k=1..n} 1/k.
A349050 (program): Number of multisets of size n that have no alternating permutations and cover an initial interval of positive integers.
A349055 (program): Number of multisets of size n that have an alternating permutation and cover an initial interval of positive integers.
A349056 (program): Number of weakly alternating permutations of the multiset of prime factors of n.
A349066 (program): a(n) = H(2*n, n), where H(n,x) is n-th Hermite polynomial.
A349067 (program): a(n) = H(3*n, n), where H(n,x) is n-th Hermite polynomial.
A349068 (program): a(n) = H(n, 2*n), where H(n,x) is n-th Hermite polynomial.
A349069 (program): a(n) = H(n, 3*n), where H(n,x) is n-th Hermite polynomial.
A349070 (program): a(n) = T(3*n, n), where T(n, x) is the Chebyshev polynomial of the first kind.
A349071 (program): a(n) = T(n, 2*n), where T(n, x) is the Chebyshev polynomial of the first kind.
A349072 (program): a(n) = T(n, 3*n), where T(n, x) is the Chebyshev polynomial of the first kind.
A349073 (program): a(n) = U(2*n, n), where U(n, x) is the Chebyshev polynomial of the second kind.
A349074 (program): a(n) = U(3*n, n), where U(n, x) is the Chebyshev polynomial of the second kind.
A349075 (program): a(n) = U(n, 2*n), where U(n, x) is the Chebyshev polynomial of the second kind.
A349076 (program): a(n) = U(n, 3*n), where U(n, x) is the Chebyshev polynomial of the second kind.
A349077 (program): a(n) = 4^n * P(2*n, n), where P(n, x) is n-th Legendre polynomial.
A349087 (program): a(n) = n! * Sum_{k=0..floor(n/4)} (-1)^k / (4*k)!.
A349088 (program): a(n) = n! * Sum_{k=0..floor((n-1)/3)} 1 / (3*k+1)!.
A349089 (program): a(n) = n! * Sum_{k=0..floor((n-1)/4)} 1 / (4*k+1)!.
A349093 (program): a(n) is the smallest nonprime number m (m = A018252(t)) such that n divides the product P(t) of all nonprime numbers up to and including m (P(t) = A036691(t-1)).
A349094 (program): a(n) = 2^(n-1) - tau(n) where tau(n) is the number of divisors of n.
A349102 (program): Increase the odd part of n to the next greater odd number.
A349113 (program): a(n) = 8^n * P(3*n, n), where P(n, x) is n-th Legendre polynomial.
A349116 (program): a(n) = Sum_{m=1..n} (Sum_{k=1..m} (Sum_{j=1..k} j^n)).
A349117 (program): a(n) = Sum_{m=1..n} (Sum_{k=1..m} (Sum_{j=1..k} j^k)).
A349118 (program): Row sums of a triangle based on A261327.
A349122 (program): Inverse Möbius transform of A349128, where A349128(n) = phi(A064989(n)), A064989 is multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p, and phi is Euler totient function.
A349123 (program): a(n) = Sum_{d|n} A038040(n/d) * A003415(d), where A038040(n) = n*tau(n), and A003415 is the arithmetic derivative of n.
A349124 (program): a(n) = A349123(n) / A003557(n), where A349123 is the Dirichlet convolution of the arithmetic derivative with n*tau(n).
A349125 (program): Dirichlet inverse of A064989, where A064989 is multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p.
A349126 (program): Sum of A064989 and its Dirichlet inverse, where A064989 is multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p.
A349127 (program): Möbius transform of A064989, where A064989 is multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p.
A349128 (program): a(n) = phi(A064989(n)), where A064989 is multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p, and phi is Euler totient function.
A349129 (program): a(n) = Sum_{d|n} A003958(d) * A003959(n/d), where A003958 is fully multiplicative with a(p) = (p-1), and A003959 is fully multiplicative with a(p) = (p+1).
A349130 (program): a(n) = Sum_{d|n} d * A003958(n/d), where A003958 is fully multiplicative with a(p) = (p-1).
A349131 (program): a(n) = Sum_{d|n} phi(d) * A003958(n/d), where A003958 is fully multiplicative with a(p) = (p-1), and phi is Euler totient function.
A349132 (program): a(n) = Sum_{d|n} psi(d) * A003958(n/d), where A003958 is fully multiplicative with a(p) = (p-1), and psi is Dedekind psi function, A001615.
A349136 (program): Möbius transform of Kimberling’s paraphrases, A003602.
A349137 (program): a(n) = phi(A003602(n)), where A003602 is Kimberling’s paraphrases, and phi is Euler totient function.
A349138 (program): Inverse Möbius transform of A349137, where A349137(n) = phi(A003602(n)).
A349140 (program): a(n) = Sum_{d|n} d * A348507(n/d), where A348507(n) = A003959(n) - n, where A003959 is fully multiplicative with a(p) = (p+1).
A349141 (program): a(n) = Sum_{d|n} phi(n/d) * A348507(d), where A348507(n) = A003959(n) - n, and A003959 is fully multiplicative with a(p) = (p+1).
A349144 (program): Numbers k for which A342671(k) [= gcd(sigma(k), A003961(k)] and A349161(k) [= A003961(k)/A342671(k)] are relatively prime, where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors function.
A349147 (program): Triangle T(n,m) read by rows: the sum of runs of all sequences arranging n objects of one type and m objects of another type.
A349149 (program): Number of even-length integer partitions of n with at most one odd part in the conjugate partition.
A349161 (program): a(n) = A003961(n) / gcd(sigma(n), A003961(n)), where A003961 shifts the prime factorization of n one step towards larger primes, and sigma is the sum of divisors function.
A349162 (program): a(n) = sigma(n) / gcd(sigma(n), A003961(n)), where A003961 shifts the prime factorization of n one step towards larger primes, and sigma is the sum of divisors function.
A349163 (program): a(n) = A064989(gcd(sigma(n), A003961(n))), where A003961 shifts the prime factorization of n one step towards larger primes, while A064989 shifts it back towards smaller primes, and sigma is the sum of divisors function.
A349164 (program): a(n) = A064989(A003961(n) / gcd(sigma(n), A003961(n))), where A003961 shifts the prime factorization of n one step towards larger primes, while A064989 shifts it back towards smaller primes, and sigma is the sum of divisors function.
A349165 (program): Numbers k such that sigma(k) and A003961(k) are relatively prime, where A003961(n) is fully multiplicative function with a(prime(k)) = prime(k+1).
A349166 (program): Numbers k such that sigma(k) and A003961(k) share a prime factor, where A003961(n) is fully multiplicative function with a(prime(k)) = prime(k+1).
A349167 (program): a(n) = 1 if sigma(n) and A003961(n) are relatively prime, otherwise 0.
A349168 (program): Numbers k such that sigma(k) and A003961(k) share a prime power divisor that is not a unitary divisor of A003961(k). Here A003961(n) is fully multiplicative function with a(prime(k)) = prime(k+1).
A349170 (program): a(n) = Sum_{d|n} d * A003959(n/d), where A003959 is fully multiplicative with a(p) = (p+1).
A349171 (program): a(n) = Sum_{d|n} phi(d) * A003959(n/d), where A003959 is fully multiplicative with a(p) = (p+1), and phi is Euler totient function.
A349172 (program): a(n) = Sum_{d|n} psi(d) * A003959(n/d), where A003959 is fully multiplicative with a(p) = (p+1), and psi is Dedekind psi function, A001615.
A349182 (program): a(0) = 1; for n>0, a(n) is the smallest positive integer such that |n - a(n-1)| + a(n) is a square.
A349191 (program): a(n) = A000720(A348907(n+1)).
A349201 (program): a(n) = [x^n] ((x^2*(1 + 3*x + x^2 - 2*x^3 + 3*x^4 + x^5 - x^6))/((-1 + x)^4 *(1 + x)^3)).
A349211 (program): a(n) = Sum_{d|n} d^((d+1) mod 2).
A349212 (program): a(n) = Sum_{d|n} n^(d mod 2).
A349213 (program): a(n) = Sum_{d|n} n^((d+1) mod 2).
A349214 (program): a(n) = Sum_{k=1..n} k^c(k), where c is the prime characteristic (A010051).
A349215 (program): a(n) = Sum_{d|n} d^c(d), where c is the prime characteristic (A010051).
A349216 (program): Number of ternary triples (u,v,w) with 1 <= u < v < w <= n.
A349217 (program): a(n) = Sum_{d|n} n^c(d), where c is the prime characteristic (A010051).
A349221 (program): Triangle read by rows: T(n, k) = 1 if k divides binomial(n-1, k-1), T(n, k) = 0 otherwise (n >= 1, 1 <= k <= n).
A349229 (program): a(n) = Sum_{k=1..n} (-1)^A001222(k)*(-1)^A001222(k+1).
A349236 (program): Gaps between cubefree numbers: a(n) = A004709(n+1) - A004709(n).
A349237 (program): Decimal expansion of lim_{x->oo} (1/x) * Sum_{c(k+1) <= x} (c(k+1) - c(k))^2, where c(k) = A004709(k) is the k-th cubefree number.
A349243 (program): Indices of triangular numbers A000217 with only odd digits.
A349253 (program): G.f. A(x) satisfies: A(x) = 1 / ((1 - x) * (1 - 2 * x * A(x)^2)).
A349254 (program): G.f. A(x) satisfies: A(x) = 1 / ((1 - x) * (1 - 3 * x * A(x)^2)).
A349255 (program): G.f. A(x) satisfies: A(x) = 1 / ((1 + x) * (1 - 2 * x * A(x)^2)).
A349256 (program): G.f. A(x) satisfies: A(x) = 1 / ((1 + x) * (1 - 3 * x * A(x)^2)).
A349264 (program): Generalized Euler numbers, a(n) = n!*x^n.
A349267 (program): Generalized Euler numbers, a(n) = n!*x^n.
A349268 (program): Generalized Euler numbers, a(n) = n!*x^n.
A349269 (program): Triangle read by rows, T(n, k) = (n - k)! * k! / floor(k / 2)! ^ 2.
A349270 (program): a(n) = Sum_{k=0..n} (n - k)! * k! / floor(k / 2)!^2, row sums of A349269.
A349273 (program): Number of odd divisors of prime(n) - 1.
A349278 (program): a(n) is the product of the sum of the last i digits of n, with i going from 1 to the total number of digits of n.
A349289 (program): G.f. A(x) satisfies: A(x) = 1 / ((1 - x) * (1 - x * A(x)^3)).
A349290 (program): G.f. A(x) satisfies: A(x) = 1 / ((1 - x) * (1 - x * A(x)^4)).
A349291 (program): G.f. A(x) satisfies: A(x) = 1 / ((1 - x) * (1 - x * A(x)^5)).
A349292 (program): G.f. A(x) satisfies: A(x) = 1 / ((1 - x) * (1 - x * A(x)^6)).
A349293 (program): G.f. A(x) satisfies: A(x) = 1 / ((1 - x) * (1 - x * A(x)^7)).
A349297 (program): Triangle T(n,k) = 1 if both n and k are even or if n and k are divisible by 3.
A349299 (program): G.f. A(x) satisfies: A(x) = 1 / ((1 + x) * (1 - x * A(x)^3)).
A349300 (program): G.f. A(x) satisfies: A(x) = 1 / ((1 + x) * (1 - x * A(x)^4)).
A349301 (program): G.f. A(x) satisfies: A(x) = 1 / ((1 + x) * (1 - x * A(x)^5)).
A349302 (program): G.f. A(x) satisfies: A(x) = 1 / ((1 + x) * (1 - x * A(x)^6)).
A349303 (program): G.f. A(x) satisfies: A(x) = 1 / ((1 + x) * (1 - x * A(x)^7)).
A349304 (program): Terms of sequence A133342 interpreted as numbers written in base 2 and converted here to base 10.
A349309 (program): Numbers k such that A254926(k) = A254926(k+1).
A349310 (program): G.f. A(x) satisfies: A(x) = (1 + x * A(x)^4) / (1 - x).
A349311 (program): G.f. A(x) satisfies: A(x) = (1 + x * A(x)^5) / (1 - x).
A349312 (program): G.f. A(x) satisfies: A(x) = (1 + x * A(x)^6) / (1 - x).
A349313 (program): G.f. A(x) satisfies: A(x) = (1 + x * A(x)^7) / (1 - x).
A349314 (program): G.f. A(x) satisfies: A(x) = (1 + x * A(x)^8) / (1 - x).
A349317 (program): Triangle T(n,k): T(n,k) = 1 if gcd(n, k) > 1, else 0.
A349318 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x)^3 / (1 - 2 * x).
A349322 (program): a(n) = Sum_{d|n} d^c(d), where c is the refactorable characteristic (A336040).
A349326 (program): a(n) is the number of prime powers (not including 1) that are bi-unitary divisors of n.
A349330 (program): a(n) = Sum_{d|n} d^c(d), where c is the characteristic function of squares (A010052).
A349331 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x)^4 / (1 - x).
A349332 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x)^5 / (1 - x).
A349333 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x)^6 / (1 - x).
A349334 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x)^7 / (1 - x).
A349335 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x)^8 / (1 - x).
A349338 (program): Dirichlet convolution of A000010 (Euler totient phi) with A080339 (characteristic function of noncomposite numbers).
A349339 (program): Odd bisection of the Möbius transform of A126760.
A349340 (program): Dirichlet inverse of A003557, where A003557 is multiplicative with a(p^e) = p^(e-1).
A349341 (program): Dirichlet inverse of A026741, which is defined as n if n is odd, n/2 if n is even.
A349342 (program): Sum of A026741 and its Dirichlet inverse.
A349343 (program): Dirichlet inverse of A193356, which is defined as n if n is odd, 0 if n is even.
A349350 (program): Dirichlet inverse of A057521, the powerful part of n.
A349355 (program): Dirichlet convolution of A003958 with A063441 (Dirichlet inverse of A003959), where A003958 and A003959 are fully multiplicative with a(p) = p-1 and p+1 respectively.
A349356 (program): Dirichlet convolution of A003959 with A097945 (Dirichlet inverse of A003958), where A003958 and A003959 are fully multiplicative with a(p) = p-1 and p+1 respectively.
A349360 (program): Number of positive integer pairs (s,t), with s,t <= n and s <= t such that either both s and t divide n or both do not.
A349361 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x)^5 / (1 + x).
A349362 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x)^6 / (1 + x).
A349363 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x)^7 / (1 + x).
A349364 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x)^8 / (1 + x).
A349371 (program): Inverse Möbius transform of Kimberling’s paraphrases (A003602).
A349372 (program): Dirichlet convolution of Kimberling’s paraphrases (A003602) with tau (number of divisors, A000005).
A349373 (program): Dirichlet convolution of Kimberling’s paraphrases (A003602) with Dirichlet inverse of Euler phi (A023900).
A349379 (program): Möbius transform of A057521 (powerful part of n).
A349385 (program): Dirichlet convolution of A048673 with the Dirichlet inverse of A003961, where A003961 is fully multiplicative with a(p) = nextprime(p), and A048673(n) = (1+A003961(n))/2.
A349388 (program): Dirichlet convolution of A000027 with A346234 (Dirichlet inverse of A003961), where A003961 is fully multiplicative with a(p) = nextprime(p).
A349392 (program): Dirichlet convolution of A126760 with tau (number of divisors function).
A349393 (program): Inverse Möbius transform of A126760.
A349394 (program): a(p^e) = p^(e-1) for prime powers, a(n) = 0 for all other n; Dirichlet convolution of A003415 (arithmetic derivative of n) with A055615 (Dirichlet inverse of n).
A349403 (program): Sum of the digits of Sum_{k=1..n} k!.
A349407 (program): The Farkas map: a(n) = x/3 if x mod 3 = 0; a(n) = (3x+1)/2 if x mod 3 <> 0 and x mod 4 = 3; a(n) = (x+1)/2 if x mod 3 <> 0 and x mod 4 = 1, where x = 2n-1.
A349413 (program): Number of smooth positroid varieties corresponding to derangements in S_n.
A349414 (program): a(n) = A324245(n) - n.
A349415 (program): Number of ways an n-set can be written as the union of 2 sets each with 4 or more elements and whose intersection contains exactly 3 elements.
A349416 (program): a(n) is the Wiener index of a broom on 2n vertices of which n+2 are pendant.
A349417 (program): a(n) is the Wiener index of a sling on n+1 vertices.
A349418 (program): a(n) is the Wiener index of a tridon on n vertices.
A349427 (program): a(n) = ((n+1)^2 - 2) * binomial(2*n-2,n-1) / 2.
A349431 (program): Dirichlet convolution of A003602 (Kimberling’s paraphrases) with A055615 (Dirichlet inverse of n)
A349440 (program): a(n) = n / gcd(A001608(n), n), where A001608 = Perrin sequence.
A349441 (program): Dirichlet convolution of A057521 (powerful part of n) with A055615 (Dirichlet inverse of n).
A349442 (program): Dirichlet convolution of A000027 (the identity function) with A349350 (Dirichlet inverse of the powerful part of n).
A349444 (program): Dirichlet convolution of A003602 (Kimberling’s paraphrases) with A092673 (Dirichlet inverse of A001511).
A349447 (program): Dirichlet convolution of A003602 (Kimberling’s paraphrases) with A326937 (Dirichlet inverse of A000265).
A349454 (program): Number T(n,k) of endofunctions on [n] with exactly k fixed points, all of which are isolated; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
A349458 (program): Number of smooth positroids in the Grassmannian variety Gr(k,n) for a fixed n and any 0 <= k <= n.
A349461 (program): Primes of the form m^2 + 9*m + 81.
A349466 (program): Expansion of 1/((1-12*x)*(1-16*x)*(1-18*x)*(1-24*x)).
A349468 (program): a(n) = (4*n)! / (n! * (2*n)!).
A349469 (program): Dirichlet g.f.: Sum_{n>0} a(n)/n^s = zeta(s-1)*zeta(s-3)/(zeta(s-2))^2.
A349470 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(k*n,n).
A349471 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(k*n,k).
A349480 (program): a(n) = Sum_{j=0..n} (-1)^(n-j) * Product_{k=(j-1)*n+1..j*n} k.
A349481 (program): a(n) is the number of Boolean factors of the contranominal scale of size n by the GreConD algorithm for Boolean matrix factorization.
A349487 (program): a(n) = A132739((n-5)*(n+5)).
A349489 (program): a(n) = Sum_{k=1..n} k * floor(sqrt(2*k-1)).
A349490 (program): Sum of the n-th powers of the first n odd numbers.
A349496 (program): Numbers of the form 4*t^2-2 (A060626) when t >= 1 is an integer that is not a term in A001542.
A349506 (program): a(n) is the numerator of n!^(2*n)/(n^n^2).
A349507 (program): a(n) is the denominator of n!^(2*n)/(n^n^2).
A349509 (program): a(n) is the denominator of binomial(n^3 + 6*n^2 - 6*n + 2, n^3 - 1)/n^3.
A349513 (program): a(n) = n! * Sum_{k=0..n} (2*k)! / (k!)^3.
A349514 (program): G.f. A(x) satisfies: A(x) = (1 + x * A(x)^3) / (1 - 3 * x).
A349515 (program): G.f. A(x) satisfies: A(x) = (1 + x * A(x)^3) / (1 - 4 * x).
A349516 (program): G.f. A(x) satisfies: A(x) = (1 + 3 * x * A(x)^3) / (1 - x).
A349517 (program): G.f. A(x) satisfies: A(x) = (1 + 4 * x * A(x)^3) / (1 - x).
A349520 (program): Let S_k denote the list of pairs (1,k), (2,k), (3,k), …, (k,k); sequence lists the pairs in S_1, S_2, S_3, …
A349523 (program): a(n) = Sum_{k=1..n} A339399(k).
A349526 (program): Modified lexicographic ordering of all pairs i,j with 1 <= i <= j; every pair i,j of positive integers occurs exactly once.
A349531 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x)^3 / (1 - 3 * x).
A349532 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x)^3 / (1 - 4 * x).
A349533 (program): G.f. A(x) satisfies: A(x) = 1 / ((1 - 2 * x) * (1 - x * A(x)^2)).
A349534 (program): G.f. A(x) satisfies: A(x) = 1 / ((1 - 3 * x) * (1 - x * A(x)^2)).
A349535 (program): G.f. A(x) satisfies: A(x) = 1 / ((1 - 4 * x) * (1 - x * A(x)^2)).
A349536 (program): Consider a circle on the Z X Z lattice with radius equal to the Pythagorean hypotenuse h(n) (A009003); a(n) = number of Pythagorean triples inside a Pi/4 sector of the circle.
A349538 (program): The number of pseudo-Pythagorean triples (which allow negative or 0 sides) on a 2D lattice that are on or inside a circle of radius n.
A349540 (program): E.g.f.: exp(x) * (BesselI(0,6*x) + BesselI(1,6*x)).
A349541 (program): E.g.f.: exp(x) * (BesselI(0,8*x) + BesselI(1,8*x)).
A349552 (program): a(n) is the number of halving partitions of n (see Comments for definition).
A349554 (program): a(n) = A054108(n) + 4*(-1)^n.
A349555 (program): a(n) = Sum_{p<=n, p prime} p^floor(1/gcd(n/p)).
A349562 (program): Number of labeled rooted forests with 2-colored leaves.
A349573 (program): a(n) = A048673(n) - n, where A048673(n) = (A003961(n)+1) / 2, and A003961(n) shifts the prime factorization of n one step towards larger primes.
A349576 (program): Recurrence a(1) = 1, a(2) = 5; a(n) = (a(n-1) + a(n-2))/GCD(a(n-1),a(n-2)) + 1.
A349581 (program): G.f. A(x) satisfies: A(x) = 1 / (1 - 2*x) + x * (1 - 2*x)^2 * A(x)^4.
A349582 (program): G.f. A(x) satisfies: A(x) = 1 / (1 - 2*x) + x * (1 - 2*x)^3 * A(x)^5.
A349584 (program): G.f. A(x) satisfies: A(x) = 1 / (1 - 2*x) + x * (1 - 2*x)^4 * A(x)^6.
A349590 (program): G.f. A(x) satisfies: A(x) = 1 / (1 - 2*x) + x * (1 - 2*x)^5 * A(x)^7.
A349591 (program): G.f. A(x) satisfies: A(x) = 1 / (1 - 2*x) + x * (1 - 2*x)^6 * A(x)^8.
A349594 (program): Number of 2 X n mazes that can be navigated from the top left corner to the bottom right corner.
A349595 (program): Number of self-counting sequences of length n (sequences indexed from 0 to (n-1) where a(i) is the number of times i appears in the sequence).
A349603 (program): a(n) = Sum_{k=0..n} binomial(n,k) * A000108(k) * k^(n-k).
A349609 (program): Number of solutions to x^2 + y^2 <= n^2, where x, y are positive odd integers.
A349612 (program): Dirichlet convolution of A342001 [{arithmetic derivative of n}/A003557(n)] with A325126 [Dirichlet inverse of rad(n)].
A349629 (program): Numerators of the Dirichlet inverse of the abundancy index, sigma(n)/n.
A349630 (program): Denominators of the Dirichlet inverse of the abundancy index, sigma(n)/n.
A349639 (program): a(n) = Sum_{k=0..n} binomial(n,k) * A000108(k) * k^k.
A349640 (program): a(n) = Sum_{k=0..n} binomial(n,k) * A000108(k) * k!.
A349648 (program): Expansion of g.f.: Catalan(x)/Catalan(-x).
A349658 (program): Number of nonrefactorable divisors of n.
A349659 (program): Sum of the nonrefactorable divisors of n.
A349660 (program): Numbers which are the sum of a prime and the square of the next prime.
A349662 (program): a(n) is the number of squares strictly between n^2 and n^3.
A349664 (program): a(n) is the number of solutions for n^4 = z^2 - x^2 with {z,x} >= 1.
A349666 (program): Primes of the form 4*k+3 that are still a prime of the form 4*k+3 after 2 Collatz steps.
A349668 (program): a(n) is the n-th safe prime reduced mod n.
A349669 (program): a(n) is the n-th Sophie Germain prime reduced mod n.
A349673 (program): a(n) is the smallest positive integer m such that the set of numbers {f(k) : 1 <= k <= n} are pairwise distinct modulo m for f(x)=x^3+x.
A349675 (program): a(n) is the number of attainable partitions of n.
A349679 (program): a(n) = n*(n+1)/2 - (n-2)*phi(n)/2 for n >= 2, with a(1)=1.
A349680 (program): a(n) = Sum_{k=1..n} (n-k)^c(n/k), where c(n) = 1 - ceiling(n) + floor(n).
A349682 (program): a(n) = A000292(6*n + 1) where A000292 are the tetrahedral numbers.
A349693 (program): Dirichlet convolution of the ruler function (A001511) with itself.
A349694 (program): Dirichlet convolution of the squarefree kernel function (A007947) with itself.
A349695 (program): a(n) = (2n^2 - n + 2) * (2n)! / ((n + 1) * (n + 2) * n!^2).
A349706 (program): Array T(n,k) = Sum_{j=0, k} binomial(k,j)*j^n) for n and k >= 0, read by ascending antidiagonals.
A349707 (program): Numbers that are congruent to {0, 1, 4, 6, 8, 10, 11} (mod 12).
A349710 (program): Paschal full moon dates expressed as days after March 21 (Julian calendar).
A349713 (program): Antidiagonal sums of triangle A104684.
A349714 (program): E.g.f. satisfies: A(x) = exp( x * (1 + A(x)^3)/2 ).
A349715 (program): E.g.f. satisfies: A(x) = exp( x * (1 + A(x)^4)/2 ).
A349716 (program): E.g.f. satisfies: A(x) = exp( x * (1 + A(x)^5)/2 ).
A349723 (program): Atomic number corresponding to the element that is the first of the two middle elements in the n-th row of the periodic table of elements.
A349727 (program): Triangle read by rows, T(n, k) = [x^(n - k)] hypergeom([-n, -1 + n], [-n], x).
A349728 (program): Triangle read by rows, T(n, k) = RisingFactorial(k, n) / FallingFactorial(n, k).
A349730 (program): Row sums of A349728.
A349731 (program): a(n) = -(-n)^n * FallingFactorial(1/n, n) for n >= 1 and a(0) = -1.
A349740 (program): Number of partitions of set [n] in a set of <= k noncrossing subsets. Number of Dyck n-paths with at most k peaks. Both with 0 <= k <= n, read by rows.
A349750 (program): Odd numbers k such that sigma(k) == k (mod 3), where sigma is the sum of divisors function.
A349751 (program): Odd numbers k such that sigma(k) == -k (mod 3), where sigma is the sum of divisors function.
A349754 (program): a(n) = phi(A003961(n)) - 2*phi(n), where A003961 is fully multiplicative with a(p) = nextprime(p), and phi is Euler totient function.
A349756 (program): Numbers k such that the odd part of sigma(k) is equal to gcd(sigma(k), A003961(k)), where A003961 is fully multiplicative with a(p) = nextprime(p), and sigma is the sum of divisors function.
A349757 (program): Even numbers that are both the sum of a twin prime pair and the sum of 1 and a prime.
A349766 (program): Numbers of the form 2*t^2-4 when t > 1 is a term in A001541.
A349767 (program): Numbers m such that 2^m - m is divisible by 5.
A349768 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+k,k) * binomial(2*k,k) / (k+1).
A349769 (program): a(n) = Sum_{k=0..n} binomial(n,k)^2 * binomial(k,floor(k/2)).
A349775 (program): The maximum cardinality of an irreducible subset of {0, 1, 2, …, n}.
A349776 (program): Triangle read by rows: T(n,k) is the number of partitions of set [n] into a set of at most k lists, with 0 <= k <= n. Also called broken permutations.
A349781 (program): a(n) = n! * (hypergeom([1 - n], [2], -1]) - 1) for n >= 1 and a(0) = 0.
A349801 (program): Number of integer partitions of n into three or more parts or into two equal parts.
A349803 (program): a(3*n) = 1 + 4*n^2, a(1+3*n) = 2 + 4*n*(n+1), a(2+3*n) = 5 + 4*n*(n+1).
A349804 (program): Decimal expansion of cosh(1) - cos(1).
A349808 (program): Number of cells in a regular 7-gon after n generations of mitosis.
A349812 (program): Triangle read by rows: row 1 is [1]; for n >= 1, row n gives coefficients of expansion of (-1/x + x)*(1/x + 1 + x)^(n-1) in order of increasing powers of x.
A349817 (program): Number of 4 X n Fibonacci minimal checkerboards.
A349824 (program): a(0) = 0; for n >= 1, a(n) = (number of primes, counted with repetition) * (sum of primes, counted with repetition).
A349829 (program): Numbers k such that there is a number m with m + s_4(m) = k, where s_b(m) = sum of digits in base-b expansion of m.
A349834 (program): Expansion of sqrt(1 + 4*x)/(1 - 4*x).
A349835 (program): Expansion of (1 + 4*x)/sqrt(1 - 4*x).
A349836 (program): Expansion of Sum_{k>=0} (k * x)^k/(1 - k^2 * x).
A349839 (program): Triangle T(n,k) built by placing all ones on the left edge, [1,0,0,0] repeated on the right edge, and filling the body using the Pascal recurrence T(n,k) = T(n-1,k) + T(n-1,k-1).
A349840 (program): The number of compositions of n using elements from the set {1,3,5,7,8}.
A349841 (program): Triangle T(n,k) built by placing all ones on the left edge, [1,0,0,0,0] repeated on the right edge, and filling the body using the Pascal recurrence T(n,k) = T(n-1,k) + T(n-1,k-1).
A349842 (program): Expansion of 1/((1 - 2*x)*(1 + x + x^2 + x^3 + x^4)).
A349843 (program): Expansion of (1 - x^2)/((1 - x^10)(1 - x - x^2)).
A349846 (program): Expansion of -(1 - 8*x) / sqrt(1 - 4*x).
A349847 (program): Expansion of (1 + 8*x) / sqrt(1 - 4*x).
A349852 (program): Expansion of Sum_{k>=0} k * x^k/(1 + k * x).
A349853 (program): Expansion of Sum_{k>=0} k^2 * x^k/(1 + k * x).
A349854 (program): Expansion of Sum_{k>=0} k^3 * x^k/(1 + k * x).
A349855 (program): Expansion of Sum_{k>=0} k^4 * x^k/(1 + k * x).
A349856 (program): Expansion of Sum_{k>=0} x^k/(1 + k^2 * x).
A349857 (program): Expansion of Sum_{k>=0} x^k/(1 + k^3 * x).
A349858 (program): Expansion of Sum_{k>=0} x^k/(1 + k^4 * x).
A349859 (program): Expansion of Sum_{k>=0} k * x^k/(1 + k^2 * x).
A349860 (program): Expansion of Sum_{k>=0} k * x^k/(1 + k^3 * x).
A349861 (program): Expansion of Sum_{k>=0} k * x^k/(1 + k^4 * x).
A349862 (program): a(n) is the maximum value of binomial(n-2*k,k) with 0 <= k <= floor(n/3).
A349863 (program): Expansion of Sum_{k>=0} k^2 * x^k/(1 + k^2 * x).
A349874 (program): Expansion of A(x)^3, where A(x) is g.f. of n^n (A000312).
A349878 (program): Expansion of Sum_{k>=0} k^3 * x^k/(1 - k * x).
A349879 (program): Expansion of Sum_{k>=0} k^4 * x^k/(1 - k * x).
A349880 (program): Expansion of Sum_{k>=0} x^k/(1 - k^3 * x).
A349881 (program): Expansion of Sum_{k>=0} x^k/(1 - k^4 * x).
A349882 (program): Expansion of Sum_{k>=0} k^2 * x^k/(1 - k^2 * x).
A349883 (program): Expansion of Sum_{k>=0} (k * x)^k/(1 - k^3 * x).
A349884 (program): Expansion of Sum_{k>=0} (k * x)^k/(1 + k^2 * x).
A349885 (program): Expansion of Sum_{k>=0} (k * x)^k/(1 + k^3 * x).
A349889 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(2*n).
A349893 (program): a(n) = Sum_{k=0..n} k^(k*(n-k)).
A349894 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(k*(n-k)).
A349895 (program): Length of the longest self avoiding walk through a grid such that either x or y is changed by +1 or -1 in each step, and with 0 <= y, 0 <= x <= y, x + y <= n starting at (0,0) and terminating at (x,y) = (n,0).
A349899 (program): Least number in A349898 divisible by the n-th prime.
A349901 (program): a(n) = Sum_{k=0..n} k^(3*n).
A349902 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(3*n).
A349905 (program): Arithmetic derivative of A003961(n), where A003961 is fully multiplicative with a(p) = nextprime(p).
A349909 (program): Partial sums of A347870; Number of terms of A347877 (numbers k with an odd arithmetic derivative of sigma(k)) in range 1..n.
A349910 (program): a(n) = Sum_{d|n, d<n} A048673(d).
A349911 (program): Dirichlet inverse of A336466, which is fully multiplicative with a(p) = oddpart(p-1).
A349912 (program): Sum of A336466 and its Dirichlet inverse, where A336466 is fully multiplicative with a(p) = oddpart(p-1).
A349914 (program): Sum of A000593 (the sum of odd divisors function) and its Dirichlet inverse.
A349919 (program): Number of transitive relations on an n-set with exactly two ordered pairs.
A349928 (program): a(n) = Sum_{k=0..n} (k+n)^k.
A349930 (program): a(n) is the number of groups of order A340511(n) which have no subgroup of order d, for some divisor d of A340511(n).
A349932 (program): Product of n and its binary ones’ complement.
A349936 (program): Central pentanomial coefficients.
A349946 (program): a(n) = A349526(n) + A349526(n+1).
A349948 (program): Tetrahedral-sided isosceles Heron triangle pairs.
A349961 (program): a(n) = Sum_{k=0..n} (2*n)^k.
A349962 (program): a(n) = Sum_{k=0..n} (2*k)^k.
A349963 (program): a(n) = Sum_{k=0..n} (2*k)^n.
A349964 (program): a(n) = Sum_{k=0..n} (k*n)^n.
A349965 (program): a(n) = Sum_{k=0..n} (k * (n-k))^k.
A349966 (program): a(n) = Sum_{k=0..n} (k * (n-k))^n.
A349969 (program): a(n) = Sum_{k=0..n} (k*n)^(n-k).
A349970 (program): a(n) = Sum_{k=0..n} (2*k)^(n-k).
A349971 (program): Array read by ascending antidiagonals, A(n, k) = -(-n)^k*FallingFactorial(1/n, k) for n, k >= 1.
A349975 (program): Expansion of g.f. (x^4*(x^2 + 2*x + 3))/((x - 1)^4*(x + 1)*(x^2 + x + 1)).
A349983 (program): a(n) is the largest k such A000792(k) <= n.
A349993 (program): a(n) is the number of squares k^2 with n^2 <= k^2 <= n^3.

License Info