Programs for A350000-A399999

List of integer sequences with links to LODA programs.

A350008 (program): a(n) = Sum_{k=0..n} k^(2*k).
A350014 (program): Numbers whose square has a number of divisors coprime to 6.
A350037 (program): a(n) = n^2 mod round(sqrt(n)).
A350040 (program): Number of integer-sided right triangles with hypotenuse A009003(n).
A350042 (program): Sum of all the parts in the partitions of n into 3 positive integer parts.
A350044 (program): Loop starting at 187 in the Collatz-like map {x -> 3x+5 if x is odd, x/2 otherwise}.
A350050 (program): a(n) = (2*n^4 - 6*(-1)^n*n^2 - 2*n^2 + 3*(-1)^n - 3)/96.
A350051 (program): Part three of the trisection of A017101: a(n) = 19 + 24*n.
A350052 (program): Third part of the trisection of A017077: a(n) = 17 + 24*n.
A350053 (program): a(n) = (2^(3*n + 3 + (-1)^n) - (6 + (-1)^n))/9, for n >= 1.
A350054 (program): a(n) = (4^(3*n+2) - 7)/9, n >= 1.
A350055 (program): a(n) = 36*n + 35, for n >= 0.
A350059 (program): Numbers k such that 3k and 4k have the same number of divisors.
A350062 (program): a(n) is the smallest number with the same prime signature as A156552(n), with a(1) = 0.
A350063 (program): a(n) is the smallest number with the same prime signature as A322993(n), with a(1) = 0.
A350071 (program): a(n) = gcd(sigma(n^2), A003961(n^2)), where A003961 shifts the prime factorization of n one step towards larger primes, and sigma is the sum of divisors function.
A350072 (program): a(n) = sigma(n^2) / gcd(sigma(n^2), A003961(n^2)), where A003961 shifts the prime factorization of n one step towards larger primes, and sigma is the sum of divisors function.
A350073 (program): a(n) = A064989(sigma(n)), where A064989 is multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p.
A350090 (program): a(n) is the number of indices i in the range 0 <= i <= n-1 such that A003215(n) - A003215(i) is an oblong number (A002378), where A003215 are the hex numbers.
A350091 (program): a(n) = a(floor(n/4)) for n == 2 (mod 4), otherwise n.
A350092 (program): a(n) = floor(x^n) where x = 1 + sqrt(5)/2 = A176055.
A350093 (program): a(n) = Sum_{k=0..n} n OR k where OR is the bitwise logical OR operator (A003986).
A350094 (program): a(n) = Sum_{k=0..n} n CNIMPL k where CNIMPL = NOT(n) AND k is the bitwise logical converse non-implication operator (A102037).
A350102 (program): Number of self-measuring subsets of the initial segment of the natural numbers strictly below n. Number of subsets S of [n] with S = distset(S).
A350103 (program): Triangle read by rows. Number of self-measuring subsets of the initial segment of the natural numbers strictly below n and cardinality k. Number of subsets S of [n] with S = distset(S) and |S| = k.
A350104 (program): a(n) = Sum_{k=0..n} A350102(k).
A350105 (program): Number of subsets of the initial segment of the natural numbers strictly below n which are not self-measuring. Number of subsets S of [n] with S != distset(S).
A350106 (program): Square array T(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where T(n,k) = Sum_{j=1..n} j * floor(n/j)^k.
A350107 (program): a(n) = Sum_{k=1..n} k * floor(n/k)^2.
A350108 (program): a(n) = Sum_{k=1..n} k * floor(n/k)^3.
A350109 (program): a(n) = Sum_{k=1..n} k * floor(n/k)^n.
A350114 (program): Number of Deutsch paths with peaks at odd height.
A350116 (program): Number of ways to partition the set of vertices of a convex {n+8}-gon into 3 non-intersecting polygons.
A350122 (program): Square array T(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where T(n,k) = Sum_{j=1..n} floor(n/(2*j-1))^k.
A350123 (program): a(n) = Sum_{k=1..n} k^2 * floor(n/k)^2.
A350124 (program): a(n) = Sum_{k=1..n} k^2 * floor(n/k)^3.
A350125 (program): a(n) = Sum_{k=1..n} k^2 * floor(n/k)^n.
A350128 (program): a(n) = Sum_{k=1..n} k^n * floor(n/k)^2.
A350133 (program): Last denominator in each run of odd terms in the greedy rearrangement of the alternating harmonic series that converges to 2.
A350134 (program): Number of endofunctions on [n] with at least one isolated fixed point.
A350143 (program): a(n) = Sum_{k=1..n} floor(n/(2*k-1))^2.
A350144 (program): a(n) = Sum_{k=1..n} floor(n/(2*k-1))^3.
A350145 (program): a(n) = Sum_{k=1..n} floor(n/(2*k-1))^n.
A350146 (program): Partial sums of A002131.
A350147 (program): a(n) = Sum_{k=1..n} floor(n/(2*k-1))^k.
A350149 (program): Triangle read by rows: T(n, k) = n^(n-k)*k!.
A350156 (program): Inverse Moebius transform of A000056.
A350159 (program): Number of subgroups of the dicyclic group Dic_n.
A350160 (program): Odd numbers whose Collatz trajectory does not include 5 as a term.
A350162 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/(2*k-1))^2.
A350163 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/(2*k-1))^3.
A350164 (program): a(n) = Sum_{k=1..n}(-1)^(k+1) * floor(n/(2*k-1))^n.
A350166 (program): Partial sums of A050469.
A350167 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/(2*k-1))^k.
A350168 (program): Count from 0 to 1st prime 2, then from 0 to 2nd prime 3, then from 0 to 3rd prime 5, etc …
A350169 (program): Write 1st prime and decrement 0 times, then write 2nd prime and decrement once, write 3rd prime and decrement twice, write 4th prime and decrement 3 times, etc …
A350170 (program): Start from the sequence of primes, keep the 1st, then delete 2 primes, keep the next, delete 3 primes, keep the next, delete 5 primes, etc …
A350171 (program): Add 1 to the 1st prime, then write the 2nd prime, then add 1 to the 3rd prime, then write the 4th prime, etc., alternately adding a 1 or not.
A350172 (program): Start from 1st prime 2, and write it twice, then add 3 to get 5 and write it 3 times, then add 5 to get 10 and write it 5 times, and so on.
A350173 (program): Write the square of 1st prime, then the 2nd prime, then the square of 3rd prime, alternately squaring or not.
A350174 (program): For k = 0, 1, 2, 3, … write k prime(k+1) times.
A350178 (program): Take n and subtract the greatest square less than or equal to n. Repeat this process until 0 is reached. a(n) is the sum of all residues after subtractions.
A350179 (program): Primes of the form ( A349309(n) + 1 ) ^ (1/3).
A350190 (program): Numbers k such that A083723(k) is prime.
A350212 (program): Number T(n,k) of endofunctions on [n] with exactly k isolated fixed points; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
A350215 (program): A048715, written in binary.
A350221 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * floor((n/k)^2).
A350222 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * floor((n/k)^3).
A350225 (program): Number of ordered pairs (a,g) with a in IS_n the symmetric inverse semigroup on [n] and g in symmetric group on [n] such that ag=ga.
A350229 (program): a(n) is the sum of n and the balanced ternary digits in n.
A350236 (program): a(n) is the sum of the entries in an n X n X n 3D matrix whose elements start at 1 in the corner cells and increase by 1 with each step towards the center.
A350247 (program): Positive integers k such that the concatenation of k and 11 is the lesser of a pair of twin primes (i.e., a term of A001359).
A350266 (program): Triangle read by rows. T(n, k) = binomial(n, k) * n! / (n - k + 1)! if k >= 1, if k = 0 then T(n, k) = k^n. T(n, k) for 0 <= k <= n.
A350267 (program): a(n) = n*hypergeom([1, 1 - n, -n], [2], 1) if n >= 1, a(0) = 1.
A350268 (program): a(n) = Sum_{k=0..n} (n - k)! * (n - 1)^k. Row sums of A350269.
A350269 (program): Triangle read by rows, T(n, k) = (n - k)!*(n - 1)^k, for 0 <= k <= n.
A350286 (program): Number of different ways to partition the set of vertices of a convex (n+11)-gon into 4 nonintersecting polygons.
A350289 (program): Infinite binary Walsh matrix read by antidiagonals.
A350290 (program): a(n) = Sum_{k=0..n} (-1)^(n - k) * binomial(n, k) * binomial(n + k - 1, n - k).
A350292 (program): Triangle read by rows: the n-th row gives the saturated vertex Turán numbers for the cube graph Q_n.
A350294 (program): a(n) = floor(n*2^n/(n + 1)).
A350295 (program): 2nd subdiagonal of the triangle A350292.
A350297 (program): Triangle read by rows: T(n,k) = n!*(n-1)^k/k!.
A350303 (program): a(n) is the number of ways to partition the set of vertices of a convex (n+14)-gon into 5 nonintersecting polygons.
A350309 (program): a(n) = (n+2)*a(n-1) + (n+1)*(A003422(n) - 4)/6 for n > 0 with a(0) = 1.
A350311 (program): Replace 2^k in the binary expansion of n with A000930(k+2), Narayana’s cows sequence.
A350314 (program): The catch-up points of the Redstone permutation A350313.
A350315 (program): Length of the rows of the Redstone permutation A350313.
A350324 (program): Missing even distances in full prime rulers, i.e., even numbers k, 0 < k < p-3 for some prime p, such that k is not the difference of two primes less than or equal to p.
A350325 (program): Binomial transform of A339399(n).
A350326 (program): Binomial transform of A339443(n).
A350327 (program): Maximum domination number of connected graphs with n vertices and minimum degree 2.
A350331 (program): Number of divisors of n that are prime or the product of 2 (not necessarily distinct) primes.
A350337 (program): Sum of the divisors of n that are prime or the product of 2 (not necessarily distinct) primes.
A350338 (program): Number of nontrivial divisors of n that are the product of up to 3 (not necessarily distinct) primes.
A350339 (program): Sum of the nontrivial divisors of n that are the product of up to 3 (not necessarily distinct) primes.
A350342 (program): Numbers k such that k^2 is an abelian order.
A350343 (program): Square numbers k that are abelian orders.
A350352 (program): Products of three or more distinct prime numbers.
A350353 (program): Numbers whose multiset of prime factors has a permutation that is not weakly alternating.
A350361 (program): 2-tone chromatic number of a tree with maximum degree n.
A350362 (program): 2-tone chromatic number of an n-cycle.
A350371 (program): Numbers with exactly 4 semiprime divisors.
A350372 (program): Numbers with exactly 5 semiprime divisors.
A350374 (program): Numbers with exactly 7 semiprime divisors.
A350375 (program): Numbers with exactly 8 semiprime divisors.
A350380 (program): Triangle read by rows in which row n lists A014963(d), the exponential of Mangoldt function, for each divisor d of n.
A350382 (program): a(n) = 9 + 4 * 10^n.
A350383 (program): a(n) = [x^n] 1/(1 + x + x^2)^n.
A350384 (program): a(n) = (-1728)^n.
A350386 (program): a(n) is the sum of the even exponents in the prime factorization of n.
A350387 (program): a(n) is the sum of the odd exponents in the prime factorization of n.
A350388 (program): a(n) is the largest unitary divisor of n that is a square.
A350390 (program): a(n) is the largest exponentially odd divisor of n.
A350395 (program): Numbers m such that a term with the largest coefficient in Product_{k=1..m} (1 + x^k) is unique.
A350396 (program): Numbers m such that there are two or more terms with the largest coefficient in Product_{k=1..m} (1 + x^k).
A350406 (program): a(n) = [x^n] 1/(1 + x + x^2 + x^3)^n.
A350407 (program): a(n) = [x^n] 1/(1 + x + x^2 + x^3 + x^4)^n.
A350409 (program): Primes p such that 2*p+1 has exactly three prime factors (not necessarily distinct).
A350414 (program): a(1)=1; for n > 1, a(n) = a(n-1) + (sum of odd-indexed digits of a(n-1)) - (sum of even-indexed digits of a(n-1)).
A350456 (program): G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 + 2*x)) / (1 + 2*x).
A350460 (program): Positive integers k such that if p is the next prime > k then p - k is prime.
A350461 (program): Number of ways to choose a subset of size n from [2n] and arrange its elements into a set of lists.
A350467 (program): a(n) = hypergeom([1/2 - n/2, -n/2], [-n], -8*n).
A350468 (program): a(n) = hypergeom([1/2 - n/2, -n/2], [-n], -56).
A350469 (program): a(n) = hypergeom([1/2 - n/2, -n/2], [-n], -72).
A350470 (program): Array read by ascending antidiagonals. T(n, k) = J(k, n) where J are the Jacobsthal polynomials.
A350471 (program): The number of days elapsed since the Gregorian date Sunday, December 31, 1 BC on 1/1/n, where 1/1/n is the Gregorian date in the format month/day/year, the New Year’s Day of the year n.
A350473 (program): a(n) = Fibonacci(n+1)^3 - Fibonacci(n-1)^3.
A350493 (program): a(n) = floor(sqrt(prime(n)))^2 mod n.
A350494 (program): Divide n by the greatest common divisor of the nonzero digits of n.
A350496 (program): Positive integers k such that if p is the largest prime less than k then k - p is prime.
A350498 (program): Convolution of triangular numbers with every third number of Narayana’s Cows sequence.
A350500 (program): Even numbers that are both the sum of a twin prime pair and the sum of 1 and a semiprime.
A350509 (program): a(n) = n/A055874(n).
A350512 (program): Triangle read by rows with T(n,0) = 1 for n >= 0 and T(n,k) = binomial(n-1,k-1)*(2*k*(n-k) + n)/k for 0 < k <= n.
A350515 (program): a(n) = (n-1)/3 if n mod 3 = 1; a(n) = n/2 if n mod 6 = 0 or n mod 6 = 2; a(n) = (3n+1)/2 if n mod 6 = 3 or n mod 6 = 5.
A350520 (program): The number of degree-n^2 polynomials over Z/2Z that can be written as f(f(x)) where f is a polynomial.
A350521 (program): a(n) = 18*n + 4.
A350522 (program): a(n) = 18*n + 16.
A350526 (program): a(n) = f(n*r)*c(n/r), where f = floor, c = ceiling, and r = golden ratio (A001622).
A350527 (program): a(n) = c(n*r)*f(n/r), where f = floor, c = ceiling, and r = golden ratio (A001622).
A350538 (program): a(n) is the smallest proper multiple of n which contains only even digits.
A350539 (program): Chronological Julian day number of the first day (Muharram 1) of Tabular Islamic year n.
A350551 (program): Convolution of Jacobsthal numbers and Pell numbers.
A350557 (program): Triangle T(n,k) read by rows with T(n,0) = (2*n)! / (2^n * n!) for n >= 0 and T(n,k) = (Sum_{i=k..n} binomial(i-1,k-1) * 2^i * i! / (2*i)!) * (2*n)! / (2^n * n!) for 0 < k <= n.
A350567 (program): a(n) is the maximum number of key comparisons required to perform an indirect sort of n records with distinct keys using a two-way merge (A. D. Woodall’s mergesort).
A350576 (program): a(n) = n/A055874(n) - A055874(n).
A350584 (program): Triangle read by rows, T(n, k) = [x^k] ((2*x^3 - 3*x^2 - x + 1)/(1 - x)^(n + 2)), for n >= 1 and 0 <= k < n.
A350589 (program): Sum over all partitions of [n] of the number of blocks containing their own index.
A350593 (program): Numbers k such that tau(k) + tau(k+1) = 6, where tau is the number of divisors function A000005.
A350595 (program): a(n) = Sum_{k=0..2*n} (-1)^(n+k) * binomial(2*n,k)^n.
A350616 (program): Indices of odd terms in A350877.
A350617 (program): Odd-valued terms in A350877.
A350618 (program): Terms in A350877 that immediately follow an odd term.
A350622 (program): a(n) = numerator of the X-coordinate of n*P where P is the generator [0,0] for rational points on the curve y^2 + y = x^3 + x^2.
A350623 (program): a(n) = denominator of the X-coordinate of n*P where P is the generator [0,0] for rational points on the curve y^2 + y = x^3 + x^2.
A350625 (program): a(n) = denominator of the Y-coordinate of n*P where P is the generator [0,0] for rational points on the curve y^2 + y = x^3 + x^2.
A350628 (program): Number of ways to write 2*n as 3^i (i >= 1) plus a prime.
A350629 (program): Positive even numbers that cannot be written as 3^i (i >= 1) plus a prime.
A350630 (program): Positive numbers k such that 2k cannot be written as 3^i (i >= 1) plus a prime.
A350631 (program): a(n) is the smallest multiple of n that has at least twice as many divisors as n.
A350634 (program): Products of the parts s,t in each partition of k (= 2,3,..) into two parts, ordered by increasing k and then by increasing values of s*t (see example).
A350637 (program): Triangle read by rows: T(n,k) in which row n lists the first n terms of A024916 in reverse order, 1 <= k <= n.
A350640 (program): a(n) is the minimum lcm of the part sizes of a partition of n into parts of size 3 or more.
A350643 (program): Expansion of Product_{k>=1} (1-q^(2*k))^2/(1-q^k)^7.
A350645 (program): Number of permutations avoiding 132 of length 3n composed of only 3-cycles.
A350652 (program): a(n) is where the chosen card needs to be placed in a deck of 2n cards when performing “Persistimis Possessiamo” trick.
A350653 (program): a(n) is the number of weak compositions of n into n-1 parts in which at least one part is zero.
A350661 (program): a(1) = 1; a(n) = a(A007947(n) - 1) + n.
A350666 (program): Numbers congruent to 0, 5, and 7 modulo 9: positions of 0 in A159955.
A350667 (program): Numbers congruent to 1, 3, and 8 modulo 9: positions of 1 in A159955.
A350668 (program): Numbers congruent to 2, 4, and 6 modulo 9: positions of 2 in A159955.
A350669 (program): Numerators of Sum_{j=0..n} 1/(2*j+1), for n >= 0.
A350670 (program): Denominators of Sum_{j=0..n} 1/(2*j+1), for n >= 0.
A350678 (program): Partial sums of A185381.
A350689 (program): a(n) = n*(1 - (-1)^n - 2*(3 + (-1)^n)*n^2 + 2*n^4)/384.
A350697 (program): Smallest number m > 1 such that n * m = A350538(n) contains only even digits.
A350698 (program): Consider the positive squares summing to n as obtained by the greedy algorithm; a(n) is the least of these squares.
A350700 (program): a(n) is the number of 1’s minus the number of 0’s in A004685(n).
A350716 (program): a(n) is the minimum number of vertices of degree 3 over all 3-collapsible graphs with n vertices.
A350717 (program): a(n) = 4*a(n-1) - n - 1, for n > 0, a(0) = 1.
A350740 (program): Number of integer points (x, y, z, w) at distance <= 1/2 from 3-sphere of radius n.
A350744 (program): Numbers m such that A061078(m)/A061077(m) = 4/5.
A350749 (program): Triangle read by rows: T(n,k) is the number of oriented graphs on n labeled nodes with k arcs, n >= 0, k = 0..n*(n-1)/2.
A350757 (program): a(1)=1; for n>1, a(n) is the smallest number k > a(n-1) such that a(n-1) + k is not a square.
A350765 (program): Triangle read by rows: T(n,k) is the minimum number of 1’s required to reach the maximum possible number A350764(n,k), when the stepping stone puzzle of A337663 is played on the n X k grid, 1 <= k <= n.
A350766 (program): Reversed sum of the two previous terms, with a(1) = 1 and a(2) = 11.
A350770 (program): Triangle read by rows: T(n, k) = 2^(n-k-1) + 2^k - 2, 0 <= k <= n-1.
A350771 (program): Triangle read by rows: T(n, k) = (2^(n-k-1) + 2^k - 2)*binomial(n-1, k), 0 <= k <= n-1.
A350775 (program): The balanced ternary expansion of a(n) is obtained by multiplying adjacent digits in the balanced ternary expansion of n: a(Sum_{k >= 0} t_k * 3^k) = Sum_{k >= 0} t_k * t_{k+1} * 3^k (with -1 <= t_k <= 1 for any k >= 0).
A350776 (program): Nonnegative integers whose balanced ternary expansion has no two consecutive nonzero digits.
A350786 (program): a(n) is the number of divisors of A061799(n).
A350787 (program): Convolution of A001654 and A007598.
A350801 (program): a(n) = n*(tau(n) + 1) - 2*sigma(n) for n>=1, with a(0)=0.
A350803 (program): Numbers k with at least one partition into two parts (s,t), s<=t such that t | s*k.
A350804 (program): Numbers k with exactly one partition into two parts (s,t), s<=t, such that t | s*k.
A350809 (program): a(n) = Card({ p - (n mod p) ; p prime, p <= n }).
A350816 (program): Number of minimum dominating sets in the 2 X n king graph.
A350833 (program): Run lengths of even terms in A350877 (half if even, add next prime if odd).
A350834 (program): Number of ways to tile an n X n right triangle with squares and dominoes, where vertical dominoes are only allowed in the largest vertical column.
A350847 (program): Number of even parts in the conjugate of the integer partition with Heinz number n.
A350851 (program): Cumulative sums of the first ceiling(n/2)+1 elements of rows 0 to n in Pascal’s triangle.
A350855 (program): a(0) = 1, a(n) = (n+1)*a(n-1) + (n-2).
A350856 (program): Initial members of prime triples (p, p+2, p+14).
A350865 (program): Sum of the larger parts in the partitions of n into two prime parts.
A350866 (program): a(n) = A010051(A339399(n)).
A350869 (program): a(n) = Sum_{i=0..10^n-1} i^3.
A350872 (program): Number of coincidence site lattices of index n in square lattice.
A350883 (program): Sum of the smaller parts of the partitions of n into two prime parts.
A350885 (program): Decimal expansion of 1 - 2*cotan(2).
A350895 (program): a(n) = 1 + a(n-1) * prime(n), starting a(0) = 1.
A350917 (program): a(0) = 1, a(1) = 2, and a(n) = 23*a(n-1) - a(n-2) - 4 for n >= 2.
A350919 (program): a(0) = 9, a(1) = 9, and a(n) = 3*a(n-1) - a(n-2) - 4 for n >= 2.
A350920 (program): a(0) = 5, a(1) = 5, and a(n) = 4*a(n-1) - a(n-2) - 4 for n >= 2.
A350921 (program): a(0) = 3, a(1) = 3, and a(n) = 6*a(n-1) - a(n-2) - 4 for n >= 2.
A350922 (program): a(0) = 2, a(1) = 5, and a(n) = 7*a(n-1) - a(n-2) - 4 for n >= 2.
A350923 (program): a(0) = 2, a(1) = 2, and a(n) = 10*a(n-1) - a(n-2) - 4 for n >= 2.
A350924 (program): a(0) = 1, a(1) = 3, and a(n) = 16*a(n-1) - a(n-2) - 4 for n >= 2.
A350925 (program): a(0) = 1, a(1) = 9, and a(n) = 16*a(n-1) - a(n-2) - 4 for n >= 2.
A350926 (program): a(0) = 1, a(1) = 17, and a(n) = 23*a(n-1) - a(n-2) - 4 for n >= 2.
A350941 (program): Number of odd conjugate parts minus number of even conjugate parts in the integer partition with Heinz number n.
A350957 (program): Number of ways to write 2*n as 3^i (i >= 0) plus a prime.
A350958 (program): Positive numbers k such that 2k cannot be written as 3^i (i >= 0) plus a prime.
A350959 (program): Number of ways to write 2*n+1 as 2^i (i >= 0) plus a prime.
A350960 (program): a(n) = (A006285(n)-1)/2.
A350961 (program): a(n) = Sum_{k=1..n} 3^Omega(k).
A350962 (program): a(n) = A068527(2*n).
A350965 (program): a(n) = sqrt(6*A138288(n)^2 - 2).
A350966 (program): a(n) = sqrt(28*A296377(n)^2 - 3).
A350967 (program): a(n) = sqrt(84*A144930(n)^2 - 3).
A350968 (program): a(n) = (A350967(n)-1)/2.
A350972 (program): E.g.f. = tan(x).
A350973 (program): T(n,n-5), where T(*,*) is A350970.
A350979 (program): a(0)=1, a(1)=652, thereafter a(n) = 254*a(n-1)-a(n-2)+378.
A350980 (program): a(0)=17, a(1)=4700, thereafter a(n) = 254*a(n-1)-a(n-2)+378.
A350981 (program): Union of A350979 and A350980.
A350982 (program): a(0)=0, a(1)=49, thereafter a(n) = 14*a(n-1)-a(n-2)+42.
A350983 (program): a(0)=1, a(1)=25, a(2)=865; a(n) = 35*(a(n-1)-a(n-2))+a(n-3).
A350984 (program): a(0)=0, a(1)=18, a(2)=612; a(n) = 35*(a(n-1)-a(n-2))+a(n-3).
A350985 (program): a(0)=4, a(1)=148, a(2)=5044; a(n) = 35*(a(n-1)-a(n-2))+a(n-3).
A350986 (program): a(0)=3, a(1)=105, a(2)=3567; a(n) = 35*(a(n-1)-a(n-2))+a(n-3).
A350994 (program): a(n) = (40*100^n + 6*10^n - 1)/3.
A350995 (program): a(n) = (16*10^n-1)/3.
A350996 (program): a(n) = Sum_{k=1..n} k * rad(k).
A350997 (program): a(n) = Sum_{k=1..n} k^rad(k).
A351010 (program): Numbers k such that the k-th composition in standard order is a concatenation of twins (x,x).
A351028 (program): G.f. A(x) satisfies: A(x) = x + x^2 * A(x/(1 - 2*x)) / (1 - 2*x).
A351046 (program): a(1)=1; a(2)=4; for n>2, a(n) = a(n-1) + A000217(n)*a(n-2).
A351049 (program): G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - 3*x)) / (1 - 3*x).
A351050 (program): G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - 4*x)) / (1 - 4*x).
A351053 (program): G.f. A(x) satisfies: A(x) = x + x^2 * A(x/(1 - 3*x)) / (1 - 3*x).
A351056 (program): G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - 5*x)) / (1 - 5*x).
A351057 (program): G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - 6*x)) / (1 - 6*x).
A351058 (program): Number of numbers <= n that are either nonprime divisors of n or primes not dividing n.
A351083 (program): a(n) = gcd(n, A003415(A276086(n))), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.
A351090 (program): Lexicographically earliest infinite sequence such that a(i) = a(j) => A351091(i) = A351091(j) and A351092(i) = A351092(j), for all i, j >= 1.
A351103 (program): a(n) is the total number of polygons left over with maximum number of sides when partitioning the set of vertices of a convex n-gon into nonintersecting polygons.
A351112 (program): Number of balanced numbers dividing n.
A351113 (program): Sum of the balanced numbers dividing n.
A351114 (program): Characteristic function of balanced numbers.
A351115 (program): Number of balanced numbers <= n.
A351116 (program): Sum of the balanced numbers <= n.
A351118 (program): a(n) is the number of endofunctions on an n-set where there is an element with a preimage of cardinality greater than n/2.
A351121 (program): Numbers k such that k^2 - k + 1 is not squarefree.
A351125 (program): Numbers that are sums of consecutive primorial numbers.
A351128 (program): G.f. A(x) satisfies: A(x) = x + x^2 * A(x/(1 - 4*x)) / (1 - 4*x).
A351132 (program): G.f. A(x) satisfies: A(x) = x + x^2 * A(x/(1 - 5*x)) / (1 - 5*x).
A351140 (program): a(1) = 1, a(n) = smallest prime > a(n-1) + n.
A351143 (program): G.f. A(x) satisfies: A(x) = 1 + x^2 * A(x/(1 - 2*x)) / (1 - 2*x).
A351144 (program): G.f. A(x) satisfies: A(x) = 1 + x^2 * A(x/(1 - 3*x)) / (1 - 3*x).
A351150 (program): G.f. A(x) satisfies: A(x) = 1 + x^2 * A(x/(1 - 4*x)) / (1 - 4*x).
A351151 (program): G.f. A(x) satisfies: A(x) = 1 + x^2 * A(x/(1 - 5*x)) / (1 - 5*x).
A351152 (program): G.f. A(x) satisfies: A(x) = 1 + x^2 * A(x/(1 - 6*x)) / (1 - 6*x).
A351153 (program): Triangle read by rows: T(n, k) = n*(k - 1) - k*(k - 3)/2 with 0 < k <= n.
A351161 (program): G.f. A(x) satisfies: A(x) = x + x^2 * A(x/(1 - 6*x)) / (1 - 6*x).
A351164 (program): Decimal expansion of gamma * BesselI(0,2) + BesselK(0,2).
A351168 (program): If n = p_1^e_1 * … * p_k^e_k, where p_1 < … < p_k are primes, then a(n) is obtained by replacing the last factor p_k^e_k by (p_k - 1)^e_k; a(1) = 1.
A351169 (program): a(n) is the minimum number of vertices of degree 4 over all 4-collapsible graphs with n vertices.
A351184 (program): G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 + 3*x)) / (1 + 3*x).
A351185 (program): G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 + 4*x)) / (1 + 4*x).
A351186 (program): G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 + 5*x)) / (1 + 5*x).
A351187 (program): G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 + 6*x)) / (1 + 6*x).
A351188 (program): G.f. A(x) satisfies: A(x) = x + x^3 * A(x/(1 + x)) / (1 + x).
A351189 (program): G.f. A(x) satisfies: A(x) = x^2 + x^3 * A(x/(1 + x)) / (1 + x).
A351193 (program): Sum of the 5th powers of primes dividing n.
A351194 (program): Sum of the 6th powers of the primes dividing n.
A351195 (program): Sum of the 7th powers of the primes dividing n.
A351196 (program): Sum of the 8th powers of the primes dividing n.
A351197 (program): Sum of the 9th powers of the primes dividing n.
A351198 (program): Sum of the 10th powers of the primes dividing n.
A351208 (program): Decimal expansion of the 11th root of 3.
A351209 (program): Decimal expansion of the 12th root of 3.
A351210 (program): Decimal expansion of the 13th root of 3.
A351219 (program): Multiplicative with a(p^e) = Fibonacci(e+1).
A351223 (program): a(n) is the number of triangular arrays containing the first 3*(n - 1) positive integers arranged with number n on each side and having different set of the sets of the side integers.
A351225 (program): a(n) = A276086(n) - n, where A276086 is the primorial base exp-function.
A351226 (program): Numbers k for which A276086(k) < k, where A276086 is the primorial base exp-function.
A351227 (program): Numbers k for which A276086(k) > k, where A276086 is the primorial base exp-function.
A351230 (program): Numerator of A003415(n) / A276086(n), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.
A351231 (program): Denominator of A003415(n) / A276086(n), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.
A351232 (program): a(n) = floor(A276086(n) / A003415(n)), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.
A351233 (program): a(n) = A276085(A351231(n)).
A351234 (program): a(n) = A276085(gcd(A003415(n), A276086(n))).
A351238 (program): Numbers M such that 87 * M = 1M1, where 1M1 denotes the concatenation of 1, M and 1.
A351242 (program): a(n) = n^3 * Sum_{p|n, p prime} 1/p^3.
A351244 (program): a(n) = n^4 * Sum_{p|n, p prime} 1/p^4.
A351245 (program): a(n) = n^5 * Sum_{p|n, p prime} 1/p^5.
A351246 (program): a(n) = n^6 * Sum_{p|n, p prime} 1/p^6.
A351247 (program): a(n) = n^7 * Sum_{p|n, p prime} 1/p^7.
A351248 (program): a(n) = n^8 * Sum_{p|n, p prime} 1/p^8.
A351249 (program): a(n) = n^9 * Sum_{p|n, p prime} 1/p^9.
A351250 (program): Numerator of n / A276086(n).
A351251 (program): Denominator of n / A276086(n).
A351252 (program): a(n) = sigma(n) * A276086(n), pointwise product of the sum of divisors function and the primorial base exp-function.
A351253 (program): a(n) = A276085(A351251(n)).
A351254 (program): a(n) = A276085(gcd(n, A276086(n))).
A351262 (program): a(n) = n^10 * Sum_{p|n, p prime} 1/p^10.
A351265 (program): Sum of the squares of the squarefree divisors of n.
A351266 (program): Sum of the cubes of the squarefree divisors of n.
A351267 (program): Sum of the 4th powers of the squarefree divisors of n.
A351268 (program): Sum of the 5th powers of the squarefree divisors of n.
A351269 (program): Sum of the 6th powers of the squarefree divisors of n.
A351270 (program): Sum of the 7th powers of the squarefree divisors of n.
A351271 (program): Sum of the 8th powers of the squarefree divisors of n.
A351272 (program): Sum of the 9th powers of the squarefree divisors of n.
A351273 (program): Sum of the 10th powers of the squarefree divisors of n.
A351279 (program): a(n) = Sum_{k=0..n} 2^k * k^(n-k).
A351282 (program): a(n) = Sum_{k=0..n} 3^k * k^(n-k).
A351283 (program): G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - x)) / (1 - x)^4.
A351294 (program): Heinz numbers of Look-and-Say partitions. Numbers whose multiset of prime factors has at least one permutation with all distinct run-lengths.
A351295 (program): Heinz numbers of non-Look-and-Say partitions. Numbers whose multiset of prime factors has no permutation with all distinct run-lengths.
A351300 (program): a(n) = n^5 * Product_{p|n, p prime} (1 + 1/p^5).
A351301 (program): a(n) = n^6 * Product_{p|n, p prime} (1 + 1/p^6).
A351302 (program): a(n) = n^7 * Product_{p|n, p prime} (1 + 1/p^7).
A351303 (program): a(n) = n^8 * Product_{p|n, p prime} (1 + 1/p^8).
A351304 (program): a(n) = n^9 * Product_{p|n, p prime} (1 + 1/p^9).
A351305 (program): a(n) = n^10 * Product_{p|n, p prime} (1 + 1/p^10).
A351307 (program): Sum of the squares of the square divisors of n.
A351308 (program): Sum of the cubes of the square divisors of n.
A351309 (program): Sum of the 4th powers of the square divisors of n.
A351310 (program): Sum of the 5th powers of the square divisors of n.
A351311 (program): Sum of the 6th powers of the square divisors of n.
A351313 (program): Sum of the 7th powers of the square divisors of n.
A351314 (program): Sum of the 8th powers of the square divisors of n.
A351315 (program): Sum of the 9th powers of the square divisors of n.
A351316 (program): Sum of the 10th powers of the square divisors of n.
A351319 (program): a(n) = floor(n/k), where k is the nearest square to n.
A351331 (program): a(n) = (n+1)*n^n + n - 1.
A351340 (program): a(n) = Sum_{k=0..n} n^k * k^(n-k).
A351346 (program): Dirichlet g.f.: Product_{p prime} 1 / (1 - 2*p^(-s) - p^(-2*s)).
A351347 (program): Dirichlet g.f.: Product_{p prime} 1 / (1 - p^(-s) - 2*p^(-2*s)).
A351348 (program): Dirichlet g.f.: Product_{p prime} (1 + 2*p^(-s)) / (1 - p^(-s) - p^(-2*s)).
A351353 (program): Numbers k such that k^2 is a centered 40-gonal number.
A351354 (program): Numbers k such that the k-th centered 40-gonal numbers (A195317) is a square.
A351355 (program): Number of ways the numbers from 1..n do not divide numbers from n+1..2n.
A351362 (program): Number of ways the numbers from 1..n do not divide the numbers from n..2n-1.
A351364 (program): Number of necklaces with n black and n white beads that avoid the pattern BBBB.
A351365 (program): a(n) = Sum_{p|n, p prime} n^p.
A351366 (program): a(n) = Sum_{p|n, p prime} p^p.
A351368 (program): a(n) = Sum_{p|n, p prime} prime(p).
A351369 (program): a(n) = Sum_{p|n, p prime} p * prime(p).
A351371 (program): a(n) = Sum_{p|n, p prime} (p + n/p).
A351381 (program): Table read by downward antidiagonals: T(n,k) = n*(k+1)^2.
A351385 (program): Triangle read by rows: T(n,k) = Sum_{j=k..n} binomial(n + j, n)*binomial(n, j)/(j + 1).
A351389 (program): Maximum k for which the grid graph P_3 X P_k is a subgraph of the n X n knight graph.
A351394 (program): Number of divisors of n that are either squarefree, prime powers, or both.
A351395 (program): Sum of the divisors of n that are either squarefree, prime powers, or both.
A351397 (program): Sum of the exponents in the prime factorizations of the prime power divisors of n.
A351398 (program): Numbers k >= 3 such that the arithmetic mean of the divisors of k AND the arithmetic mean of the nondivisors of k are integers.
A351402 (program): G.f. A(x) satisfies: 1 / (1 - x) = Product_{i>=1, j>=1} A(x^(i*j)).
A351403 (program): G.f. A(x) satisfies: (1 - x) = Product_{i>=1, j>=1} A(x^(i*j)).
A351411 (program): Number of divisors of n not of the form p^p, p prime.
A351412 (program): a(1) = 1, a(2) = 2, a(3) = 3. Then if n is even a(n) is the least positive integer not yet in the sequence, otherwise if n is odd a(n) = a(n-1) + a(n-3).
A351414 (program): Number of divisors of n that are either prime or have at least 1 square divisor > 1 and at least two distinct prime factors.
A351415 (program): Intersection of Beatty sequences for (1+sqrt(5))/2 and sqrt(5).
A351416 (program): Number of divisors of n that are either squarefree semiprimes, numbers of the form p^k (p prime, k>1), or numbers with at least one square divisor > 1 and 3 or more distinct prime factors.
A351417 (program): Number of divisors of n that are either prime or have at least one square divisor > 1.
A351418 (program): Number of divisors of n that are either of the form p^k (p prime, k>1) or are nonprime squarefree numbers.
A351419 (program): If n = p_1^e_1 * … * p_k^e_k, where p_1 < … < p_k are primes, then a(n) is obtained by replacing the last factor p_k^e_k by (p_k - 1)^(e_k + 1); a(1) = 1.
A351425 (program): If n = p_1^e_1 * … * p_k^e_k, where p_1 < … < p_k are primes, then a(n) is obtained by replacing the last factor p_k^e_k by (p_k + 1)^(e_k - 1); a(1) = 1.
A351434 (program): If n = Product (p_j^k_j) then a(n) = Product ((p_j - 1)^(k_j + 1)).
A351435 (program): If n = Product (p_j^k_j) then a(n) = Product ((p_j + 1)^(k_j + 1)).
A351436 (program): a(n) = n - A351168(n).
A351437 (program): G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - x)) / (1 - x)^2.
A351438 (program): G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - x)) / (1 - x)^3.
A351442 (program): a(n) = A003958(sigma(n)), where A003958 is multiplicative with a(p^e) = (p-1)^e and sigma is the sum of divisors function.
A351444 (program): a(n) = n - A003958(n) + A003958(sigma(n)), where A003958 is multiplicative with a(p^e) = (p-1)^e and sigma is the sum of divisors function.
A351445 (program): a(n) = A003958(sigma(n)) - A003958(n), where A003958 is multiplicative with a(p^e) = (p-1)^e and sigma is the sum of divisors function.
A351446 (program): Numbers k for which A003958(sigma(k)) = A003958(k), where A003958 is multiplicative with a(p^e) = (p-1)^e and sigma is the sum of divisors function.
A351449 (program): a(n) = A064989(A295294(A003961(n))).
A351450 (program): a(n) = A064989(A048250(A003961(n))).
A351454 (program): Lexicographically earliest infinite sequence such that a(i) = a(j) => A006530(i) = A006530(j), A329697(i) = A329697(j) and A331410(i) = A331410(j) for all i, j >= 1.
A351456 (program): a(n) = A003958(sigma(A003961(n))), where A003958 is multiplicative with a(p^e) = (p-1)^e, A003961 multiplicative with a(prime(k)^e) = prime(1+k)^e, and sigma is the sum of divisors function.
A351457 (program): a(n) = A351456(n) - A339905(n).
A351460 (program): Lexicographically earliest infinite sequence such that a(i) = a(j) => A006530(i) = A006530(j), A206787(i) = A206787(j) and A336651(i) = A336651(j) for all i, j >= 1.
A351466 (program): a(n) = (a(n-1) + a(n-3))/2 if a(n) is even. If a(n) is odd, do not divide by 2.
A351489 (program): Irregular triangle read by rows: T(n,k) is the minimum number of alphabetic symbols in a regular expression for the k lexicographically first palindromes of length 2*n over a binary alphabet, n >= 0, 1 <= k <= 2^n.
A351490 (program): Irregular triangle read by rows: T(n,k) is the minimum number of alphabetic symbols in a regular expression for the k lexicographically first palindromes of odd length 2*n-1 over a binary alphabet, n >= 1, 1 <= k <= 2^n.
A351491 (program): Irregular triangle read by rows: T(n,k) is the minimum number of alphabetic symbols in a regular expression for the k lexicographically first palindromes of length 2*n over a ternary alphabet, n >= 0, 1 <= k <= 3^n.
A351501 (program): a(n) = binomial(n^2 + n - 1, n) / (n^2 + n - 1).
A351503 (program): Expansion of e.g.f. 1/(1 + x^2 * log(1 - x)).
A351505 (program): Expansion of e.g.f. 1/(1 + x^2/2 * log(1 - x)).
A351516 (program): a(n) is the maximum number of 3-letter words that can be contained in an n X n crossword puzzle.
A351517 (program): a(n) = Product_{p|n, p prime} p^(pi(p) mod 2).
A351518 (program): a(n) = Product_{p|n, p prime} p^((pi(p)+1) mod 2).
A351519 (program): a(n) = tau(n) + pi(n) - omega(n).
A351520 (program): Number of numbers <= n that are either squarefree, a divisor of n, or both.
A351521 (program): Dirichlet g.f.: Product_{p prime} (1 + 4*p^(-s)).
A351528 (program): Prime numbers ordered by their binary reversal.
A351529 (program): The number of quaternary strings of length n containing 00.
A351530 (program): The number of quinary strings of length n containing 00.
A351531 (program): a(0)=1; a(1)=1; for n>1, a(n) = a(n-1) + 3*n*a(n-2).
A351533 (program): Odd numbers k that are multiples of 3 and for which sigma(k) is congruent to 2 modulo 4.
A351544 (program): a(n) is the largest unitary divisor of sigma(n) such that its every prime factor also divides A003961(n), where A003961 is fully multiplicative with a(p) = nextprime(p), and sigma is the sum of divisors function.
A351546 (program): a(n) is the largest unitary divisor of sigma(n) coprime with A003961(n), where A003961 is fully multiplicative with a(p) = nextprime(p), and sigma is the sum of divisors function.
A351556 (program): a(n) = gcd(n, A019565(n)).
A351557 (program): a(n) = gcd(sigma(n), A019565(n)).
A351559 (program): a(n) = A048675(gcd(sigma(n), A019565(n))).
A351560 (program): a(n) is a binary representation of the primes that divide sigma(n) [the sum of divisors of n function], shown in decimal.
A351561 (program): a(n) = n + d(n) - phi(n), where d is the number of divisors function, and phi is the Euler totient function.
A351562 (program): Odd composites k such that A342926(2*k) is a multiple of 3.
A351563 (program): a(n) is the exponent of the second smallest prime factor of n, or 0 if n is a power of a prime.
A351564 (program): a(n) = 1 if all the exponents in the prime factorization of n are distinct, and 0 otherwise.
A351565 (program): Odd part of Kimberling’s paraphrases: a(n) = A000265(A003602(n)).
A351566 (program): Radix of the second least significant nonzero digit in the primorial base expansion of n, or 1 if there is no such digit.
A351567 (program): The second least significant nonzero digit in the primorial base expansion of n, or 0 if there is no such digit.
A351569 (program): Sum of divisors of the largest unitary divisor of n that is an exponentially odd number.
A351571 (program): Arithmetic derivative of the sum of the divisors of the largest unitary divisor of n that is an exponentially odd number.
A351577 (program): a(n) = A003557(A276076(n)).
A351580 (program): a(n) is the number of multisets of size n-1 consisting of permutations of n elements.
A351599 (program): a(n) is the smallest integer m > 0 such that m*n is a digitally balanced number (A031443).
A351600 (program): a(n) = n^2 * Sum_{d^2|n} 1 / d^2.
A351601 (program): a(n) = n^3 * Sum_{d^2|n} 1 / d^3.
A351602 (program): a(n) = n^4 * Sum_{d^2|n} 1 / d^4.
A351603 (program): a(n) = n^5 * Sum_{d^2|n} 1 / d^5.
A351604 (program): a(n) = n^6 * Sum_{d^2|n} 1 / d^6.
A351605 (program): a(n) = n^7 * Sum_{d^2|n} 1 / d^7.
A351606 (program): a(n) = n^8 * Sum_{d^2|n} 1 / d^8.
A351607 (program): a(n) = n^9 * Sum_{d^2|n} 1 / d^9.
A351608 (program): a(n) = n^10 * Sum_{d^2|n} 1 / d^10.
A351612 (program): Number of ordered pairs, (s,t), 1 <= s <= t, such that (t^s) | n.
A351619 (program): a(n) = Sum_{p|n, p prime} (-1)^p.
A351620 (program): a(1) = 1; a(n) = a(n-1) + Sum_{k=2..n} a(floor(n/k)).
A351621 (program): a(1) = 1; a(n) = 1 + a(n-1) + Sum_{k=2..n} a(floor(n/k)).
A351628 (program): Partial sums of A352717.
A351631 (program): The numbers that are not doubled in column -1 of the extended Trithoff (tribonacci) array.
A351632 (program): Number of copies of the star graph S(2,1,1,1) contained in the n-dimensional hypercube graph.
A351635 (program): a(n) is the number of perfect matchings of an edge-labeled 2 X n Klein bottle grid graph, or equivalently the number of domino tilings of a 2 X n Klein bottle grid. (The twist is on the length-n side.)
A351647 (program): Sum of the squares of the odd proper divisors of n.
A351648 (program): G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - x)) / (1 - x)^5.
A351653 (program): a(n) is the concatenation of the length of each run of digits in the decimal representation of n.
A351654 (program): Dirichlet g.f.: zeta(s) / (zeta(s-1) * zeta(s-2)).
A351655 (program): Dirichlet g.f.: Product_{p prime} 1 / (1 - p^(-s) - p^(-2*s) - p^(-3*s)).
A351656 (program): Dirichlet g.f.: Product_{p prime} 1 / (1 - p^(-s) - p^(-2*s) - p^(-3*s) - p^(-4*s)).
A351658 (program): G.f. A(x) satisfies: A(x) = 1 - x * A(x/(1 - x)^2) / (1 - x).
A351659 (program): G.f. A(x) satisfies: A(x) = 1 - x * A(x/(1 - x)^2) / (1 - x)^2.
A351660 (program): G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 * A(x/(1 - x)) / (1 - x)^2.
A351683 (program): Squares that are also 4-dimensional pyramidal numbers.
A351697 (program): 32*a(n) is the denominator of the squared circumradius of a cyclic quadrilateral with sides n, n+1, n+2, n+3.
A351702 (program): In the balanced ternary representation of n, reverse the order of digits other than the most significant.
A351704 (program): Sums of the ascending diagonals of the triangle A162609.
A351706 (program): For any nonnegative number n with binary expansion Sum_{k >= 0} b_k * 2^k, a(n) is the denominator of d(n) = Sum_{k >= 0} b_k * 2^A130472(k). See A351705 for the numerators.
A351707 (program): G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 * A(x/(1 - x)) / (1 - x)^2.
A351709 (program): a(n) = Sum_{p|n, p prime} p!.
A351711 (program): a(n) = Sum_{p|n, p prime} Sum_{d|n} gcd(d,p).
A351714 (program): Lucas-Niven numbers: numbers that are divisible by the number of terms in their minimal (or greedy) representation in terms of the Lucas numbers (A130310).
A351733 (program): Expansion of e.g.f. exp( 2 * x * (exp(x) - 1) ).
A351734 (program): Expansion of e.g.f. exp( 3 * x * (exp(x) - 1) ).
A351736 (program): Expansion of e.g.f. exp( x * (exp(2 * x) - 1) ).
A351737 (program): Expansion of e.g.f. exp( x * (exp(3 * x) - 1) ).
A351742 (program): Number of partitions of 2n into n parts of size 1, 5, 10 or 25.
A351744 (program): Increment all even digits of n.
A351746 (program): a(n) = Sum_{p|n, p prime} (p-1) * tau(n/p).
A351749 (program): a(n) = Sum_{p|n, p prime} sigma_p(p).
A351750 (program): a(n) = Sum_{p|n, p prime} p * sigma_p(p).
A351752 (program): Floor of the average of the numbers |x-y| over all pairs (x,y) with x*y = n, x <= y.
A351754 (program): G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 + x^5 * A(x/(1 - x)) / (1 - x)^2.
A351755 (program): G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 * A(x/(1 - x)) / (1 - x)^2.
A351756 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 2*x)) / (1 - 2*x)^2.
A351757 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 3*x)) / (1 - 3*x)^2.
A351760 (program): a(n) = Sum_{1 <= i < j <= n} (i*j)^4.
A351762 (program): Expansion of e.g.f. 1/(1 - 2*x*exp(x)).
A351763 (program): Expansion of e.g.f. 1/(1 - 3*x*exp(x)).
A351765 (program): a(n) = n! * Sum_{k=0..n} n^(n-k) * (n-k)^k/k!.
A351766 (program): a(n) = Sum_{j=1..n} Sum_{i=1..j} (i*j)^4.
A351768 (program): a(n) = n! * Sum_{k=0..n} k^(n-k) * (n-k)^k/k!.
A351770 (program): a(n) = Sum_{j=1..n} Sum_{i=1..j} (i*j)^5.
A351777 (program): Expansion of e.g.f. 1/(1 + 2*x*exp(x)).
A351778 (program): Expansion of e.g.f. 1/(1 + 3*x*exp(x)).
A351779 (program): a(n) = n! * Sum_{k=0..n} (-n)^(n-k) * (n-k)^k/k!.
A351780 (program): a(n) = n! * Sum_{k=0..n} (-k)^(n-k) * (n-k)^k/k!.
A351782 (program): a(n) = n-2 if n is a multiple of 4, a(n) = n-1 otherwise.
A351792 (program): Expansion of e.g.f. 1/(1 - x*exp(-3*x)).
A351793 (program): Expansion of e.g.f. 1/(1 - x*exp(-4*x)).
A351795 (program): a(n) = n! * Sum_{k=0..n} (k * (n-k))^k/k!.
A351796 (program): a(n) = n! * Sum_{k=0..n} (-k * (n-k))^k/k!.
A351805 (program): a(n) = Sum_{1 <= i < j <= n} j^5*i^5.
A351810 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 4*x)) / (1 - 4*x)^2.
A351811 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 5*x)) / (1 - 5*x)^2.
A351812 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 6*x)) / (1 - 6*x)^2.
A351813 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - x)^3) / (1 - x).
A351816 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - x)^3) / (1 - x)^3.
A351825 (program): Total number of size 2 lists in all sets of lists partitioning [n] (cf. A000262).
A351827 (program): Sum of the numbers <= n that are either prime, a divisor of n, or both.
A351828 (program): Sum of the numbers <= n that are either squarefree, a divisor of n, or both.
A351831 (program): Vector in the 26-dimensional even Lorentzian unimodular lattice II_25,1 used to construct the Leech lattice.
A351833 (program): Number of partitions of n into exactly two parts, at least one of which is squarefree.
A351843 (program): a(n) = sigma(n) * sopf(n).
A351846 (program): Irregular triangle read by rows: T(n,k), n >= 0, k >= 0, in which n appears 4*n + 1 times in row n.
A351850 (program): a(n) is the number of iterations of the computation of the A351849 tag system when started from the word encoding n, or -1 if the number of iterations is infinite.
A351856 (program): Number of nonnegative integer solutions to 2*n = x_1 + x_2 + … + x_n + 2*y_1 + 2*y_2 + … + 2*y_n.
A351857 (program): Number of nonnegative integer solutions to n = x_1 + x_2 + … + x_(2*n) + 2*y_1 + 2*y_2 + … + 2*y_(2*n).
A351858 (program): a(n) = [x^n] (1 + x + x^2)^(3*n)/(1 + x)^(2*n).
A351863 (program): Numbers k with at least one divisor, d, such that k-d is prime.
A351864 (program): Numerator of zeta({6}_n)/Pi^(6n).
A351867 (program): Heptagonal numbers (or 7-gonal numbers) which are products of four distinct primes.
A351871 (program): a(1) = 1, a(2) = 2; a(n) = gcd(a(n-1), a(n-2)) + (a(n-1) + a(n-2))/gcd(a(n-1), a(n-2)).
A351873 (program): Number of subsets of {1,2,…,n} whose elements do not differ by 3 or 4.
A351874 (program): Number of subsets of {1,2,…,n} such that any pair of elements do not differ by 1, 3, or 4.
A351875 (program): Positive difference of the distinct prime factors of A129521(n).
A351894 (program): Numbers that contain only odd digits in their factorial-base representation.
A351898 (program): Decimal expansion of metallic ratio for N = 14.
A351905 (program): Expansion of e.g.f. exp(x * (1 - x^3)).
A351911 (program): a(n) is the least integer m such that every m-element subset of {1,2,3,…,n} contains two nonempty and disjoint subsets whose sums are equal.
A351912 (program): Period of binary representation of 1/n, or 0 if 1/n terminates.
A351914 (program): Numbers m such that the average of the prime numbers up to m is greater than or equal to m/2.
A351923 (program): Number of ordered pairs of positive integers (s,t), s,t <= n, such that (s^t) | n.
A351929 (program): Expansion of e.g.f. exp(x - x^3/6).
A351930 (program): Expansion of e.g.f. exp(x - x^4/24).
A351931 (program): Expansion of e.g.f. exp(x - x^5/120).
A351932 (program): Number of set partitions of [n] such that block sizes are either 1 or 4.
A351933 (program): Expansion of e.g.f. exp(x / (1 - x^2/2)).
A351940 (program): a(n) is the number of partitions of the set {1,2,…,n} into lists having a prime number of elements.
A351942 (program): Arithmetic derivative of A181819(n), where A181819(n) = Product prime(e(i)) when n = Product prime(i)^e(i).
A351943 (program): a(n) = A069359(A181819(n)).
A351944 (program): a(n) = A003557(A181819(n)).
A351946 (program): a(n) = A051903(A181819(n)).
A351950 (program): Arithmetic derivative of the factorial base exp-function: a(n) = A003415(A276076(n)).
A351951 (program): a(n) = A069359(A276076(n)).
A351952 (program): a(n) = A351950(n) / A351577(n).
A351954 (program): Arithmetic derivative without its inherited divisor applied to the prime shadow of the factorial base exp-function: a(n) = A342001(A181819(A276076(n))).
A351956 (program): a(n) = 1 if either n = 1 or the primorial inflation of n is equal to k * p#, where p# is the primorial (A034386) of some prime p, and 1 <= k < p, otherwise 0.
A351957 (program): a(n) = 1 if the primorial inflation of k is a sum of distinct primorial numbers, otherwise 0.
A351958 (program): a(1) = 1, followed by numbers k for which the primorial inflation of k is equal to x * p#, where p# is the primorial (A034386) of some prime p, and 1 <= x < p.
A351974 (program): a(n) is the first maximum reached by iterating the reduced Collatz function R on 4n-1: a(n) = R^s(4n-1), where R(k) = A139391(k) and s the number of iterations required.
A351979 (program): Numbers whose prime factorization has all odd prime indices and all even prime exponents.
A351985 (program): If n = abcd… in decimal, a(n) = |a^3 - b^3 + c^3 - d^3 + …|.
A351990 (program): Number of minimum edge covers of the complete graph K_n.
A351992 (program): Number of minimum edge covers in the n-vertex wheel graph.
A352002 (program): a(n) = prime(n)# + prime(n), where prime(n)# is the n-th primorial number A002110(n).
A352013 (program): a(n) = Sum_{d|n} (-1)^(n/d+1) * (n-1)!/(d-1)!.
A352024 (program): Largest digit in the decimal expansion of 1/A352023(n).
A352025 (program): a(n) = floor(sqrt(6*prime(n))).
A352027 (program): a(n) = binomial(2*n-1,n) - n*(n-1) - 1.
A352031 (program): Sum of the cubes of the odd proper divisors of n.
A352032 (program): Sum of the 4th powers of the odd proper divisors of n.
A352033 (program): Sum of the 5th powers of the odd proper divisors of n.
A352034 (program): Sum of the 6th powers of the odd proper divisors of n.
A352035 (program): Sum of the 7th powers of the odd proper divisors of n.
A352036 (program): Sum of the 8th powers of the odd proper divisors of n.
A352037 (program): Sum of the 9th powers of the odd proper divisors of n.
A352038 (program): Sum of the 10th powers of the odd proper divisors of n.
A352044 (program): a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-1,2*k) * a(k).
A352047 (program): Sum of the divisor complements of the odd proper divisors of n.
A352048 (program): Sum of the squares of the divisor complements of the odd proper divisors of n.
A352049 (program): Sum of the cubes of the divisor complements of the odd proper divisors of n.
A352050 (program): Sum of the 4th powers of the divisor complements of the odd proper divisors of n.
A352051 (program): Sum of the 5th powers of the divisor complements of the odd proper divisors of n.
A352052 (program): Sum of the 6th powers of the divisor complements of the odd proper divisors of n.
A352053 (program): Sum of the 7th powers of the divisor complements of the odd proper divisors of n.
A352054 (program): Sum of the 8th powers of the divisor complements of the odd proper divisors of n.
A352055 (program): Sum of the 9th powers of the divisor complements of the odd proper divisors of n.
A352056 (program): Sum of the 10th powers of the divisor complements of the odd proper divisors of n.
A352060 (program): a(n) = (n - 1)! * omega(n), where omega(n) = number of distinct primes dividing n (A001221).
A352063 (program): Number of ordered factorizations of 2*n + 1 into odd factors > 1.
A352069 (program): Expansion of e.g.f. 1 / (1 + log(1 - 3*x) / 3).
A352071 (program): Expansion of e.g.f. 1 / (1 + log(1 - 4*x) / 4).
A352074 (program): a(n) = Sum_{k=0..n} Stirling1(n,k) * k! * (-n)^(n-k).
A352080 (program): a(n) is the number of times that the square root operation must be applied to n in order to reach an irrational number.
A352082 (program): a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^n.
A352100 (program): Number of partitions of 2n into two odd parts that are not both prime.
A352103 (program): a(n) is the maximal (or lazy) tribonacci representation of n using a binary system of vectors not containing three consecutive 0’s.
A352104 (program): a(n) is the number of 1’s in the maximal tribonacci representation of n (A352103).
A352111 (program): In the factorial base expansion of n, replace each place value, say k! with k > 0, by (-1)^(k-1) * k!.
A352112 (program): In the primorial base expansion of n, replace each place value, say A002110(k) with k >= 0, by (-1)^k * A002110(k).
A352115 (program): Partial sums of the even triangular numbers (A014494).
A352116 (program): Partial sums of the odd triangular numbers (A014493).
A352117 (program): Expansion of e.g.f. 1/sqrt(2 - exp(2*x)).
A352119 (program): Expansion of e.g.f. 1/(2 - exp(4*x))^(1/4).
A352141 (program): Numbers whose prime factorization has all even indices and all even exponents.
A352149 (program): a(n) = Sum_{k=0..n-1} binomial(n,k)^2 * (n-k-1)!.
A352150 (program): a(n) = Sum_{k=0..n-1} (-1)^k * binomial(n,k)^2 * (n-k-1)!.
A352161 (program): Numbers m such that the smallest digit in the decimal expansion of 1/m is k = 8, ignoring leading and trailing 0’s.
A352165 (program): Number of partitions of n into odd prime powers (1 included).
A352166 (program): Number of partitions of n into distinct odd prime powers (1 included).
A352167 (program): a(n) is the sum of the prime factors of n (with multiplicity) that are less than n.
A352172 (program): a(n) is the product of the cubes of the nonzero digits of n.
A352177 (program): a(n) is the number of symmetric Toeplitz anti-Hadamard matrices of order n whose sum of the inverse squares of their singular values is maximal.
A352178 (program): Let S = {t_1, t_2, …, t_n} be a set of n distinct integers and consider the sums t_i + t_j (i<j); a(n) is the maximum number of such sums that are powers of 2, over all choices for S.
A352180 (program): a(n) = 9*A006190(n)+1.
A352181 (program): a(n) = A200993(n)/2.
A352182 (program): Twice A200994.
A352190 (program): Indices of records in A352188.
A352202 (program): a(n) = binary weight of A115510(n).
A352206 (program): a(n) = A109812(A352205(n) + 1).
A352217 (program): Smallest power of 2 that is one more than a multiple of 2n-1.
A352227 (program): Number of length-n blocks in the Thue-Morse sequence with intertwining pattern AB AB AB… .
A352228 (program): Number of length-n blocks in the Thue-Morse sequence with intertwining pattern ABBA ABBA ABBA… .
A352229 (program): Numbers that can be expressed as the sum of two primes in exactly 7 ways.
A352230 (program): Numbers that can be expressed as the sum of two primes in exactly 8 ways.
A352232 (program): a(n) is the smallest positive integer k such that 1 + k * prime(n) is a power of two.
A352241 (program): Maximal number of nonattacking black-square queens on an n X n chessboard.
A352251 (program): Expansion of e.g.f. 1 / (1 - x * sinh(x)) (even powers only).
A352253 (program): Expansion of e.g.f. 1 / (1 - x * sinh(x) / 2) (even powers only).
A352254 (program): Expansion of e.g.f. exp( x * sinh(x) / 2 ) (even powers only).
A352257 (program): Sum of all parts of all partitions of n into an odd number of consecutive parts.
A352272 (program): Numbers whose squarefree part is congruent to 1 modulo 6.
A352273 (program): Numbers whose squarefree part is congruent to 5 modulo 6.
A352275 (program): a(0) = 1 and a(n) = Sum_{k = 0..2*n} n/(n + 2*k)*binomial(n + 2*k,k) for n >= 1.
A352276 (program): a(0) = 1 and a(n) = Sum_{k = 0..3*n} n/(n + 2*k)*binomial(n + 2*k,k) for n >= 1.
A352277 (program): a(0) = 1; a(n) = -2 * Sum_{k=1..n} binomial(2*n-1,2*k-1) * a(n-k).
A352278 (program): a(0) = 1; a(n) = -3 * Sum_{k=1..n} binomial(2*n-1,2*k-1) * a(n-k).
A352279 (program): a(0) = 1; a(n) = 2 * Sum_{k=0..floor((n-1)/2)} binomial(n-1,2*k) * a(n-2*k-1).
A352280 (program): a(0) = 1; a(n) = 3 * Sum_{k=0..floor((n-1)/2)} binomial(n-1,2*k) * a(n-2*k-1).
A352284 (program): a(n) is 2^(2*n) times the derivative of order 2*n of the logarithm of I_0(x) (the modified Bessel function of the first kind of order zero) evaluated at zero.
A352306 (program): Expansion of e.g.f. 1/(2 - exp(x) - x^2/2).
A352307 (program): Expansion of e.g.f. 1/(2 - exp(x) - x^3/6).
A352308 (program): Expansion of e.g.f. 1/(2 - exp(x) - x^4/24).
A352313 (program): a(n) is -2^(2n) times the derivative of order 2n of the logarithm of J_0(x) (the Bessel function of the first kind of order zero) evaluated at zero.
A352317 (program): Numbers m such that A352688(m) = 1.
A352320 (program): Pell-Niven numbers: numbers that are divisible by the sum of the digits in their minimal (or greedy) representation in terms of the Pell numbers (A317204).
A352326 (program): Expansion of e.g.f.: 1/(2 - exp(x) - sinh(x)).
A352327 (program): Expansion of e.g.f.: 1/(3 - exp(x) - cosh(x)).
A352328 (program): Nonnegative numbers that are the sum of distinct Pell numbers (A000129).
A352361 (program): Array read by ascending antidiagonals. T(n, k) = F(k, n), where F are the Fibonacci polynomials.
A352362 (program): Array read by ascending antidiagonals. T(n, k) = L(k, n) where L are the Lucas polynomials.
A352373 (program): a(n) = [x^n] ( 1/((1 - x)^2*(1 - x^2)) )^n for n >= 1.
A352375 (program): Sum of digits of A007618.
A352383 (program): G.f. A(x) satisfies: A(x) = (1 + 2*x*A(x)^3)^2 / (1 + x*A(x)^3).
A352384 (program): G.f. A(x) satisfies: A(x) = (1 + 2*x*A(x))^6 / (1 + x*A(x))^3.
A352395 (program): Denominator of Sum_{k=0..n} (-1)^k / (2*k+1).
A352397 (program): Numerators of partial sums of the Madhava series for Pi/(2*sqrt(3)) = A093766.
A352398 (program): Denominators of partial sums of the Madhava series for Pi/(2*sqrt(3)) = A093766.
A352405 (program): a(n) = binomial(n,2)*(binomial(n-1,2) + 2).
A352410 (program): Expansion e.g.f. LambertW( -x/(1-x) ) / (-x).
A352419 (program): Triangle read by rows T(n,k): number of three-in-a-rows in n-dimensional tic-tac-toe through a cell that is central in k dimensions (for k=0..n).
A352422 (program): Number of points available in a frame of snooker when there are n object balls remaining on the table.
A352427 (program): a(n) is the number of trailing 0’s in the minimal representation of n in terms of the positive Pell numbers (A317204).
A352428 (program): a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n,3*k+1) * a(n-3*k-1).
A352434 (program): The number of simple vertices on a diagonal of a regular 2n-gon when all its vertices are connected by lines and where the diagonal passes through the center of the 2n-gon.
A352446 (program): Total number of parts in all partitions of n into an even number of consecutive parts.
A352447 (program): Numbers k such that BarnesG(k) is divisible by Gamma(k).
A352449 (program): 2^k appears in the binary expansion of a(n) iff 2^k appears in the binary expansion of n and k AND n = k (where AND denotes the bitwise AND operator).
A352453 (program): Decimal expansion of the area of intersection of 4 unit-radius circles that have the vertices of a unit-side square as centers.
A352457 (program): Codimension of Lyndon symmetric functions of degree n.
A352467 (program): a(0) = 1; a(n) = Sum_{k=1..n} binomial(2*n,2*k)^2 * a(n-k).
A352468 (program): a(0) = 1; a(n) = Sum_{k=1..n} binomial(2*n,2*k)^3 * a(n-k).
A352470 (program): a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n,2*k+1)^2 * a(n-2*k-1).
A352475 (program): Numbers m such that gcd(d(m),6) = 1.
A352476 (program): Expansion of g.f.: 1/Sum_{p prime} x^p.
A352478 (program): a(n) is the number of Toeplitz anti-Hadamard matrices of order n whose sum of the inverse squares of their singular values is maximal.
A352479 (program): Expansion of g.f.: 1/Sum_{p odd prime} x^p (odd powers only).
A352482 (program): Denominator of (n-d)/n*d where d = A000005(n) is the number of divisors of n.
A352483 (program): Numerator of 1/d - 1/n = (n-d)/(n*d) where d is the number of divisors of n (A000005).
A352485 (program): Decimal expansion of the probability that when a unit interval is broken at two points uniformly and independently chosen at random along its length the lengths of the resulting three intervals are the altitudes of a triangle.
A352486 (program): Heinz numbers of non-self-conjugate integer partitions.
A352487 (program): Excedance set of A122111. Numbers k < A122111(k), where A122111 represents partition conjugation using Heinz numbers.
A352488 (program): Weak nonexcedance set of A122111. Numbers k >= A122111(k), where A122111 represents partition conjugation using Heinz numbers.
A352489 (program): Weak excedance set of A122111. Numbers k <= A122111(k), where A122111 represents partition conjugation using Heinz numbers.
A352491 (program): n minus the Heinz number of the conjugate of the integer partition with Heinz number n.
A352494 (program): Primes congruent to 0, 1, or 10 mod 11.
A352502 (program): a(n) is the number of integers k in the interval 0..n such that k and n-k can be added without carries in balanced ternary.
A352505 (program): Sum of all parts of all partitions of n into an even number of consecutive parts.
A352512 (program): Number of fixed points in the n-th composition in standard order.
A352513 (program): Number of nonfixed points in the n-th composition in standard order.
A352514 (program): Number of strong nonexcedances (parts below the diagonal) of the n-th composition in standard order.
A352515 (program): Number of weak nonexcedances (parts on or below the diagonal) of the n-th composition in standard order.
A352516 (program): Number of excedances (parts above the diagonal) of the n-th composition in standard order.
A352517 (program): Number of weak excedances (parts on or above the diagonal) of the n-th composition in standard order.
A352520 (program): Number of integer compositions y of n with exactly one nonfixed point y(i) != i.
A352526 (program): a(n) = Product_{k=0..n} Nimsum (2*k + 2), with Nimsum (2 + 2) = 0 replaced by 1.
A352529 (program): Expansion of 1/Sum_{k>=0} x^(k^4).
A352530 (program): Expansion of 1/Sum_{k>=0} x^(k^5).
A352531 (program): Numbers with multiplicative persistence value 10.
A352532 (program): Numbers with multiplicative persistence value 11.
A352535 (program): Numbers m such that A257588(m) = 0.
A352598 (program): a(n) is the product of the squares of the nonzero digits of n.
A352601 (program): a(n) = RisingFactorial(2*n, n) = A124320(2*n, n).
A352602 (program): a(n) = 4^n*(2^(2*n+1)-1)*(2*n)!.
A352608 (program): a(n) = Bell(n)*n!!.
A352617 (program): Expansion of e.g.f. exp( exp(x) + sinh(x) - 1 ).
A352618 (program): Squares that are 7-smooth.
A352624 (program): Expansion of e.g.f. exp(exp(x) + cosh(x) - 2).
A352625 (program): A (25,-29) Somos-4 sequence.
A352626 (program): a(n) = (n+1)*(3*n-2)*C(2*n,n-1)/(4*n-2).
A352644 (program): Expansion of e.g.f. exp(2 * x * cosh(x)).
A352645 (program): Expansion of e.g.f. exp(3 * x * cosh(x)).
A352648 (program): Expansion of e.g.f. 1/(1 - 2 * x * cosh(x)).
A352649 (program): Expansion of e.g.f. 1/(1 - 3 * x * cosh(x)).
A352650 (program): Triangle read by rows: T(n,k) = n * T(n-1,k) + (-1)^(n-k) for 0 <= k <= n with initial values T(n,k) = 0 if n < 0 or k < 0 or k > n.
A352653 (program): a(n) = Sum_{k = 0..n-1} binomial(n,k)*binomial(n-1,k)*binomial(n+k,k)*binomial(n-1+k,k).
A352654 (program): a(0) = 0, a(n) = [x^n] P(n-1,(1 + x)/(1 - x)) for n >= 1, where P(n,x) denotes the n-th Legendre polynomial.
A352655 (program): a(n) = (1/2)*(A005258(n) + A005258(n-1)).
A352659 (program): a(n) = n! * Sum_{k=0..floor(n/3)} 1 / (3*k)!.
A352660 (program): a(n) = n! * Sum_{k=0..floor(n/4)} 1 / (4*k)!.
A352667 (program): Maximum number of induced copies of the paw graph in an n-node graph.
A352669 (program): Maximum number of induced cycles in an n-node graph.
A352672 (program): Decimal expansion of r = (3/2)*(1+sqrt(3)).
A352673 (program): Decimal expansion of r = (3/13)(4+sqrt(3)).
A352674 (program): Beatty sequence for (3/2)(1+sqrt(3)).
A352675 (program): Beatty sequence for (3/13)(4+sqrt(3)).
A352681 (program): a(n) = [x^n] (3*x + 1)*(1 - sqrt(1 - 4*x))/(2*x).
A352683 (program): a(n) = A352682(4, n).
A352692 (program): a(n) + a(n+1) = 2^n for n >= 0 with a(0) = 4.
A352696 (program): a(n) = k if the binary representation of k has a 1 (0) exactly where a 1 in the n-th row of A237048 occurs at an odd (even) position, reading from left to right.
A352717 (program): Greatest Lucas number that does not exceed n.
A352718 (program): a(n) = floor(n^(3/2)) - floor(n^(1/2))^3.
A352719 (program): Indices k of tribonacci numbers T(k) such that T(k+1) - (tribonacci constant)*T(k) is nonnegative.
A352721 (program): Perfect cubes whose decimal digits appear in nonincreasing order.
A352729 (program): The binary expansion of a(n) contains the runs of consecutive 1’s that appear both in the binary expansions of n and n+1.
A352737 (program): Number of oriented two-component rational links (or two-bridge links) with crossing number n (a chiral pair is counted as two distinct ones).
A352744 (program): Array read by ascending antidiagonals. Generalized Fibonacci numbers F(n, k) = (psi^k*(phi - n) - phi^k*(psi - n)) / (phi - psi) where phi = (1 + sqrt(5))/2 and psi = (1 - sqrt(5))/2. F(n, k) for n >= 0 and k >= 0.
A352745 (program): a(n) is the number of Lyndon factors of the Fibonacci string of length n.
A352748 (program): Indices k of tribonacci numbers T(k) such that T(k+1) - (tribonacci constant)*T(k) is negative.
A352749 (program): a(n) = pi(n) * (pi(2n-1) - pi(n-1)).
A352753 (program): a(n) = (pi(2n-1) - pi(n-1)) * Sum_{p <= n, p prime} p.
A352754 (program): a(n) = pi(n) * Sum_{n <= q < 2n, q prime} q.
A352756 (program): Positive numbers k such that the centered cube number k^3 + (k+1)^3 is equal to the difference of two positive cubes and to A352755(n).
A352757 (program): a(n) = (3*(2*n - 1)^2*((2*n - 1)^2 + 2) + 2*n + 1)/2 for n > 0.
A352758 (program): a(n) = (3*(2*n - 1)^2*((2*n - 1)^2 + 2) - 2*n + 3)/2 for n > 0.
A352759 (program): Centered cube numbers that are the difference of two positive cubes; a(n) = 27*t^3*(27*t^6 + 1)/4 with t = 2*n-1.
A352767 (program): Number of n-node graphs with the maximum number (A352766(n)) of orientations.
A352776 (program): Numbers k such that w(k + w(k)) = w(k), where w(k) is the binary weight of k, A000120(k).
A352777 (program): a(n) = Sum_{p <= n <= q < 2n, p,q prime} (p * q).
A352778 (program): Numbers k such that w(k + w(k)) > w(k), where w(k) is the binary weight of k, A000120(k).
A352779 (program): a(n) = (-3)^n.
A352784 (program): a(n) = w(n - w(n)), where w(n) is the binary weight of n, A000120(n).
A352789 (program): Number of ways to tile a 3 X n strip with squares and P-shaped heptominoes.
A352795 (program): Number of ways to tile a 4 X n strip with squares and L-shaped heptominoes with legs of equal length.
A352800 (program): Numbers k such that 2*k^2 + 29 is prime.
A352804 (program): a(n) = A028876(n)/2; numbers k such that 4*k^2 - 5 is prime.
A352805 (program): a(n) = A296507(n+1)/6; numbers k such that 36*k^2 - 13 is prime.
A352806 (program): Orders of the finite groups PSL_2(K) when K is a finite field with q = A246655(n) elements.
A352824 (program): Number of fixed points y(i) = i, where y is the integer partition with Heinz number n.
A352825 (program): Number of nonfixed points y(i) != i, where y is the integer partition with Heinz number n.
A352826 (program): Heinz numbers of integer partitions y without a fixed point y(i) = i. Such a fixed point is unique if it exists.
A352827 (program): Heinz numbers of integer partitions y with a fixed point y(i) = i. Such a fixed point is unique if it exists.
A352830 (program): Numbers whose weakly increasing prime indices y have no fixed points y(i) = i.
A352839 (program): Expansion of g.f. 1/(1 - Sum_{k>=1} sigma_k(k) * x^k).
A352842 (program): Expansion of e.g.f. exp(Sum_{k>=1} sigma_k(k) * x^k).
A352847 (program): Number of copies of the star graph S(2,1,1) contained within the n-dimensional hypercube graph.
A352851 (program): a(n) = prime(n)^2 + prime(n+1).
A352861 (program): a(n) = 1 + Sum_{k=0..n-1} binomial(n+2,k+3) * a(k).
A352862 (program): a(n) = 1 + Sum_{k=0..n-1} binomial(n+3,k+4) * a(k).
A352863 (program): a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n+3,k+3) * a(k).
A352868 (program): Expansion of e.g.f. exp(Sum_{k>=1} mu(k) * x^k), where mu() is the Moebius function (A008683).
A352872 (program): Numbers whose weakly increasing prime indices y have a fixed point y(i) = i.
A352873 (program): Heinz numbers of integer partitions with nonnegative crank, counted by A064428.
A352874 (program): Heinz numbers of integer partitions with positive crank, counted by A001522.
A352880 (program): Triangle read by rows: T(n,k) = number of vertices of degree k in an origami flip graph OFG(A2n).
A352886 (program): Number of B-periodic numbers of bit pseudo-length n.
A352890 (program): Number of iterations of map x -> A341515(x) needed to reach x <= 2 when starting from x=n, or -1 if such number is never reached. Here A341515 is the Collatz or 3x+1 map (A006370) conjugated by unary-binary-encoding (A156552).
A352893 (program): Number of iterations of map x -> A352892(x) needed to reach x <= 2 when starting from x=n, or -1 if such number is never reached. Here A352892 is the next odd term in the Collatz or 3x+1 map (A139391) conjugated by unary-binary-encoding (A156552).
A352910 (program): The j-values of pairs (i,j) listed in A352909.
A352914 (program): Expansion of e.g.f. exp(Sum_{k>=1} prime(k)*x^k).
A352921 (program): Let c(s) denote A109812(s). Suppose c(s) = 2^n - 1, and define m(n), p(n), r(n) by m(n) = c(s-1)/2^n, p(n) = c(s+1)/2^n, r(n) = max(m(n), p(n)); sequence gives p(n).
A352923 (program): Let c(s) denote A109812(s). Suppose c(s) = 2^n - 1, and define m(n), p(n), r(n) by m(n) = c(s-1)/2^n, p(n) = c(s+1)/2^n, r(n) = max(m(n), p(n)); sequence gives r(n).
A352940 (program): The largest positive integer k such that binomial(k+1,2) <= binomial(n,2)^2.
A352944 (program): a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^k.
A352945 (program): a(n) = Sum_{k=0..floor(n/3)} k^(n-3*k).
A352946 (program): a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^k.
A352949 (program): Composite numbers of the form 2*k^2 + 29.
A352956 (program): For n>1, a(n) = a(n - a(n-1)) + a(n-2) starting with a(0) = a(1) = 1.
A352961 (program): a(0) = 0, a(1) = 1, and for any n > 1, a(n) = a(n-2^e) + a(n-2^(e+1)) with e as large as possible (e = A070939(n) - 2).
A352967 (program): Array read by antidiagonals: A(i, j) = abs(i - j) if min(i, j) < max(i, j) <= 2*min(i, j), and otherwise 0, with i >= 0 and j >= 0.
A352981 (program): a(n) = Sum_{k=0..floor(n/2)} k^n.
A352982 (program): a(n) = Sum_{k=0..floor(n/3)} k^n.
A352983 (program): a(n) = Sum_{k=0..floor(n/2)} k^(2*n).
A352984 (program): a(n) = Sum_{k=0..floor(n/3)} k^(3*n).
A352985 (program): a(n) = Sum_{k=0..floor(n/2)} k^(2*(n-2*k)).
A352986 (program): a(n) = Sum_{k=0..floor(n/3)} k^(3*(n-3*k)).
A352988 (program): Matrix inverse of triangle A352650.
A352990 (program): Numbers k such that the k-th triangular number == 1 mod the integer log of k.
A352994 (program): Number of copies of the star graph S(2,2,1) contained within the n-dimensional hypercube graph.
A352996 (program): a(n) = n*(n+1)/2 mod (sum (with multiplicity) of prime factors of n).
A352997 (program): Numbers k such that A352996(k) is prime.
A353004 (program): Numbers k such that 2*k^2 + 29 is semiprime.
A353009 (program): a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^(n-2*k).
A353013 (program): a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^(n-k).
A353014 (program): a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^(n-2*k).
A353015 (program): a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^n.
A353016 (program): a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^(2*k).
A353017 (program): a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^(3*k).
A353018 (program): a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^(n-3*k).
A353029 (program): Number of copies of the star graph S(2,2,2) contained in the n-dimensional hypercube graph.
A353041 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(3*x/(1 + 2*x)) / (1 - x).
A353042 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(4*x/(1 + 3*x)) / (1 - x).
A353047 (program): Number of length n words on alphabet {0,1,2} that contain each of the subwords 01, 02, 10, 12, 20, and 21 as (not necessarily contiguous) subwords.
A353049 (program): Decimal expansion of 8*sqrt(2) / 3.
A353051 (program): Starting with x = n and repeatedly apply the map x -> x - sopfr(x) until 0, 1 or a prime is reached.
A353053 (program): Decimal expansion of Pi * BesselY(0,2) / 2 - gamma * BesselJ(0,2).
A353058 (program): Minimum number of iterations {add or subtract 1, or half if even} needed to reach 1, starting from n.
A353072 (program): Numbers k such that nextprime(k)-k is a positive square.
A353078 (program): Inverse Moebius transform of odd primes.
A353083 (program): The second column of the Trithoff (tribonacci) array.
A353084 (program): Column 0 of the extended Trithoff (tribonacci) array.
A353086 (program): Column -1 of the extended Trithoff (Tribonacci) array.
A353090 (program): Column -2 of the extended Trithoff (tribonacci) array.
A353094 (program): a(1) = 2; for n>1, a(n) = 3 * a(n-1) + 3 - n.
A353095 (program): a(1) = 3; for n>1, a(n) = 4 * a(n-1) + 4 - n.
A353096 (program): a(1) = 4; for n>1, a(n) = 5 * a(n-1) + 5 - n.
A353097 (program): a(1) = 5; for n>1, a(n) = 6 * a(n-1) + 6 - n.
A353098 (program): a(1) = 6; for n>1, a(n) = 7 * a(n-1) + 7 - n.
A353099 (program): a(1) = 7; for n>1, a(n) = 8 * a(n-1) + 8 - n.
A353100 (program): a(1) = 8; for n>1, a(n) = 9 * a(n-1) + 9 - n.
A353104 (program): Base-4 representation of A007908(n).
A353105 (program): Base-5 representation of A007908(n).
A353106 (program): Base-6 representation of A007908(n).
A353107 (program): Base-9 representation of A007908(n).
A353109 (program): Array read by antidiagonals: A(n, k) is the digital root of n*k with n >= 0 and k >= 0.
A353110 (program): Binary representation of A000422(n).
A353111 (program): Base-3 representation of A000422(n).
A353112 (program): Base-4 representation of A000422(n).
A353113 (program): Base-5 representation of A000422(n).
A353114 (program): Base-6 representation of A000422(n).
A353115 (program): Base-7 representation of A000422(n).
A353116 (program): Base-8 representation of A000422(n).
A353117 (program): Base-9 representation of A000422(n).
A353128 (program): Antidiagonal sums of A353109.
A353133 (program): Coefficients of expansion of f(x) = (1+x*m(x))^5*(x^2*(x*m(x))’+1) where m(x) is the generating function for A001006.
A353142 (program): Decimal repunits written in base 3.
A353143 (program): Decimal repunits written in base 4.
A353144 (program): Decimal repunits written in base 5.
A353145 (program): Decimal repunits written in base 6.
A353146 (program): Decimal repunits written in base 7.
A353147 (program): Decimal repunits written in base 8.
A353148 (program): Decimal repunits written in base 9.
A353149 (program): Sum of the odd-indexed terms in the n-th row of the triangle A196020.
A353154 (program): Sum of the even-indexed terms in the n-th row of the triangle A196020.
A353156 (program): a(0) = 1; a(n) = -Sum_{k=1..n} prime(k+1) * a(n-k).
A353157 (program): a(n) is the distance from n to the nearest integer whose binary expansion has no common 1-bits with that of n.
A353158 (program): a(n) is the distance from n to the nearest integer that can be added to n without carries in base 3.
A353164 (program): Expansion of 1/(1 - Sum_{p prime} p * x^p).
A353166 (program): Expansion of e.g.f. exp(Sum_{k>=1} prime(k)*x^k/k).
A353167 (program): Polynomials over GF(2) that are divisible by (x+1)^2 = x^2+1, encoded as binary numbers.
A353168 (program): Polynomials over GF(2) that are divisible by x^2+x+1, encoded as binary numbers.
A353179 (program): a(n) is the first nonzero digit in the decimal expansion of 1/prime(n).
A353182 (program): Number of n-digit numbers in which more than half of the digits are the same.
A353183 (program): Number of numbers < 10^n in which more than half of the digits are the same.
A353188 (program): Number of partitions of n that contain at least one composite part.
A353189 (program): Expansion of e.g.f. exp(Sum_{k>=1} mu(k) * x^k / k), where mu() is the Moebius function (A008683).
A353190 (program): a(n) is the (n-1)st odd number minus the sum of the aliquot parts of n.
A353196 (program): Number of stabilizer states on n qubits.
A353202 (program): Positive integers which can be expressed as the sum of three or fewer squares, no more than two of which are greater than 1.
A353206 (program): Number of graph minors in the cycle graph C_n.
A353211 (program): a(n) is the number of diagonalizable 2 X 2 matrices over GF(prime(n)).
A353212 (program): Hadwiger number of the n-path complement graph.
A353215 (program): a(n) is the result of n applications of the function f on n, where f(x) = floor((3*x - 1)/2) (A001651).
A353219 (program): Positive integers which cannot be expressed as the sum of three or fewer squares, no more than two of which are greater than 1.
A353220 (program): a(n) is the result of n applications of the function f to n, where f(x) = floor((3*x + 1)/2) (A007494).
A353230 (program): Number of Condorcet voting profiles with three candidates and 2n-1 voters where all the choices are from {123, 231, 312}.
A353232 (program): a(n) is the number of ways to split [n] = {1,2,…,n} into two (possibly empty) complementary intervals {1,2,…,i} and {i+1,i+2,…,n} and then, if both intervals are nonempty, select 2 nonempty blocks/cells (i.e., subintervals) from each of them, or if one of the intervals is empty, select 2 nonempty blocks/cells from the nonempty interval.
A353235 (program): Number of divisors of n whose arithmetic derivative is odd.
A353236 (program): Number of divisors of n whose arithmetic derivative is even.
A353237 (program): a(n) = Sum_{d|n} (-1)^(d’), where d’ is the arithmetic derivative of d (A003415).
A353250 (program): a(0) = 1, a(n) = harmonic_mean(a(n-1), n), where harmonic_mean(p, q) = 2/(1/p + 1/q); numerators.
A353251 (program): a(0) = 1, a(n) = harmonic_mean(a(n-1), n), where harmonic_mean(p, q) = 2/(1/p + 1/q); denominators.
A353259 (program): Solution to Snake Numbers Problems for Snakes from 1 to n for an n X n square grid (see Comments).
A353265 (program): Partial sums of A208981.
A353269 (program): a(n) = 1 if A156552(n) is a multiple of 3, otherwise 0.
A353280 (program): n is a term if n = 0 or n does not divide F(n, k) for all k >= 0, where F(n, k) are the Fibonacci numbers A352744.
A353282 (program): a(n) is the number of solutions (x,y) to the Diophantine equation S(x,y) = (x+y) + (x-y) + (x*y) + (x/y) = A013929(n) when x >= y > 1 and y | x.
A353292 (program): a(n) is the number of positive integers k <= n that have at least one common 1-bit with n.
A353295 (program): Square nearest to the sum of the first n positive squares.
A353297 (program): The i-values of pairs (i,j) listed in A353296.
A353298 (program): The i-values of pairs (i,j) listed in A353296.
A353307 (program): a(n) = 1 if A156552(n) == 1 (mod 3), otherwise 0.
A353313 (program): If n is of the form 3k, then a(n) = k, and if n is of the form 3k+r, with r = 1 or 2, then a(n) = 5*k + 3 + r.
A353314 (program): If n is of the form 3k, then a(n) = n, and if n is of the form 3k+r, with r = 1 or 2, then a(n) = 5*k + 3 + r.
A353327 (program): If n is a multiple of 3, then a(n) = 0, and if n is of the form 3k+r, with r = 1 or 2, then a(n) = 2*k + 3.
A353328 (program): Number of divisors d of n for which A332823(d) is positive (+1).
A353329 (program): Number of divisors d of n for which A332823(d) is negative (-1).
A353330 (program): a(n) = A006047(A156552(n)).
A353331 (program): a(n) = 1 if A001222(n) [bigomega(n)] and A056239(n) are both even, otherwise a(n) = 0.
A353332 (program): Number of divisors d of n for which both A001222(d) and A056239(d) are even.
A353350 (program): a(n) = 1 if A048675(n) is a multiple of 3, otherwise 0.
A353351 (program): Number of divisors d of n for which A048675(d) is not a multiple of 3.
A353352 (program): Number of divisors d of n for which A048675(d) is a multiple of 3.
A353354 (program): Inverse Möbius transform of A332823.
A353360 (program): a(n) = A006047(A048675(n)).
A353361 (program): Number of divisors d of n for which A156552(d) is not a multiple of 3.
A353362 (program): Number of divisors d of n for which A156552(d) is a multiple of 3.
A353364 (program): Inverse Möbius transform of A332814.
A353370 (program): a(n) = 1 if the prime factorization of n contains as many even as odd prime indices, when counted with multiplicity, otherwise 0.
A353371 (program): Number of divisors of n that are not in A325698.
A353372 (program): Inverse Möbius transform of A353370.
A353374 (program): a(n) = 1 if the prime factorization of n has an even number of prime factors that sum to an even number, otherwise 0.
A353375 (program): Number of divisors of n that are not in A345452.
A353376 (program): Inverse Möbius transform of A353374.
A353380 (program): a(n) = 1 if A353354(n) [= Sum_{d|n} A332823(d)] is zero, otherwise 0.
A353381 (program): Number of divisors of n not in A353355.
A353382 (program): Inverse Möbius transform of A353380.
A353412 (program): The odd part of hybrid shift: a(n) = A000265(A252463(n)).
A353413 (program): a(n) = A000265(A064216(n)).
A353416 (program): a(n) = A000593(A252463(n)), where A000593 is the sum of odd divisors, and A252463 is the hybrid shift.
A353417 (program): a(n) = A113415(A252463(n)), where A113415 is the arithmetic mean between the number of odd divisors and their sum, and A252463 is the hybrid shift.
A353420 (program): a(n) = A126760(A003961(n)).
A353445 (program): Let f be the completely multiplicative function from the positive integers to the cube roots of unity defined by f(prime(m)) = w^(2^(m-1)), where w is the cube root with positive imaginary part. a(n) is twice the real part of f(n).
A353446 (program): Let g be the inverse Möbius transform of the Eisenstein integer-valued function f defined in A353445. a(n) is twice the real part of g(n).
A353456 (program): Numbers k such that A353627(k) is less than A353628(k).
A353457 (program): a(1) = 1, for n > 1, a(n) = -Sum_{d|n, d<n} a(A064989(n/d)) * a(d).
A353458 (program): Dirichlet inverse of A353457.
A353463 (program): Characteristic function of lesser twin primes: a(n) = 1 if both n and n+2 are primes, otherwise 0.
A353464 (program): Characteristic function of greater twin primes: a(n) = 1 if both n and n-2 are primes, otherwise 0.
A353465 (program): Numbers k for which A276086(k) is of the form 4k+1.
A353466 (program): Numbers k for which A276086(k) is of the form 4k+3.
A353470 (program): a(n) = 1 if the number of its divisors, tau(n), is divisible by 3, otherwise 0.
A353471 (program): a(n) = 1 if n is a prime or a squarefree semiprime, otherwise 0.
A353476 (program): a(n) = 1 if n is a semiprime of the form p * q, where p and q are (not necessarily distinct) primes with p <= q < p^2, otherwise 0.
A353477 (program): a(n) = 1 if n is a semiprime of the form 4k+1, otherwise 0.
A353478 (program): a(n) = 1 if n is an even semiprime (2*prime), otherwise 0.
A353480 (program): a(n) = 1 if n is an odd semiprime, otherwise 0.
A353486 (program): Primorial base exp-function reduced modulo 4.
A353487 (program): a(n) = A276086(2*n) mod 4, where A276086 is the primorial base exp-function.
A353488 (program): If A276086(n) is of the form 4k+1, then a(n) = 1, otherwise a(n) = 0.
A353489 (program): If A276086(n) is of the form 4k+3, then a(n) = 1, otherwise a(n) = 0.
A353490 (program): The largest proper divisor of n, reduced modulo 4, with a(1) = 1.
A353491 (program): a(1) = 1, and for n > 1, a(n) = 1 if the largest proper divisor of n is of the form 4k+1, otherwise 0.
A353492 (program): a(1) = 0, and for n > 1, a(n) = 1 if the largest proper divisor of n is of the form 4k+3, otherwise 0.
A353493 (program): The arithmetic derivative of n, reduced modulo 4.
A353494 (program): a(n) = 1 if the arithmetic derivative of n is a multiple of 4, otherwise 0.
A353495 (program): a(n) = 1 if the arithmetic derivative of n is of the form 4k+2, otherwise 0.
A353496 (program): The arithmetic derivative of the largest proper divisor of n, reduced modulo 4, with a(1) = 0.
A353497 (program): The smallest prime factor of n, reduced modulo 4, with a(1) = 1.
A353498 (program): a(n) = 1 if n > 1 and the 2-adic valuation of phi(n) does not exceed the 2-adic valuation of n-1, otherwise 0.
A353499 (program): a(n) = 1 if n is a squarefree number for which the 2-adic valuation of phi(n) does not exceed the 2-adic valuation of n-1, otherwise 0.
A353507 (program): Product of multiplicities of the prime exponents (signature) of n; a(1) = 0.
A353511 (program): Positions of odd terms in A001001, where A001001(n) = Sum_{d|n} d*sigma(d).
A353512 (program): n multiplied by the least nonzero digit missing from its primorial base representation.
A353513 (program): a(n) = 1 if A328572(n) is of the form 4m+3, and 0 otherwise.
A353514 (program): a(n) = 1 if A328572(2*n) is of the form 4m+3, and 0 otherwise.
A353516 (program): The largest proper divisor of the primorial base exp-function, reduced modulo 4.
A353517 (program): The largest proper divisor of A276086(2*n) reduced modulo 4, where A276086(n) the primorial base exp-function.
A353518 (program): a(n) = 1 if n is a product of superprimorials (A006939), otherwise 0.
A353519 (program): a(n) = 1 if n has an odd number of square divisors, otherwise 0.
A353524 (program): A003557 applied to the prime shadow of primorial base exp-function: a(n) = A003557(A181819(A276086(n))).
A353525 (program): a(n) = 1 if the number of trailing zeros in primorial base representation of n is odd, otherwise 0.
A353526 (program): The smallest prime not dividing n, reduced modulo 4.
A353527 (program): The smallest prime not dividing 2*n, reduced modulo 4.
A353528 (program): a(n) = 1 if A053669(n) [the smallest prime not dividing n] is of the form 4m+1, otherwise a(n) = 0.
A353529 (program): a(n) = 1 if A053669(n) [the smallest prime not dividing n] is of the form 4m+3, otherwise a(n) = 0.
A353530 (program): Numbers k such that the smallest prime that does not divide them is of the form 4m+1.
A353531 (program): Numbers k such that the smallest prime that does not divide them is of the form 4m+3.
A353545 (program): a(n) is the numerator of Sum_{k=1..n} 1 / (k*k!).
A353546 (program): Expansion of e.g.f. -log(1-2*x) * exp(x)/2.
A353547 (program): Expansion of e.g.f. -log(1-3*x) * exp(x)/3.
A353548 (program): Expansion of e.g.f. -log(1-4*x) * exp(x)/4.
A353549 (program): Expansion of e.g.f. log(1+3*x) * exp(x)/3.
A353551 (program): a(n) = Sum_{k=1..n} tau(k^3), where tau is the number of divisors function A000005.
A353555 (program): a(n) = 1 if n is an even number with an even number of prime factors (counted with multiplicity), otherwise 0.
A353556 (program): a(n) = 1 if n is an even number with an odd number of prime factors (counted with multiplicity), otherwise 0.
A353557 (program): a(n) = 1 if n is an odd number with an even number of prime factors (counted with multiplicity), otherwise 0.
A353558 (program): a(n) = 1 if n is an odd number with an odd number of prime factors (counted with multiplicity), otherwise 0.
A353559 (program): a(n) = 1 if A003968(n) is a multiple of n, where A003968 is multiplicative with a(p^e) = p*(p+1)^(e-1), otherwise 0.
A353563 (program): Primorial base exp-function applied to Euler totient function: a(n) = A276086(phi(n)).
A353566 (program): a(n) = 1 if n is a multiple of its prime shadow A181819(n), and 0 otherwise.
A353567 (program): Number of divisors d of n such that d is a multiple of its prime shadow A181819(d).
A353569 (program): a(n) = 1 if n is an odd number divisible by a square, otherwise 0.
A353571 (program): Prime-shifted variant of A342001: a(n) = A349905(n) / A003557(A003961(n)).
A353572 (program): Shifted variant of A342002: a(n) = A353571(A276086(n)), where A353571(x) = A003415(A003961(x)) / A003557(A003961(x)) and A276086 is the primorial base exp-function.
A353576 (program): Arithmetic derivative applied to the prime shadow of the primorial base exp-function: a(n) = A003415(A181819(A276086(n))).
A353577 (program): Arithmetic derivative without its inherited divisor applied to the prime shadow of the primorial base exp-function: a(n) = A342001(A181819(A276086(n))).
A353580 (program): a(n) = 2*a(n-1) + a(n-2) - 1, with a(0) = 0 and a(1) = 2.
A353581 (program): a(n) = 2*a(n-1) + 2*a(n-3) + a(n-4), with a(0) = 0 = a(1), a(2) = 2, and a(3) = 1.
A353582 (program): a(n) = 2*a(n-1) + 2*a(n-3) + a(n-4) - 1, with a(0) = 0 = a(1), a(2) = 2, and a(3) = 3.
A353595 (program): Array read by ascending antidiagonals. Generalized Fibonacci numbers F(n, k) = (psi^(k - 1)*(phi + n) - phi^(k - 1)*(psi + n)) / (psi - phi) where phi = (1+sqrt(5))/2 and psi = (1-sqrt(5))/2. F(n, k) for n >= 0 and k >= 0.
A353612 (program): Triangle read by rows: T(n,k) = (n + k) if (n + k) is a prime number, otherwise T(n,k) = 0; n >= 1, k >= 1.
A353626 (program): a(n) = 1 if n is a multiple of the square of an odd prime (equally: if the odd part of n is not squarefree), otherwise 0.
A353627 (program): a(n) = 1 if the odd part of n is squarefree, otherwise 0.
A353628 (program): Parity of A001001(n), where A001001(n) = Sum_{d|n} d*sigma(d).
A353629 (program): a(n) = 1 if n is a product of an even number of distinct primes, otherwise 0.
A353630 (program): Arithmetic derivative of primorial base exp-function, reduced modulo 4.
A353632 (program): Even bisection of A353630: Arithmetic derivative of primorial base exp-function, reduced modulo 4, computed for even numbers.
A353633 (program): a(n) = 1 if A351546(n) is a unitary divisor of n, otherwise 0. Here A351546(n) is the largest unitary divisor of sigma(n) coprime with A003961(n).
A353635 (program): Numbers k such that phi(k) = phi(sigma(k)) and A003958(k) = A003958(sigma(k)).
A353636 (program): Difference between phi(sigma(n)) and phi(n).
A353637 (program): a(n) = 1 if phi(sigma(n)) is equal to phi(n), otherwise 0.
A353640 (program): Čiurlionis sequence A342002, reduced modulo 4.
A353641 (program): Odd bisection of A353640.
A353642 (program): Even bisection of A353640.
A353643 (program): The greatest common divisor of phi(n) and phi(sigma(n)).
A353644 (program): a(n) = phi(n) / gcd(phi(n), phi(sigma(n))).
A353646 (program): a(n) = phi(sigma(n)) / gcd(phi(n), phi(sigma(n))).
A353651 (program): Unique monotonic sequence of positive integers satisfying a(a(n)) = k*(n-1) + 3, where k = 4.
A353652 (program): Unique monotonic sequence of positive integers satisfying a(a(n)) = k*(n-1) + 3, where k = 5.
A353653 (program): Unique monotonic sequence of positive integers satisfying a(a(n)) = k*(n-1) + 3, where k = 6.
A353666 (program): a(n) = gcd(n, A351546(n)).
A353667 (program): a(n) = n / gcd(n, A351546(n)).
A353668 (program): a(n) = A351546(n) / gcd(n, A351546(n)).
A353669 (program): a(n) = 1 if n is a nonsquare that has an even number of prime factors with multiplicity, otherwise 0.
A353670 (program): a(n) = 1 if the odd part of n is a prime, otherwise 0.
A353671 (program): a(n) = 1 if n is even and the odd part of n is a prime, otherwise 0.
A353672 (program): a(n) = 1 if n is an even number with an even number of distinct prime factors, otherwise 0.
A353673 (program): a(n) = 1 if n is an odd number with an odd number of distinct prime factors, otherwise 0.
A353674 (program): a(n) = 1 if n is an even number with an odd number of distinct prime factors, otherwise 0.
A353675 (program): a(n) = 1 if n is an odd number with an even number of distinct prime factors, otherwise 0.
A353680 (program): a(n) = 1 if n is odd and phi(sigma(n)) is equal to phi(n), otherwise 0.
A353681 (program): a(n) = 1 if phi(sigma(n)) > phi(n), otherwise 0.
A353682 (program): a(n) = 1 if phi(sigma(n)) >= phi(n), otherwise 0.
A353683 (program): Numbers k for which phi(sigma(k)) > phi(k).
A353684 (program): Numbers k for which phi(sigma(k)) >= phi(k).
A353685 (program): Numbers k for which phi(sigma(k)) <= phi(k).
A353686 (program): Numbers k for which phi(sigma(k)) < phi(k).
A353687 (program): a(n) = 1 if A098987(n) == 1, otherwise 0.
A353688 (program): a(n) = n / A098988(n).
A353689 (program): Convolution of A000716 and the positive integers.
A353725 (program): Records in A353724.
A353747 (program): a(n) = phi(n) + A064989(n), where phi is Euler totient function, and A064989 shifts the prime factorization one step towards lower primes.
A353748 (program): a(n) = phi(n) - A064989(n), where phi is Euler totient function, and A064989 shifts the prime factorization one step towards lower primes.
A353749 (program): a(n) = phi(n) * A064989(n), where phi is Euler totient function, and A064989 shifts the prime factorization one step towards lower primes.
A353750 (program): a(n) = phi(sigma(n)) * A064989(sigma(n)), where A064989 shifts the prime factorization one step towards lower primes.
A353751 (program): a(n) = gcd(n, sigma(sigma(n))), where sigma is the sum of divisors function.
A353767 (program): a(n) = phi(sigma(A003961(n))), where A003961 is fully multiplicative with a(p) = nextprime(p).
A353768 (program): a(n) = phi(n) mod 4; Euler totient function reduced modulo 4.
A353776 (program): a(n) = Sum_{d|n} (n/d mod d).
A353788 (program): a(n) = 1 if the number of divisors of n is either 2 or 4, otherwise 0.
A353789 (program): Multiplicative with a(p^e) = (q - 1) * q^(e-1) * p^e, where q is the least prime greater than p.
A353790 (program): a(n) = A353749(sigma(A003961(n))), where A353749(k) = phi(k) * A064989(k), and A064989 shifts the prime factorization one step towards lower primes, while A003961 shifts the factorization one step towards higher primes.
A353791 (program): Multiplicative with a(p^e) = ((p-1)*q)^e, where q is the largest prime less than p, and 1 if p = 2.
A353792 (program): a(n) = A003958(sigma(n)) * A064989(sigma(n)).
A353793 (program): Multiplicative with a(p^e) = ((q-1)*p)^e, where q is the least prime larger than p.
A353794 (program): a(n) = A353791(sigma(A003961(n))), where A353791(n) = A003958(n) * A064989(n).
A353800 (program): a(n) = 1 if n is a power of prime with an even exponent, otherwise 0.
A353810 (program): a(n) = 1 if sigma(n) has an odd number of prime factors (with multiplicity), and 0 otherwise. Here sigma is the sum of divisors function.
A353811 (program): a(n) = 1 if sigma(n) is odd, and has an odd number of prime factors (with multiplicity), otherwise 0. Here sigma is the sum of divisors function.
A353812 (program): a(n) = 1 if sigma(n) is of the form 4m+2, otherwise 0.
A353813 (program): a(n) = 1 if n has exactly one prime factor of form 4*k+1 (when counted with multiplicity) and no prime factor 4*k+3 with odd multiplicity, otherwise 0.
A353814 (program): a(n) = 1 if n is the sum of 2 distinct nonzero squares, 0 otherwise.
A353815 (program): a(n) = 1 if sigma(n) is not a multiple of 3, otherwise 0.
A353816 (program): a(n) = 1 if n is a number of the form x^2 + xy + y^2, otherwise 0.
A353817 (program): a(n) = 1 if n is a prime power with an odd exponent, otherwise 0.
A353828 (program): The positions of nonzero digits in the balanced ternary expansions of n and a(n) are the same, and the k-th leftmost nonzero digit in a(n) equals the product of the k leftmost nonzero digits in n.
A353830 (program): The positions of nonzero digits in the balanced ternary expansions of n and a(n) are the same, and the k-th rightmost nonzero digit in a(n) equals the product of the k rightmost nonzero digits in n.
A353886 (program): Nonnegative numbers k such that k^2 + k + 1 is squarefree.
A353887 (program): Squarefree numbers of the form k^2 + k + 1 for some k >= 0.
A353897 (program): a(n) is the largest divisor of n whose exponents in its prime factorization are all powers of 2 (A138302).
A353898 (program): a(n) is the number of divisors of n whose exponents in their prime factorizations are all powers of 2 (A138302).
A353900 (program): a(n) is the sum of divisors of n whose exponents in their prime factorizations are all powers of 2 (A138302).
A353906 (program): a(n) is the {alternating sum of the digits of n} raised to the power {number of digits of n}.
A353907 (program): Numbers k such that k equals {alternating sum of digits of k} raised to the power of {number of digits of k}.
A353908 (program): Decimal expansion of Pi^2/36.
A353909 (program): a(n) is the alternating sum of the sequence gcd(n, k^2), 1 <= k <= n.
A353956 (program): Sum of the divisors of n whose arithmetic derivative is odd.
A353957 (program): a(n) = (85*4^n - 1)/3.
A353958 (program): Sum of the divisors of n whose arithmetic derivative is even.
A353959 (program): a(n) = Sum_{d|n} d * (-1)^(d’), where d’ is the arithmetic derivative of d (A003415).
A353964 (program): Number of tilings of a 2 X n rectangle using 2 X 2 and 1 X 1 tiles and right trominoes.
A353965 (program): Number of tilings of a 3 X n rectangle using 2 X 2 and 1 X 1 tiles and right trominoes.
A353974 (program): a(n) is the n-th partial sum of A056992.
A353975 (program): Product of the divisors of n whose arithmetic derivative is odd.
A353976 (program): Product of the divisors of n whose arithmetic derivative is even.
A353998 (program): Expansion of e.g.f. 1/(1 - x^2/2 * (exp(x) - 1)).
A354008 (program): Numerators of Cesàro means sequence of A114112.
A354028 (program): a(n) = 1 if n is a prime power of the form 4m+3, otherwise 0.
A354029 (program): a(n) = 1 if either n or n/2 is a prime power of the form 4m+3, otherwise 0.
A354030 (program): a(n) = 1 if n is either 1 or a prime power of the form 4m+1, otherwise 0.
A354031 (program): a(n) = 1 if n > 1 and n is a power of a Pythagorean prime (prime of the form 4m+1), otherwise 0.
A354032 (program): a(n) = 1 if phi(n)+sigma(n) == 2 (mod 4), otherwise 0.
A354033 (program): a(n) = 1 if n > 1 and n is a power of a prime of the form 4m+3, otherwise 0.
A354034 (program): a(n) = 1 if n is an even number or a square, otherwise 0.
A354035 (program): a(n) = 1 if n is odd and sigma(n^2) == 3 (mod 4), otherwise 0.
A354036 (program): a(n) = 1 if n is odd and sigma(n^2) == 1 (mod 4), otherwise 0.
A354037 (program): a(n) = 1 if sigma(n)-n is a multiple of 4, otherwise 0.
A354038 (program): Numbers k such that sum of the proper divisors of k is a multiple of 4.
A354039 (program): Odd numbers k for which sigma(k^2) == 1 (mod 4).
A354044 (program): a(n) = 2*(-i)^n*(n*sin(c*(n+1)) - i*sin(-c*n))/sqrt(5) where c = arccos(i/2).
A354047 (program): A169683 read as ternary numbers.
A354054 (program): a(n) = Product_{k=0..n} (k^6 + 1).
A354074 (program): Factorials that are the sum of the divisors of some m.
A354080 (program): a(n) = a(n-1) + a(n-2) + a(n-3), with a(0)=1, a(1)=4, a(2)=5.
A354084 (program): Primes p such that p mod 6 = p mod 8.
A354086 (program): 11-gonal (or hendecagonal) numbers which are products of four distinct primes.
A354097 (program): a(n) = 1 if n-phi(n) is a multiple of 4, otherwise 0.
A354098 (program): Numbers k such that the cototient of k (= k-phi(k)) is a multiple of 4.
A354099 (program): The 3-adic valuation of Euler totient function phi.
A354100 (program): The 3-adic valuation of sigma, sum of divisors function.
A354107 (program): a(n) = A354102(n) mod 4.
A354108 (program): a(n) = 1 if n is neither an odd prime power nor twice an odd prime power, otherwise 0.
A354109 (program): Numbers that are neither an odd prime power nor twice an odd prime power.
A354120 (program): Expansion of e.g.f. 1/(1 - log(1 + x))^3.
A354121 (program): Expansion of e.g.f. 1/(1 - log(1 + x))^4.
A354128 (program): Decimal expansion of 7 - 4*sqrt(3).
A354129 (program): Decimal expansion of 7 + 4*sqrt(3).
A354131 (program): Number of tilings of a 2 X n rectangle using 2 X 2 and 1 X 1 tiles, right trominoes and dominoes.
A354138 (program): a(n) is the numerator of Sum_{k=0..n} (-1)^k / (2*k)!.
A354144 (program): Prime powers together with semiprimes.
A354147 (program): Expansion of e.g.f. 1/(1 - 4 * log(1+x)).
A354157 (program): Numerator of generalized Catalan number c_3(n) (see Comments).
A354158 (program): The Bodlaender function: a(1) = -1; a(2*n) = a(n), a(2*n+1) = a(n+1) + n.
A354170 (program): Odd numbers whose Collatz trajectory includes 11 odd numbers.
A354180 (program): Numbers k such that d(k) = 3^i*5*j with i,j >= 0, where d(k) is the number of divisors of k (A000005).
A354181 (program): Numbers whose number of divisors is not a 3-smooth number.
A354182 (program): Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the binary expansions of n and n + a(n) have no 1’s in common.
A354199 (program): a(n) = 1 if in the prime factorization of n there is no prime factor of form 4k+1 and any prime factor of form 4k+3 occurs with an even multiplicity, otherwise 0.
A354200 (program): Prime map that sends 2 to 5, and each 4k+1 and 4k+3 prime to the next larger prime of the same type.
A354210 (program): a(n) = floor(sqrt(Fibonacci(n+1)*Fibonacci(n))).
A354211 (program): a(n) is the numerator of Sum_{k=0..n} 1 / (2*k+1)!.
A354222 (program): Decimal expansion of 2 / (Pi+2).
A354227 (program): Odd numbers whose Collatz trajectory contains exactly 12 odd numbers.
A354233 (program): Least number with n runs in ordered prime signature.
A354235 (program): Heinz numbers of integer partitions with at least one part divisible by 3.
A354237 (program): Expansion of e.g.f. 1 / (1 - log(1 + 2*x) / 2).
A354238 (program): Decimal expansion of 1 - Pi^2/12.
A354242 (program): Expansion of e.g.f. 1/sqrt(5 - 4 * exp(x)).
A354252 (program): Expansion of e.g.f. 1/sqrt(7 - 6 * exp(x)).
A354253 (program): Expansion of e.g.f. 1/sqrt(9 - 8 * exp(x)).
A354263 (program): Expansion of e.g.f. 1/(1 + 3 * log(1-x)).
A354264 (program): Expansion of e.g.f. 1/(1 + 4 * log(1-x)).
A354265 (program): Array read by ascending antidiagonals for n >= 0 and k >= 0. Generalized Lucas numbers, L(n, k) = (psi^(k - 1)*(phi + n) - phi^(k - 1)*(psi + n)), where phi = (1 + sqrt(5))/2 and psi = (1 - sqrt(5))/2.
A354267 (program): A Fibonacci-Pascal triangle read by rows: T(n, n) = 1, T(n, n-1) = n - 1, T(n, 0) = T(n-1, 1) and T(n, k) = T(n-1, k-1) + T(n-1, k) for 0 < k < n-1.
A354268 (program): Table read by rows. T(n, k) = (n + k)^(n - 1) for n >= 1 and 0 <= k <= n, T(0, 0) = 0.
A354280 (program): a(n) is the numerator of Cesàro means sequence c(n) of A237420 when the denominator is A141310(n).
A354294 (program): Number of palindromic compositions of 2n into parts <= n.
A354298 (program): a(n) is the numerator of Sum_{k=1..n} (-1)^(k+1) / (2*k-1)!!.
A354299 (program): a(n) is the denominator of Sum_{k=1..n} (-1)^(k+1) / (2*k-1)!!.
A354302 (program): a(n) is the numerator of Sum_{k=0..n} 1 / (k!)^2.
A354303 (program): a(n) is the denominator of Sum_{k=0..n} 1 / (k!)^2.
A354304 (program): a(n) is the numerator of Sum_{k=0..n} (-1)^k / (k!)^2.
A354305 (program): a(n) is the denominator of Sum_{k=0..n} (-1)^k / (k!)^2.
A354313 (program): Expansion of e.g.f. 1/(1 - x/2 * (exp(2 * x) - 1)).
A354314 (program): Expansion of e.g.f. 1/(1 - x/3 * (exp(3 * x) - 1)).
A354315 (program): Expansion of e.g.f. 1/(1 + x/2 * log(1 - 2 * x)).
A354316 (program): Expansion of e.g.f. 1/(1 + x/3 * log(1 - 3 * x)).
A354321 (program): Digit above the least significant 01 digit pair in the Zeckendorf representation of n.
A354325 (program): Expansion of e.g.f. 1/(1 - x/4 * (exp(2 * x) - 1)).
A354326 (program): Expansion of e.g.f. 1/(1 - x/8 * (exp(4 * x) - 1)).
A354327 (program): Expansion of e.g.f. 1/(1 + x/4 * log(1 - 2 * x)).
A354328 (program): Expansion of e.g.f. 1/(1 + x/8 * log(1 - 4 * x)).
A354330 (program): Distance from the sum of the first n positive triangular numbers to the nearest triangular number.
A354331 (program): a(n) is the denominator of Sum_{k=0..n} 1 / (2*k+1)!.
A354332 (program): a(n) is the numerator of Sum_{k=0..n} (-1)^k / (2*k+1)!.
A354333 (program): a(n) is the denominator of Sum_{k=0..n} (-1)^k / (2*k+1)!.
A354334 (program): a(n) is the numerator of Sum_{k=0..n} 1 / (2*k)!.
A354335 (program): a(n) is the denominator of Sum_{k=0..n} 1 / (2*k)!.
A354336 (program): a(n) is the integer w such that (L(2*n)^2, -L(2*n-1)^2, -w) is a primitive solution to the Diophantine equation 2*x^3 + 2*y^3 + z^3 = 125, where L(n) is the n-th Lucas number (A000032).
A354337 (program): a(n) is the integer w such that (L(2*n)^2, -L(2*n + 1)^2, w) is a primitive solution to the Diophantine equation 2*x^3 + 2*y^3 + z^3 = 125, where L(n) is the n-th Lucas number (A000032).
A354340 (program): a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} d^(k/d + 1) )/(k * (n-k)!).
A354343 (program): Number of distinct sums of n complex 6th power roots of unity.
A354350 (program): a(n) = n + A354365(n).
A354351 (program): Dirichlet inverse of A108951, primorial inflation of n.
A354352 (program): Sum of primorial inflation (A108951) and its Dirichlet inverse.
A354353 (program): a(n) = 1 if n is either a squarefree composite or a power of squarefree composite, otherwise 0.
A354354 (program): a(n) = 1 if n is neither a multiple of 2 nor 3, and otherwise 0.
A354355 (program): Characteristic function of numbers with their sum of divisors (sigma) 3-smooth.
A354356 (program): Numbers k such that sigma(k) is 3-smooth (has no larger prime factors than 3).
A354360 (program): Positions of 1’s in A354366.
A354365 (program): Numerators of Dirichlet inverse of primorial deflation fraction A319626(n) / A319627(n).
A354366 (program): Denominators of Dirichlet inverse of primorial deflation fraction A319626(n) / A319627(n).
A354378 (program): a(n) is the denominator of Sum_{k=0..n} (-1)^k / (2*k)!.
A354383 (program): Fibonacci sequence beginning 11, 26.
A354384 (program): Difference sequence of A356133.
A354395 (program): Expansion of e.g.f. exp( -(exp(x) - 1)^2 / 2 ).
A354401 (program): a(n) is the denominator of Sum_{k=1..n} 1 / (k*k!).
A354402 (program): a(n) is the numerator of Sum_{k=1..n} (-1)^(k+1) / (k*k!).
A354404 (program): a(n) is the denominator of Sum_{k=1..n} (-1)^(k+1) / (k*k!).
A354414 (program): a(n) is the smallest positive integer which does not occur in any Lucas sequence in which the first term is at most n and the second term is at most the first term.
A354415 (program): First differences of A354414.
A354419 (program): Expansion of e.g.f. log(1+4*x) * exp(x)/4.
A354429 (program): Expansion of e.g.f. tanh(x)^3 (odd powers only).
A354430 (program): First diagonal of an array, generated from the sequence of the nonprimes.
A354436 (program): a(n) = n! * Sum_{k=0..n} k^(n-k)/k!.
A354437 (program): a(n) = n! * Sum_{k=0..n} (-k)^(n-k)/k!.
A354446 (program): 11-gonal numbers (numbers of the form k*(9*k-7)/2), which are products of three distinct primes.
A354448 (program): 11-gonal (or hendecagonal) numbers which are products of two distinct primes.
A354451 (program): Number of middle divisors of 2*n-1.
A354452 (program): Number of middle divisors of 2*n.
A354454 (program): Nearest integer to sqrt(8*Pi*n).
A354455 (program): a(n) is the first composite number in the n-th row of A328739.
A354459 (program): Lazy cutter’s sequence (see Comments).
A354463 (program): a(n) is the number of trailing zeros in (2^n)!.
A354469 (program): Write n in primorial base, then replace each nonzero digit d of radix p with p-d.
A354482 (program): Positions of 0’s in binary expansion of Pi.
A354499 (program): Number of consecutive primes generated by adding 2n to the odd squares (A016754).
A354506 (program): a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d+1) )/(k * (n-k)!).
A354507 (program): a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d+1) * d )/(k * (n-k)!).
A354512 (program): Number of solutions m >= 2 to m - gpf(m) = n, gpf = A006530.
A354519 (program): Expansion of e.g.f. exp(x) * log(sec(x)).
A354520 (program): Expansion of e.g.f. exp(x) * log(cosh(x)).
A354529 (program): a(1) = 3, a(2) = 12 and a(n) = (3n^2+8n-2)/2 if n is even or = (3n^2+8n-5)/2, if n is odd, for n >= 3.
A354535 (program): a(n) is the number of different tile sizes after n iterations of the “Square Multiscale” substitution.
A354538 (program): a(n) is the least k such that A322523(k) = n.
A354541 (program): Number of ways to tile a double-hexagon strip of n hexagons, using single and double hexagons.
A354550 (program): Expansion of e.g.f. exp( x * exp(x^2/2) ).
A354555 (program): Rectangular array read by antidiagonals. T(m,n) is the number of degree n monic polynomials in GF_2[x] such that each irreducible factor in the prime factorization has multiplicity no greater than m, m>=1, n>=0.
A354588 (program): Number of marked chord diagrams (linear words in which each letter appears twice) with n chords, whose intersection graph is connected and distance-hereditary.
A354591 (program): Numbers k that can be written as the sum of 4 divisors of k (not necessarily distinct).
A354594 (program): a(n) = n^2 + 2*floor(n/2)^2.
A354595 (program): a(n) = n^2 + 4*floor(n/2)^2.
A354598 (program): Maximal GCD of eight positive integers with sum n.
A354599 (program): Maximal GCD of nine positive integers with sum n.
A354600 (program): a(n) = Product_{k=0..9} floor((n+k)/10).
A354601 (program): Maximal GCD of ten positive integers with sum n.
A354660 (program): a(n) = A354650(n,2*n), for n >= 0.
A354673 (program): Smallest number of unit cells that must be removed from an n X n square board in order to avoid any cycles.
A354698 (program): T(n,k) is the number of points with integer coordinates strictly inside the triangle with vertices (0,0), (n,0), (n,k), where T(n,k) is a triangle read by rows, 2 <= k <= n.
A354711 (program): Numbers k such that the number of divisors of k divides k-1.
A354713 (program): Number of solutions (n, D) for Pell equation n^2 - D*y^2 = 1 with fixed n.
A354714 (program): Nonprime numbers k such that the number of divisors of k divides k+1.
A354715 (program): Numbers k such that the number of divisors of k divides k-2.
A354733 (program): a(0) = a(1) = 1; a(n) = 2 * Sum_{k=0..n-2} a(k) * a(n-k-2).
A354734 (program): a(0) = a(1) = 1; a(n) = 3 * Sum_{k=0..n-2} a(k) * a(n-k-2).
A354735 (program): a(0) = a(1) = 1; a(n) = 4 * Sum_{k=0..n-2} a(k) * a(n-k-2).
A354736 (program): a(0) = a(1) = 1; a(n) = 5 * Sum_{k=0..n-2} a(k) * a(n-k-2).
A354747 (program): Start with 2*n-1; repeatedly triple and add 2 until reaching a prime. a(n) = number of steps until reaching a prime > 2*n-1, or 0 if no prime is ever reached.
A354748 (program): a(n) is the prime reached after A354747(n) steps when repeatedly applying the map x -> 3*x+2 to 2*n-1, or 0 if no prime is ever reached.
A354750 (program): Expansion of e.g.f. 1 / (1 - log(1 + 3*x) / 3).
A354751 (program): Expansion of e.g.f. 1 / (1 - log(1 + 4*x) / 4).
A354752 (program): a(n) = Sum_{k=0..n} Stirling1(n,k) * k! * n^(n-k).
A354760 (program): a(0) = 0; for n >= 1, a(n) = a(n - A054055(n)) + 1.
A354763 (program): a(n) is the minimum number of square tiles needed for constructing a figure whose corresponding graph has n cycles.
A354776 (program): Even numbers that are the sum of two squares; also numbers which are twice the sum of two squares.
A354779 (program): a(0), …, a(5) are 0, 1, 2, 3, 3, 3; thereafter if n == 0 mod 4 then a(n) = n/2; if n == 1 mod 4, (n+1)/2; 2 mod 4, (n+2)/2; 3 mod 4, (n+1)/2.
A354782 (program): Second digit from left in decimal expansion of 2^n (n >= 4).
A354784 (program): First differences of A000213, also twice A000073.
A354785 (program): Numbers of the form 3*2^n or 9*2^n.
A354788 (program): a(2*k) = 3*2^k - 3, a(2*k+1) = 2^(k+2) - 3.
A354789 (program): a(2*k) = 9*2^k - 7, a(2*k+1) = 3*2^(k+2) - 7.
A354796 (program): Triangle read by rows. T(n, k) = Gamma(k + n) / k! for n >= 1 and 0 <= k <= n, T(0, 0) = 1.
A354801 (program): n^2 minus the sum of all aliquot divisors of all positive integers <= n.
A354812 (program): Positions of +2’s in A346242.
A354819 (program): a(n) = 1 if n is a nonprime squarefree number, otherwise 0.
A354832 (program): Integers m such that iterating the map f(x) = x^2 + 1 on m generates a number ending with m in binary format.
A354837 (program): Odd numbers k such that gcd(k, A007088(k)) != 1.
A354838 (program): For n >= 1, a(n) = A007088(n)/gcd(n, A007088(n)).
A354843 (program): a(n) = n! * Sum_{d|n} (n/d)^d / d!.
A354845 (program): a(n) = n! * Sum_{d|n} (n/d)^(d-1) / d!.
A354848 (program): a(n) = (n-1)! * Sum_{d|n} d^(n/d + 1).
A354851 (program): a(n) = (n-1)! * Sum_{d|n} d^(n/d).
A354856 (program): a(1) = 1, a(n) = the number of times a(n-1) appears among the first n-2 terms.
A354863 (program): a(n) = n! * Sum_{d|n} (n/d) / d!.
A354868 (program): Parity of Dirichlet inverse of A122111.
A354870 (program): Number of nonprime squarefree divisors of n.
A354874 (program): a(n) = 1 if A003415(n) is squarefree, otherwise 0.
A354888 (program): a(n) = n! * Sum_{d|n} d^d / d!.
A354889 (program): a(n) = n! * Sum_{d|n} d^(d-1) / d!.
A354890 (program): a(n) = n! * Sum_{d|n} d^n / d!.
A354891 (program): a(n) = n! * Sum_{d|n} d^(n - d) / d!.
A354892 (program): a(n) = n! * Sum_{d|n} d^n / (n/d)!.
A354893 (program): a(n) = n! * Sum_{d|n} d^(n - d) / (n/d)!.
A354894 (program): a(n) is the numerator of the n-th hyperharmonic number of order n.
A354895 (program): a(n) is the denominator of the n-th hyperharmonic number of order n.
A354896 (program): A fixed point of the two-block Thue-Morse substitution 00->001, 01->010, 10->101, 11->110
A354900 (program): a(n) = n! * Sum_{d|n} d^d / (n/d)!.
A354902 (program): a(n) = 2*n^2 - 6*n + 11 for n > 1 with a(0)=1 and a(1)=3.
A354911 (program): Number of factorizations of n into relatively prime prime-powers.
A354918 (program): a(n) = A344005(n) mod 2, where A344005(n) is the smallest positive m such that n divides the oblong number m*(m+1).
A354919 (program): Positions of odd terms in A344005.
A354920 (program): a(n) = A182665(n) mod 2, where A182665(n) is the greatest x < n such that n divides x*(x-1).
A354921 (program): Positions of odd terms in A182665.
A354922 (program): Positions of even terms in A182665.
A354923 (program): a(n) = 1 if n is either a power of prime or 2*prime, otherwise 0.
A354924 (program): a(n) = 1 if A047994(n) is equal to A344005(n), otherwise 0.
A354925 (program): Union of powers of primes and even semiprimes.
A354926 (program): a(n) = 1 if n is a product of three distinct primes, otherwise 0.
A354927 (program): a(n) = 1 if the product of divisors of n is n^2, otherwise 0.
A354928 (program): Numbers k such that A047994(k) = A344005(k).
A354933 (program): a(1) = 1; for n > 1, a(n) = n / the largest divisor of n that is coprime to a larger divisor of n.
A354934 (program): Row 4 of A354940: Numbers k for which A345992(k) = 4, divided by 4.
A354935 (program): Row 5 of A354940: Numbers k for which A345992(k) = 5, divided by 5.
A354936 (program): Row 6 of A354940: Numbers k for which A345992(k) = 6, divided by 6.
A354937 (program): Row 7 of A354940: Numbers k for which A345992(k) = 7, divided by 7.
A354938 (program): Row 8 of A354940: Numbers k for which A345992(k) = 8, divided by 8.
A354939 (program): Row 9 of A354940: Numbers k for which A345992(k) = 9, divided by 9.
A354941 (program): a(n) = Sum_{k=0..n} binomial(n,k)^3 * k! * (-2)^(n-k).
A354942 (program): a(n) = Sum_{k=0..n} binomial(n,k)^3 * k! * (-3)^(n-k).
A354943 (program): a(n) = Sum_{k=0..n} binomial(n,k)^3 * k! * n^(n-k).
A354944 (program): a(n) = Sum_{k=0..n} binomial(n,k)^3 * k! * (-n)^(n-k).
A354946 (program): a(n) = gcd(A001923(n),n^n).
A354958 (program): Coordination sequence for the Manhattan hexagonal lattice with respect to the point (X=0, Y=1).
A354968 (program): Triangle read by rows: T(n, k) = n*k*(n+k)*(n-k)/6.
A354973 (program): a(0)=0; for n > 0, a(n) = 2*a(n-1) if n-1 is prime, a(n-1) + 1 otherwise.
A354981 (program): a(n) = 1 if n = 2 * p^k, with p an odd prime and k >= 1, otherwise 0.
A354982 (program): a(n) = 1 if n is a prime power congruent to 1 (mod 3), otherwise 0.
A354984 (program): Numbers that are 3 * prime powers congruent to 1 (mod 3).
A354985 (program): a(n) = gcd(A047994(n), A344005(n)).
A354986 (program): a(n) = A047994(n) / gcd(A047994(n), A344005(n)).
A354987 (program): a(n) = A344005(n) / gcd(A047994(n), A344005(n)).
A354988 (program): a(n) = A345993(n) - A345992(n).
A354997 (program): a(n) = A351547(n) / A351546(n).
A355001 (program): Smallest common prime factor of A003961(n) and A276086(n), or 1 if they are coprime, where A003961 is fully multiplicative with a(p) = nextprime(p), and A276086 is primorial base exp-function.
A355003 (program): a(n) = gcd(A003415(n), A277791(n)), where A003415 is the arithmetic derivative and A277791 is the denominator of sum of reciprocals of proper divisors of n.
A355004 (program): a(n) = Sum_{k=0..n} A271703(k + n, n), row sums of A355005.
A355005 (program): Table read by rows. T(n, k) = n*((k + n)!)^2/((k + n)*(n!)^2*k!) for n > 0 and T(0, 0) = 1.
A355018 (program): Partial sums of F(1) - L(1) + F(2) - L(2) + F(3) - L(3) + …, where F = A000045 and L = A000032.
A355019 (program): Partial sums of L(1) - F(1) + L(2) - F(2) + L(3) - F(3) + …, where L = A000032 and F = A000045.
A355020 (program): a(n) = (-1)^n * F(n) + 1, where F = A000045 (Fibonacci numbers).
A355021 (program): a(n) = (-1)^n * L(n) - 1, where L = A000032 (Lucas numbers).
A355023 (program): Number of labeled trees on n nodes with maximum degree three and three vertices of degree three.
A355038 (program): a(n) = n^2 times the squarefree kernel of n.
A355044 (program): Number of coalescent histories for matching gene trees and species trees with n leaves and a 5-leaf seed tree.
A355058 (program): Numbers m such that d(m) mod 6 = 3, where d(m) is the number of divisors of m.
A355068 (program): Square array read by upwards antidiagonals: T(n,k) = k-th digit after the decimal point in decimal expansion of 1/n, for n >= 1 and k >= 1.
A355109 (program): a(n) = 1 + Sum_{k=1..n-1} binomial(n-1,k) * 2^(k-1) * a(k).
A355110 (program): Expansion of e.g.f. 2 / (3 - 2*x - exp(2*x)).
A355111 (program): Expansion of e.g.f. 3 / (4 - 3*x - exp(3*x)).
A355112 (program): Expansion of e.g.f. 4 / (5 - 4*x - exp(4*x)).
A355113 (program): Expansion of e.g.f. 5 / (6 - 5*x - exp(5*x)).
A355114 (program): Expansion of e.g.f. 6 / (7 - 6*x - exp(6*x)).
A355118 (program): The number of nonequivalent root ancestral configurations in a recursively defined family of gene trees and species trees with at least n = 9 leaves, in which for n >= 12 leaves, 3-leaf trees are successively added at the root of the tree with n-3 leaves.
A355140 (program): n/d(n) rounded to the nearest integer, where d(n) is the number of divisors of n (A000005).
A355141 (program): a(0)=1, a(1)=a(2)=0; for n > 2, a(n) = a(n-1) + s if n is odd, a(n-1) - s if n is even, where s = a(n-1) + a(n-2) + a(n-3).
A355142 (program): a(n) = 33648*3^n - 1.
A355159 (program): Numbers k such that (fractional part of k^(3/2)) < 1/2.
A355160 (program): Numbers k such that (fractional part of k^(3/2)) > 1/2.
A355161 (program): Primes p such that p - prevprime(p) is not a power of 2.
A355162 (program): a(n) = exp(-1) * Sum_{k>=0} (4*k + 2)^n / k!.
A355163 (program): a(n) = exp(-1) * Sum_{k>=0} (4*k + 3)^n / k!.
A355164 (program): a(n) = exp(-1/3) * Sum_{k>=0} (3*k + 2)^n / (3^k * k!).
A355165 (program): a(n) = exp(-1/4) * Sum_{k>=0} (4*k + 2)^n / (4^k * k!).
A355167 (program): a(n) = exp(-1/4) * Sum_{k>=0} (4*k + 3)^n / (4^k * k!).
A355168 (program): Numerators of best lower approximates h/k to sqrt(k); complement of A355169.
A355169 (program): Numbers h such that (h+1)/k is closer to sqrt(k) than h/k is, where h is the greatest integer j such that j/k < sqrt(k); complement of A355168.
A355171 (program): a(n) = Sum_{k=0..n} binomial(n, k + 1)*k!*(n + 1)!/(k + 2)!.
A355172 (program): The Fuss-Catalan triangle of order 2, read by rows. Related to ternary trees.
A355173 (program): The Fuss-Catalan triangle of order 1, read by rows. Related to binary trees.
A355174 (program): The Fuss-Catalan triangle of order 3, read by rows. Related to quartic trees.
A355177 (program): Numbers k such that omega(k^2 - 1) = omega(k) where omega(k) = A001221(k).
A355182 (program): a(n) = t(n) - s(n) where s(n) = n*(n-1)/2 is the sum of the first n nonnegative integers and t(n) is the smallest sum of consecutive integers starting from n such that t(n) > s(n).
A355183 (program): Decimal expansion of the area of the region that represents the set of points in a unit square that are closer to the center of the square than to the closest edge.
A355193 (program): Number of partitions of n that contain at least one odd prime as a part.
A355195 (program): Number of partitions of n that do not contain odd primes as parts.
A355200 (program): Numbers k that can be written as the sum of 3 divisors of k (not necessarily distinct).
A355202 (program): Square array read by upwards antidiagonals: T(n,k) = k-th binary digit after the radix point of 1/n, for n >= 1 and k >= 1.
A355218 (program): a(n) = Sum_{k>=1} (3*k - 1)^n / 2^k.
A355219 (program): a(n) = Sum_{k>=1} (4*k - 2)^n / 2^k.
A355220 (program): a(n) = Sum_{k>=1} (4*k - 1)^n / 2^k.
A355229 (program): E.g.f. A(x) satisfies A’(x) = 1 - log(1-x) * A(x).
A355231 (program): E.g.f. A(x) satisfies A’(x) = 1 - 2 * log(1-x) * A(x).
A355233 (program): E.g.f. A(x) satisfies A’(x) = 1 + 2 * (exp(x) - 1) * A(x).
A355234 (program): Decimal expansion of Li_2(-1/2), the dilogarithm of (-1/2) (negated).
A355247 (program): Expansion of e.g.f. exp(2*(exp(x) - 1 + x)).
A355249 (program): Maximal GCD of three positive integers with sum n.
A355252 (program): Expansion of e.g.f. exp(2*(exp(x) - 1) + 3*x).
A355253 (program): Expansion of e.g.f. exp(2*(exp(x) - 1) - 3*x).
A355254 (program): Expansion of e.g.f. exp(3*(exp(x) - 1) - x).
A355258 (program): a(n) = n! * [x^n] (1 - x)*log((1 - x)/(1 - 2*x)).
A355261 (program): a(n) = largest-nth-power(n, 2) * radical(n) = A000188(n) * A007947(n), where largest-nth-power(n, e) is the largest positive integer b such that b^e divides n.
A355262 (program): Array of Fuss-Catalan numbers read by ascending antidiagonals, A(n, k) = binomial(k*n + 1, k)/(k*n + 1).
A355263 (program): a(n) = largest-nth-power(n, 3) * radical(n) = A053150(n) * A007947(n), where the largest-nth-power(n, e) is the largest positive integer b such that b^e divides n.
A355264 (program): a(n) = n * largest-nth-power(n, 2) = n * A000188(n), where largest-nth-power(n, e) is the largest positive integer b such that b^e divides n.
A355268 (program): a(n) = n! * [x^n] -exp(x^2)/(x - 1).
A355280 (program): Binary numbers (digits in {0, 1}) with no run of digits with length < 2.
A355288 (program): a(0)=1, a(1)=3, a(2)=7; thereafter a(n) = a(n-1) + a(n-2) + 1.
A355293 (program): Expansion of e.g.f. 1 / (1 - x - x^2/2 - x^3/3).
A355294 (program): Expansion of e.g.f. 1 / (1 - x - x^2/2 - x^3/3 - x^4/4).
A355297 (program): a(n) = A007088(n) mod n.
A355300 (program): a(0) = 0; for n >= 1, a(n) = a(A007088(n) mod n) + 1.
A355319 (program): Maximal GCD of four positive integers with sum n.
A355321 (program): Numbers k such that the k-th composition in standard order has the same number of even parts as odd.
A355322 (program): LCM of Lucas numbers {L(1), L(2), …, L(n)}.
A355324 (program): Lower midsequence of the Fibonacci numbers (1,2,3,5,8,…) and Lucas numbers (1,3,4,7,11,…); see Comments.
A355325 (program): Upper midsequence of the Fibonacci numbers (1,2,3,5,8,…) and Lucas numbers (1,3,4,7,11,…); see Comments.
A355327 (program): Number of ways to tile a 2 X n board with squares and dominoes where vertical dominoes are only allowed in even-numbered locations.
A355341 (program): G.f.: A(x) = Sum_{n=-oo..+oo} x^(n*(n+1)/2) * C(x)^n, where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108).
A355347 (program): a(n) = binomial(3*n+3,n) + binomial(3*n+2,n-1) for n >= 0.
A355366 (program): Maximal GCD of five positive integers with sum n.
A355368 (program): Maximal GCD of six positive integers with sum n.
A355372 (program): Expansion of the e.g.f. log((1 - x) / (1 - 2*x)) / (1 - x)^3.
A355373 (program): a(n) = Sum_{k=0..n} k! * (-1)^k * n^(n-k) * Stirling2(n,k).
A355389 (program): Number of unordered pairs of distinct integer partitions of n.
A355390 (program): Number of ordered pairs of distinct integer partitions of n.
A355402 (program): Maximal GCD of seven positive integers with sum n.
A355406 (program): Positive integers that are not powers of 2 and whose Collatz trajectory has maximum power of 2 different from 2^4.
A355407 (program): Expansion of the e.g.f. log((1 - x) / (1 - 2*x)) / (1 - x)^4.
A355413 (program): Lexicographically earliest infinite sequence of positive numbers such that, for n>1, a(n) AND a(n-1) is distinct from all previous AND operations between adjacent terms, where AND is the binary AND operator.
A355414 (program): Expansion of the e.g.f. log((1 - x) / (1 - 2*x)) / (1 - x)^5.
A355430 (program): Primes starting with an even decimal digit.
A355440 (program): Expansion of e.g.f. Sum_{k>=0} exp(4^k * x) * x^k/k!.
A355441 (program): Numbers k such that the sum of the least prime factors of i=2..k is prime.
A355442 (program): a(n) = gcd(A003961(n), A276086(n)), where A003961 is fully multiplicative with a(p) = nextprime(p), and A276086 is primorial base exp-function.
A355447 (program): a(n) = 1 if n is neither squarefree nor prime power, otherwise 0.
A355448 (program): a(n) = 1 if the number of divisors of n^2 is coprime to 6, otherwise 0.
A355449 (program): a(n) = 1 if n^2 + 2 is prime, 0 otherwise.
A355450 (program): a(n) = 1 if n is odd and phi(x) = n^2 + 1 has no solutions, otherwise 0.
A355452 (program): a(n) = 1 if Bernoulli number B_{n} has denominator 6, otherwise 0.
A355453 (program): a(n) = 1 if the third smallest divisor of n is not a prime, otherwise 0.
A355456 (program): Greatest common divisor of sigma(n), A003961(n), and A276086(n).
A355462 (program): Powerful numbers divisible by exactly 2 distinct primes.
A355463 (program): Expansion of Sum_{k>=0} (x/(1 - k^k * x))^k.
A355464 (program): Expansion of Sum_{k>=0} x^k/(1 - k^k * x)^(k+1).
A355467 (program): a(n) is the smallest number which is greater than n and has more prime factors (with multiplicity) than n.
A355468 (program): Expansion of Sum_{k>=0} (k^2 * x/(1 - k^2 * x))^k.
A355469 (program): Expansion of Sum_{k>=0} (k^3 * x/(1 - k^3 * x))^k.
A355470 (program): Expansion of Sum_{k>=0} (k^3 * x)^k/(1 - k^3 * x)^(k+1).
A355471 (program): Expansion of Sum_{k>=0} (x/(1 - k^2 * x))^k.
A355472 (program): Expansion of Sum_{k>=0} (x/(1 - k^3 * x))^k.
A355473 (program): Expansion of Sum_{k>=0} x^k/(1 - k^3 * x)^(k+1).
A355474 (program): Square array T(m,n) = Card({ (i, j) : 1 <= i <= m, 1 <= j <= min(n, i), GCD(i, j) = 1 }), read by antidiagonals upwards.
A355477 (program): Maximum number of skew-tetrominoes that can be packed into an n X n square.
A355487 (program): Bitwise XOR of the base-4 digits of n.
A355488 (program): Expansion of g.f. f/(1+2*f) where f is the g.f. of nonempty permutations.
A355489 (program): Numbers k such that A000120(k) = A007814(k) + 2.
A355492 (program): a(n) = 7*3^n - 2.
A355493 (program): Expansion of Sum_{k>=0} (k^3 * x)^k/(1 - x)^(k+1).
A355494 (program): Expansion of Sum_{k>=0} (k * x/(1 - x))^k.
A355495 (program): Expansion of Sum_{k>=0} (k^2 * x/(1 - x))^k.
A355496 (program): Expansion of Sum_{k>=0} (k^3 * x/(1 - x))^k.
A355497 (program): Numbers k such that x^2 - s*x + p has only integer roots, where s and p denote the sum and product of the digits of k respectively.
A355498 (program): a(n) = A000217(A033676(n)) * A000217(A033677(n)).
A355501 (program): Expansion of e.g.f. exp(3 * x * exp(x)).
A355510 (program): a(n) is the number of monic polynomials of degree n over GF(7) without linear factors.
A355511 (program): a(n) is the number of monic polynomials of degree n over GF(11) without linear factors.
A355532 (program): Maximal augmented difference between adjacent reversed prime indices of n; a(1) = 0.
A355537 (program): Number of ways to choose a sequence of prime factors, one of each integer from 2 to n.
A355538 (program): Partial sum of A001221 (number of distinct prime factors) minus 1, ranging from 2 to n.
A355551 (program): Number of ways to select 3 or more collinear points from a 3 X n grid.
A355564 (program): Triangle read by rows: T(n,k) = n*(1+2*k) - k*(1+k), n >= 1, 0 <= k <= n-1.
A355571 (program): Complement of A007956: numbers not of the form P(k)/k where P(n) is the product of the divisors of n.
A355582 (program): a(n) is the largest 5-smooth divisor of n.
A355583 (program): a(n) is the number of the 5-smooth divisors of n.
A355584 (program): a(n) is the sum of the 5-smooth divisors of n.
A355590 (program): a(n) = (product of the first n primes) - (sum of the first n primes).
A355591 (program): a(n) = (product of the first n odd primes) - (sum of the first n odd primes).
A355624 (program): a(0) = 0, and for any n > 0, a(3*n) = 3*a(n), a(3*n+1) = 1-3*a(n), a(3*n+2) = 2-3*a(n).
A355639 (program): a(n) is the least k > 0 such that the balanced ternary expansion of k*n contains as many negative trits as positive trits.
A355640 (program): a(0) = 0, and for any n > 0, a(n) is the least positive multiple of n whose balanced ternary expansion contains as many negative trits as positive trits.
A355645 (program): The number of regions in the G-Shi arrangement when G is the cycle graph C_n.
A355659 (program): Martingale win/loss triangle, read by rows: T(n,k) = total number of dollars won (or lost) using the martingale method on all possible n trials that have exactly k losses and n-k wins, for 0 <= k <= n.
A355668 (program): Array read by upwards antidiagonals T(n,k) = J(k) + n*J(k+1) where J(n) = A001045(n) is the Jacobsthal numbers.
A355673 (program): Decimal expansion of 265/153.
A355681 (program): The “coarser” of 2 representations of the Cantor middle thirds set viewed from a quarter point that lies at a(0) (the third 1 in the data).
A355683 (program): Multiplicative with a(p^e) = 0 if e=1 and a(p^e)= -1 if e>1.
A355684 (program): Dirichlet inverse of A355448.
A355688 (program): Dirichlet inverse of A354354, characteristic function of numbers that are neither multiples of 2 nor 3.
A355689 (program): Dirichlet inverse of A166486, characteristic function of numbers that are not multiples of 4.
A355690 (program): Dirichlet inverse of A152822, characteristic function of numbers not congruent to 2 mod 4.
A355691 (program): Dirichlet inverse of A320111, number of divisors of n that are not of the form 4k+2.
A355698 (program): a(n) is the number of repdigits divisors of n (A010785).
A355703 (program): a(n) = binomial(n, floor(log(n))).
A355722 (program): Row 2 of table A355721.
A355723 (program): Row 3 of table A355721.
A355724 (program): Row 4 of table A355721.
A355725 (program): Row 5 of table A355721.
A355726 (program): a(n) = a(n-2) + prime(n-1) for a(0) = a(1) = 0.
A355729 (program): Tournament standing, under standard rules double elimination, of the participant whose elimination leaves n participants still in the tournament.
A355742 (program): Number of ways to choose a sequence of prime-power divisors, one of each prime index of n. Product of bigomega over the prime indices of n, with multiplicity.
A355750 (program): Sum of the divisors of 2n minus the number of divisors of 2n.
A355751 (program): Positive numbers k such that the centered cube number k^3 + (k+1)^3 is equal to the difference of two positive cubes and to A352759(n).
A355752 (program): a(n) = 3*(2*n - 1)*( 3*(2*n - 1)^3 + 1) / 2.
A355753 (program): a(n) = 3*(2*n - 1)*( 3*(2*n - 1)^3 - 1) / 2 for n > 0.
A355759 (program): Sums of the first ceiling((n+1)/2) entries on the diagonals of a square spiral with a starting value of 1 in the center, where the diagonal and the antidiagonal are used alternately.
A355784 (program): a(n) is the number of distinct primes of the form k*(n-k)+n where 1 <= k < n.
A355794 (program): Row 1 of A355793.
A355795 (program): Row 2 of A355793.
A355796 (program): Row 3 of A355793.
A355797 (program): Row 4 of A355793.
A355818 (program): Greatest common divisor of n, sigma(n) and A276086(n), where A276086 is primorial base exp-function.
A355820 (program): a(n) = 1 if A003961(n) and A276086(n) are relatively prime, otherwise 0, where A003961 is fully multiplicative with a(p) = nextprime(p), and A276086 is primorial base exp-function.
A355821 (program): Numbers k for which A003961(k) and A276086(k) are relatively prime, where A003961 is fully multiplicative with a(p) = nextprime(p), and A276086 is primorial base exp-function.
A355822 (program): Numbers k such that A003961(k) and A276086(k) share a prime factor, where A003961 is fully multiplicative with a(p) = nextprime(p), and A276086 is primorial base exp-function.
A355823 (program): a(n) = 1 if all exponents in prime factorization of n are powers of 2, otherwise 0.
A355825 (program): a(n) = 1 if all exponents in prime factorization of n have an odd binary weight, otherwise 0.
A355837 (program): Dirichlet inverse of A322327.
A355858 (program): a(n) = n^(2*n-1) mod (2*n-1).
A355859 (program): Triangle read by rows: T(n,k) = (n + k)/2 if (n + k) is congruent to 0 (mod 2), otherwise T(n,k) = 0; n >= 1, k >= 1.
A355882 (program): Number of ways to 4-color a 3 X n grid ignoring the variations of two colors.
A355886 (program): a(n) = n! * Sum_{k=1..n} floor(n/k)/k!.
A355887 (program): a(n) = Sum_{k=1..n} k^k * floor(n/k).
A355888 (program): a(n) = Sum_{k=1..n} k! * floor(n/k).
A355890 (program): Let s(k) = A052551(k), and write down s(0) consecutive integers beginning with 0, skip one integer, continue with s(1) consecutive numbers, skip one integer, then s(2) consecutive numbers, skip one integer, then s(3) consecutive numbers, and so on.
A355898 (program): a(1) = a(2) = 1; a(n) = gcd(a(n-1), a(n-2)) + (a(n-1) + a(n-2))/gcd(a(n-1), a(n-2)).
A355899 (program): The successive gcd’s arising in A355898.
A355905 (program): Left-most path in the tree T_0 of all negasemiternary (or NST) fractions whose 2-adic part is zero.
A355906 (program): a(0) = 0; for n >= 1, a(n) = -(3/2)*(a(n-1)+A355905(n-1)).
A355907 (program): A355906(n)/3.
A355908 (program): A335905(n) + A335906(n).
A355909 (program): Number of nodes at level n in the tree T_0 mentioned in A355905.
A355910 (program): Number of nodes at level n in the tree T_{-2}.
A355914 (program): a(n) = gcd(b(n-1),b(n)), where b(n) = A351871(n).
A355928 (program): Squarefree part of the sum of divisors of n.
A355929 (program): Difference between the squarefree part of the sum of divisors of n and the squarefree part of n.
A355930 (program): Sum of the prime indices of n minus the sum of the prime indices of the smallest number with same prime signature as n, when the sum is taken with multiplicity, as in A056239.
A355931 (program): Greatest common divisor of the odd part of n and sigma(n), where sigma is the sum of divisors function.
A355932 (program): a(n) = gcd(sigma(n), sigma(A003961(n))), where A003961 is fully multiplicative with a(p) = nextprime(p).
A355933 (program): a(n) = A003973(n) / gcd(sigma(n), A003973(n)), where A003973(n) = sigma(A003961(n)) and A003961 is fully multiplicative with a(p) = nextprime(p).
A355934 (program): a(n) = sigma(n) / gcd(sigma(n), sigma(A003961(n))), where A003961 is fully multiplicative with a(p) = nextprime(p), and sigma is the sum of divisors function.
A355936 (program): Dirichlet inverse of A295316, characteristic function of exponentially odd numbers.
A355937 (program): a(n) = 1 if the number of divisors of n is a noncomposite, otherwise 0.
A355938 (program): a(n) = 1 if sigma(n^2) is a noncomposite, otherwise 0.
A355939 (program): Dirichlet inverse of A080339, characteristic function of noncomposite numbers.
A355940 (program): a(n) = 1 if A003973(n) is a multiple of A000203(n), otherwise 0.
A355942 (program): Numbers k such that k is a multiple of A326042(k).
A355946 (program): a(n) = 1 if the odd part of sigma(k) divides A003961(k), otherwise 0, where A003961 is fully multiplicative with a(p) = nextprime(p), and sigma is the sum of divisors function.
A355947 (program): a(n) = Sum_{k=1..n} (n+1-k)*floor(n/k).
A355950 (program): a(n) = Sum_{k=1..n} k^(k-1) * floor(n/k).
A355986 (program): a(n) = Sum_{k=1..n} floor(n/k)!.
A355987 (program): a(n) = n! * Sum_{k=1..n} 1/floor(n/k)!.
A355988 (program): a(n) = n! / floor(n/3)!.
A355989 (program): a(n) = n! / (2 * floor(n/2)!).
A355990 (program): a(n) = n! / (6 * floor(n/3)!).
A356005 (program): Number of integers k such that k*tau(k) <= n.
A356006 (program): The number of prime divisors of n that are not greater than 5, counted with multiplicity.
A356011 (program): a(n) = n! * Sum_{k=1..n} 1/(k! * floor(n/k)).
A356012 (program): a(n) = n! / (6 * floor(n/3)).
A356013 (program): Triangle T(n,k), n >= 1, 1 <= k <= n, read by rows, where T(n,k) = n!/(k! * floor(n/k)).
A356018 (program): a(n) is the number of evil divisors (A001969) of n.
A356023 (program): Decimal expansion of Sum_{j>=1) 2^^j/2^^(j+1) where ^^ indicates tetration.
A356029 (program): a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^k/(2^k * (n - 2*k)!).
A356030 (program): Decimal expansion of the real root of x^3 - x - 2.
A356031 (program): Decimal expansion of the real root of 2*x^3 + x - 1.
A356032 (program): Decimal expansion of the positive real root of x^4 + x - 1.
A356033 (program): Decimal expansion of (-1 + sqrt(13))/6 = A223139/3.
A356034 (program): Decimal expansion of the real root of x^3 - x^2 - 3.
A356035 (program): Decimal expansion of the real root of x^3 - 2*x^2 - 1.
A356036 (program): Triangle read by rows, giving in the first column the powers of 3 (A000244) and in the next columns 4/3 times the previous row entry.
A356037 (program): Conjecturally, a(n) is the smallest number m such that every natural number is a sum of at most m n-simplex numbers.
A356038 (program): a(n) = Sum_{k=1..n} binomial(n,k) * sigma_2(k).
A356039 (program): a(n) = Sum_{k=1..n} binomial(n,k) * sigma_3(k).
A356042 (program): a(n) = Sum_{k=1..n} sigma_2(k) * floor(n/k).
A356043 (program): a(n) = Sum_{k=1..n} sigma_3(k) * floor(n/k).
A356047 (program): The number of links of a polyline that connects the midpoints of opposite sides of the n-th regular integer hexagon and has the following properties: the first link is 1; each subsequent one is 1 more than the previous one; the angle between adjacent links is equal to Pi/3; links of the same parity are parallel.
A356050 (program): a(n) = 2*A135318(n+1) - A135318(n).
A356056 (program): a(n) = A001951(A137803(n)).
A356057 (program): a(n) = A001951(A137804(n)).
A356058 (program): a(n) = A001952(A137803(n)).
A356059 (program): a(n) = A001952(A137804(n)).
A356061 (program): Numbers whose sum of digits is a refactorable number.
A356068 (program): Number of integers ranging from 1 to n that are not prime-powers (1 is not a prime-power).
A356069 (program): Number of divisors of n whose prime indices cover an interval of positive integers (A073491).
A356076 (program): a(n) = Sum_{k=1..n} sigma_k(k) * floor(n/k).
A356088 (program): a(n) = A001951(A022838(n)).
A356089 (program): a(n) = A001951(A054406(n)).
A356090 (program): a(n) = A001952(A022838(n)).
A356091 (program): a(n) = A001952(A054406(n)).
A356093 (program): a(n) = numerator((prime(n)-1)/prime(n)#), where prime(n)# = A002110(n) is the n-th primorial.
A356094 (program): a(n) = denominator((prime(n)-1)/prime(n)#), where prime(n)# = A002110(n) is the n-th primorial.
A356095 (program): Tetrahedral (or triangular pyramidal) numbers which are products of three distinct primes (or sphenic numbers).
A356100 (program): a(n) = Sum_{k=1..n} (k - 1)^n * floor(n/k).
A356104 (program): a(n) = A000201(A022839(n)).
A356105 (program): a(n) = A000201(A108598(n)).
A356106 (program): a(n) = A000201(A108598(n)).
A356107 (program): a(n) = A001950(A108598(n)).
A356114 (program): Number of irreducible permutations of n with partition type [2, 1, 1, …, 1] (with ‘1’ taken n - 2 times).
A356116 (program): Triangle read by row. The reduced triangle of the partition_triangle A355776.
A356117 (program): T(n, k) = [x^k] (1/2 - x)^(-n) - (1 - x)^(-n).
A356118 (program): Row sums of A174159.
A356122 (program): Number of Lucas divisors of the n-th Lucas number.
A356125 (program): a(n) = Sum_{k=1..n} k * sigma_2(k).
A356126 (program): a(n) = Sum_{k=1..n} k * sigma_3(k).
A356127 (program): a(n) = Sum_{k=1..n} k^k * binomial(floor(n/k)+1,2).
A356128 (program): a(n) = Sum_{k=1..n} k * sigma_n(k).
A356129 (program): a(n) = Sum_{k=1..n} k * sigma_{n-1}(k).
A356130 (program): a(n) = Sum_{k=1..n} sigma_{n-1}(k).
A356131 (program): a(n) = Sum_{k=1..n} (k - 1)^n * binomial(floor(n/k)+1,2).
A356133 (program): Complement of A026430.
A356138 (program): a(n) = A137803(A001951(n)).
A356139 (program): a(n) = A137804(A001951(n)).
A356140 (program): a(n) = A137803(A001952(n)).
A356141 (program): a(n) = A137804(A001952(n)).
A356162 (program): a(n) = 1 if n and A276086(n) are coprime, otherwise 0, where A276086 is primorial base exp-function.
A356163 (program): a(n) = 1 if sum of prime factors of n (taken with multiplicity) is even, otherwise 0.
A356170 (program): a(n) = 1 if A001222(n) == 2*A007814(n), and otherwise 0, where A001222 is bigomega (number of prime factors with multiplicity) and A007814 is the 2-adic valuation of n.
A356171 (program): Odd numbers that are not divisible by two consecutive prime numbers.
A356172 (program): a(n) = 1 if n is odd and not divisible by two consecutive prime numbers, otherwise 0.
A356173 (program): a(n) = 1 if n is not divisible by two consecutive prime numbers, otherwise 0.
A356174 (program): Replace all prime factors p of n with n/p, then take the integer logarithm (A001414).
A356180 (program): a(n) = A022838(A001951(n)).
A356181 (program): a(n) = A054406(A001951(n)).
A356182 (program): a(n) = A022838(A001952(n)).
A356183 (program): a(n) = A054406(A001952(n)).
A356185 (program): The difference between number of even and number of odd Grassmannian permutations of size n.
A356186 (program): Number of labeled trees on [2n] with a bicentroid.
A356191 (program): a(n) is the smallest exponentially odd number that is divisible by n.
A356193 (program): a(n) is the smallest cubefull number (A036966) that is a multiple of n.
A356194 (program): a(n) is the smallest multiple of n whose prime factorization exponents are all powers of 2.
A356198 (program): Number of edge covers in the n-book graph.
A356200 (program): Number of edge covers in the n-gear graph.
A356205 (program): T(n,k) are the numerators of the coefficients of the Legendre polynomials of degree n, with increasing exponents, where T(n,k) is a triangle read by rows.
A356206 (program): T(n,k) are the denominators of the coefficients of the Legendre polynomials of degree n, with increasing exponents, where T(n,k) is a triangle read by rows.
A356217 (program): a(n) = A022839(A000201(n)).
A356218 (program): a(n) = A108598(A000201(n)).
A356219 (program): Intersection of A001952 and A003151.
A356220 (program): a(n) = A108598(A001950(n)).
A356224 (program): Number of divisors of n whose prime indices cover an initial interval of positive integers.
A356225 (program): Number of divisors of n whose prime indices do not cover an initial interval of positive integers.
A356227 (program): Smallest size of a maximal gapless submultiset of the prime indices of n.
A356228 (program): Greatest size of a gapless submultiset of the prime indices of n.
A356229 (program): Number of maximal gapless submultisets of the prime indices of 2n.
A356237 (program): Heinz numbers of integer partitions with a neighborless singleton.
A356238 (program): a(n) = Sum_{k=1..n} (k * floor(n/k))^n.
A356241 (program): a(n) is the number of distinct Fermat numbers dividing n.
A356242 (program): a(n) is the number of Fermat numbers dividing n, counted with multiplicity.
A356243 (program): a(n) = Sum_{k=1..n} k^2 * sigma_{n-2}(k).
A356244 (program): a(n) = Sum_{k=1..n} (k-1)^n * Sum_{j=1..floor(n/k)} j^2.
A356247 (program): Denominator of the continued fraction 1/(2 - 3/(3 - 4/(4 - 5/(…(n-1) - n/(n - (n+1)))))).
A356248 (program): Image of 1 under repeated application of the map k -> (2k-1,2k,2k-1).
A356249 (program): a(n) = Sum_{k=1..n} (k * floor(n/k))^3.
A356250 (program): Square array T(n,k), n >= 1, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=1..n} (j * floor(n/j))^k.
A356251 (program): a(n) = n*(n+1)*(n+2)*(n+3)*(2*n+1)/12.
A356267 (program): a(n) = Sum_{k=0..n} binomial(2*n, k) * p(k), where p(k) is the partition function A000041.
A356269 (program): a(n) = Sum_{k=0..n} binomial(2*k, k) * p(k), where p(k) is the partition function A000041.
A356274 (program): a(n) is the number whose base-(n+1) expansion equals the binary expansion of n.
A356275 (program): a(n) is the number of tuples (t_1,t_2,m) of integers 2 <= t_1 <= t_2 and 0 < m < n such that (3 + 1/t_1)^m * (3 + 1/t_2)^(n-m) is integer.
A356276 (program): a(n) is the number of integers that can be written as (3 + 1/t_1)^m * (3 + 1/t_2)^(n-m) with integers t_1,t_2 >= 2 and 0 < m < n.
A356280 (program): a(n) = Sum_{k=0..n} binomial(2*n, n-k) * p(k), where p(k) is the partition function A000041.
A356282 (program): a(n) = Sum_{k=0..n} binomial(3*n, n-k) * p(k), where p(k) is the partition function A000041.
A356284 (program): a(n) = Sum_{k=0..n} binomial(3*n, k) * p(k), where p(k) is the partition function A000041.
A356286 (program): a(n) = Sum_{k=0..n} binomial(3*k, k) * p(k), where p(k) is the partition function A000041.
A356288 (program): Sum of numbers in n-th upward diagonal of triangle the sum of {1; 2,3; 4,5,6; 7,8,9,10; …} and {1; 2,3; 3,4,5; 4,5,6,7; …}.
A356289 (program): a(n) = Sum_{k=0..n} binomial(2*n, n-k) * v(k), where v(k) is the number of overpartitions of n (A015128).
A356290 (program): a(n) = Sum_{k=0..n} binomial(3*n, n-k) * v(k), where v(k) is the number of overpartitions of n (A015128).
A356291 (program): Number of reducible permutations.
A356295 (program): Numbers that are not the sum of a nonnegative cube and a prime.
A356296 (program): a(n) = Fibonacci(n)^2 mod n.
A356299 (program): a(n) = gcd(A276086(n), A342001(n)), where A276086 is the primorial base exp-function, and A342001 is the arithmetic derivative without its inherited divisor.
A356310 (program): a(n) = 1 if A003415(n) and A276086(n) are relatively prime, otherwise 0. Here A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
A356311 (program): Numbers k for which A003415(k) and A276086(k) are relatively prime, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
A356312 (program): Numbers k such that A003415(k) and A276086(k) are not relatively prime, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
A356327 (program): Replace 2^k in binary expansion of n with A039834(1+k).
A356334 (program): a(n) is the number of nonnegative integer solutions (x; y) with x <= y of x^(n+1) + y^(n+1) = (x+y)^n.
A356338 (program): a(n) = Sum_{k=1..n} binomial(2*n, n-k) * sigma(k).
A356344 (program): a(n) = Sum_{k=1..n} binomial(2*k, k) * sigma(k).
A356352 (program): a(n) = GCD of run lengths in binary expansion of n.
A356360 (program): Denominator of the continued fraction 1/(2-3/(3-4/(4-5/(…(n-1)-n/(n+1))))).
A356361 (program): a(n) = Sum_{k=0..floor(n/3)} n^k * |Stirling1(n,3*k)|.
A356362 (program): a(n) = Sum_{k=0..floor(n/3)} n^k * Stirling1(n,3*k).
A356373 (program): a(n) = Sum_{k=1..n} binomial(2*k, k) * A000005(k).
A356397 (program): a(n) is the product of the terms in the n-th row of triangle A343835; a(0) = 1.
A356411 (program): Sum of powers of roots of x^3 - x^2 - x - 3.
A356412 (program): First differences of A007770 (happy numbers).
A356413 (program): Numbers with an equal sum of the even and odd exponents in their prime factorizations.
A356417 (program): Numbers whose reversal is a square.
A356422 (program): Heptagonal numbers (or 7-gonal numbers, i.e., numbers of the form k*(5*k - 3)/2) which are products of three distinct primes (or sphenics).
A356424 (program): 9-gonal numbers that are semiprimes.
A356426 (program): Even bisection of A003278.
A356427 (program): a(0) = 0, a(1) = 1; for n > 1, a(n) is the last step before reaching 0 of the iterations x -> x - gpf(x) starting at n, where gpf = A006530.
A356438 (program): Numbers k such that A309892(k) = k/gpf(k), where gpf = A006530.
A356447 (program): Integers k such that (k+1)*(2*k-1) does not divide the central binomial coefficient B(k) = binomial(2*k,k) = A000984(k).
A356449 (program): Numbers k such that 2*k^2 is in A014567.
A356453 (program): Numbers k such that 2*k^2 is not in A014567; complement of A356449.
A356459 (program): a(n) = n! * Sum_{k=1..n} Sum_{d|k} d/(k/d)!.
A356463 (program): Sum of powers of roots of x^3 - 4*x^2 + x + 1.
A356464 (program): Number of black keys in each group of black keys on a standard 88-key piano (left to right).
A356469 (program): a(n) = [(n + 1)/(1 - 1/r)] - [n - n/r] where r = sqrt(2) and [] denotes the floor function.
A356472 (program): Numerator of the average of gcd(i,n) for i = 1..n.
A356473 (program): Denominator of the average of gcd(i,n) for i = 1..n.
A356474 (program): a(n) = phi(rad(prime(n)-1)), where phi = A000010 and rad = A007947.
A356476 (program): Decimal expansion of Loschmidt constant in m^-3 (273.15 K, 100 kPa).
A356480 (program): a(n) is the minimal number of river crossings necessary to solve the missionaries and cannibals problem for n missionaries and n cannibals where the boat capacity is the minimum necessary to allow a solution.
A356486 (program): a(n) = (n-1)! * Sum_{d|n} d^n / (d-1)!.
A356489 (program): a(n) = A000265(rad(prime(n)-1)), rad = A007947.
A356515 (program): For any n >= 0, let x_n(1) = n, and for any b > 1, x_n(b) is the sum of digits of x_n(b-1) in base b; x_n is eventually constant, with value a(n).
A356517 (program): Square array A(n, k), n >= 2, k >= 0, read by antidiagonals upwards; A(n, k) is the least integer with sum of digits k in base n.
A356520 (program): Numbers k such that A000005(A007953(k)) = A007953(k).
A356525 (program): Decimal expansion of number of Pascals (Pa) in 1 millimeter of mercury (mmHg).
A356529 (program): a(n) = (n-1)! * Sum_{d|n} d^(n-d+1).
A356530 (program): Expansion of e.g.f. Product_{k>0} 1/(1 - (k * x)^k)^(1/k^k).
A356533 (program): a(n) = sigma_2(n)^2.
A356534 (program): a(n) = sigma_3(n)^2.
A356535 (program): a(n) = Sum_{k=1..n} sigma_2(k)^2.
A356536 (program): a(n) = Sum_{k=1..n} sigma_3(k)^2.
A356538 (program): Expansion of e.g.f. Product_{k>0} 1/(1 - (2 * x)^k)^(1/2^k).
A356539 (program): a(n) = Sum_{d|n} d * 3^(n-d).
A356540 (program): Expansion of e.g.f. Product_{k>0} 1/(1 - (3 * x)^k)^(1/3^k).
A356546 (program): Triangle read by rows. T(n, k) = RisingFactorial(n + 1, n) / (k! * (n - k)!).
A356549 (program): a(n) is the number of divisors of 10^n whose first digit is 1.
A356556 (program): Parity of A061418.
A356560 (program): Expansion of e.g.f. Product_{k>0} 1/(1 - k^2 * x^k)^(1/k^2).
A356561 (program): Expansion of e.g.f. Product_{k>0} 1/(1 - k^3 * x^k)^(1/k^3).
A356563 (program): Sums of powers of roots of x^3 - 2*x^2 - x - 2.
A356569 (program): Sums of powers of roots of x^4 - 2*x^3 - 6*x^2 + 2*x + 1.
A356582 (program): T(n,k) is the number of degree n polynomials in GF_2[x] that have exactly k linear factors in their prime factorization when the factors are counted with multiplicity, n >= 0, 0 <= k <= n. Triangular array read by rows.
A356593 (program): Smallest k such that primorial(k) > n^2.
A356603 (program): Position in A356226 of first appearance of the n-th composition in standard order (row n of A066099).
A356619 (program): a(n) = number of k-tuples (u(1), u(2), …, u(k)) with 1 <= u(1) < u(2) < … < u(k) <= n such that u(i) - u(i-1) <= 3 for i = 2,…,k.
A356620 (program): a(n) = number of k-tuples (u(1), u(2), …, u(k)) with 1 <= u(1) < u(2) < … < u(k) <= n such that u(i) - u(i-1) <= 4 for i = 2,…,k.
A356621 (program): a(n) = number of k-tuples (u(1), u(2), …, u(k)) with 1 <= u(1) < u(2) < … < u(k) <= n such that u(i) - u(i-1) <= 5 for i = 2,…,k.
A356622 (program): Number of ways to tile a hexagonal strip made up of 4*n equilateral triangles, using triangles and diamonds.
A356623 (program): Number of ways to tile a hexagonal strip made up of 4*n+2 equilateral triangles, using triangles and diamonds.
A356628 (program): a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^k/(n - 2*k)!.
A356636 (program): Triangle read by rows. T(n, k) = binomial(n, k) * n!^2 / floor(n/2)!^2.
A356637 (program): a(n) = A000265(A263931(n)).
A356644 (program): Number of vertex cuts in the n-antiprism graph.
A356647 (program): Concatenation of runs {y..x} for each x>=1, using each y from 1 to x before moving on to the next value for x.
A356651 (program): Triangle read by rows. T(n, k) = x^k.
A356655 (program): Clausen numbers based on the strictly proper divisors of n, 1 < d < n.
A356672 (program): a(n) = n! * Sum_{k=0..n} k^(2*(n-k))/k!.
A356673 (program): a(n) = n! * Sum_{k=0..n} k^(3*(n-k))/k!.
A356674 (program): a(n) = n! * Sum_{k=0..n} k^(k*(n-k))/k!.
A356684 (program): a(n) = (n-1)*a(n-1) - n*a(n-2), with a(1) = a(2) = -1.
A356687 (program): a(n) = n! * Sum_{k=0..n} k^(2*n)/k!.
A356688 (program): a(n) = n! * Sum_{k=0..n} k^(3*n)/k!.
A356691 (program): a(n) = n! * Sum_{k=0..n} k^(2*k)/k!.
A356696 (program): a(n) = Fibonacci(2n-1) - 2^n + binomial(n,2) + 2.
A356716 (program): a(n) is the integer w such that (c(n)^2, -d(n)^2, -w) is a primitive solution to the Diophantine equation 2*x^3 + 2*y^3 + z^3 = 11^3, where c(n) = F(n+2) + (-1)^n * F(n-3), d(n) = F(n+1) + (-1)^n * F(n-4) and F(n) is the n-th Fibonacci number (A000045).
A356717 (program): a(n) is the integer w such that (c(n)^2, -d(n)^2, w) is a primitive solution to the Diophantine equation 2*x^3 + 2*y^3 + z^3 = 11^3, where c(n) = F(n+2) + (-1)^n * F(n-3), d(n) = F(n+3) + (-1)^n * F(n-2) and F(n) is the n-th Fibonacci number (A000045).
A356718 (program): T(n,k) is the total number of prime factors, counted with multiplicity, of k!*(n-k)!, for 0 <= k <= n. Triangle read by rows.
A356719 (program): a(n) = Sum_{k=0..n} k^binomial(n,k).
A356727 (program): Primes of the form 4*k^2 + 84*k + 43.
A356733 (program): Number of neighborless parts in the integer partition with Heinz number n.
A356734 (program): Heinz numbers of integer partitions with at least one neighborless part.
A356735 (program): Number of distinct parts that have neighbors in the integer partition with Heinz number n.
A356749 (program): a(n) is the number of trailing 1’s in the dual Zeckendorf representation of n (A104326).
A356754 (program): Triangle read by rows: T(n,k) = ((n-1)*(n+2))/2 + 2*k.
A356757 (program): Omit zero digits from factorial numbers.
A356758 (program): a(n) is the number of nonzero digits in n!.
A356760 (program): a(n) = L(2*F(n)) + L(2*F(n+1)), where L(n) is the n-th Lucas number (A000032), and F(n) is the n-th Fibonacci number (A000045).
A356761 (program): a(n) = L(2*L(n)) + L(2*L(n+1)), where L(n) is the n-th Lucas number (A000032).
A356764 (program): Semiprimes divisible by their indices in the sequence of semiprimes, divided by those indices.
A356768 (program): a(n) = (n^2+n+1)*(n^2+n)*n^2.
A356770 (program): a(n) is the number of equations in the set {x+2y=n, 2x+3y=n, …, k*x+(k+1)*y=n, …, n*x+(n+1)*y=n} which admit at least one nonnegative integer solution.
A356777 (program): G.f.: Sum_{n=-oo..+oo} x^(n^2) * C(x)^(2*n-1), where C(x) = 1 + x*C(x)^2 is a g.f. of the Catalan numbers (A000108).
A356785 (program): E.g.f. satisfies log(A(x)) = x * (exp(x*A(x)) - 1) * A(x).
A356800 (program): Numbers m for which Sum_{k=1..m} 1/k^s has no zero in the half-plane Re(s)>1.
A356806 (program): a(n) = Sum_{k=0..n} (k*n-1)^(n-k) * binomial(n,k).
A356807 (program): Tetranacci sequence beginning with 3, 7, 12, 24.
A356811 (program): a(n) = Sum_{k=0..n} (k*n+1)^(n-k) * binomial(n,k).
A356812 (program): Expansion of e.g.f. exp(x * (1 - exp(2*x))).
A356813 (program): Expansion of e.g.f. exp(x * (1 - exp(3*x))).
A356814 (program): a(n) = Sum_{k=0..n} (-1)^k * (k*n+1)^(n-k) * binomial(n,k).
A356815 (program): Expansion of e.g.f. exp(-x * (exp(2*x) + 1)).
A356816 (program): Expansion of e.g.f. exp(-x * (exp(3*x) + 1)).
A356817 (program): a(n) = Sum_{k=0..n} (-1)^k * (k*n-1)^(n-k) * binomial(n,k).
A356818 (program): Expansion of e.g.f. exp(-x * (exp(x) + 1)).
A356819 (program): Expansion of e.g.f. exp(-x * exp(2*x)).
A356820 (program): Expansion of e.g.f. exp(-x * exp(3*x)).
A356823 (program): Tribternary numbers.
A356827 (program): Expansion of e.g.f. exp(x * exp(3*x)).
A356829 (program): Number of vertex cuts in the n-Möbius ladder.
A356830 (program): Number of vertex cuts in the n-prism graph.
A356834 (program): a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^n/(n - 2*k)!.
A356836 (program): Coordination sequence of the {5,3,4} hyperbolic honeycomb.
A356838 (program): The smallest of the most common prime factors of n.
A356840 (program): Largest most common prime factor of n.
A356844 (program): Numbers k such that the k-th composition in standard order contains at least one 1. Numbers that are odd or whose binary expansion contains at least two adjacent 1’s.
A356849 (program): a(n) = a(n-1) - a(n-2) + 3*a(n-3) with a(0) = 1, a(1) = 2 and a(2) = 4.
A356852 (program): Minimum over all order two bases for the interval [1, n] of the maximum number of ways some number in the interval [1, n] can be written as a sum of at most two elements of the basis.
A356858 (program): a(n) is the product of the first n numbers not divisible by 5.
A356859 (program): a(n) is the number of zero digits in the product of the first n numbers not divisible by 5.
A356860 (program): a(n) is the number of digits in the product of the first n numbers not divisible by 5.
A356861 (program): a(n) is the number of nonzero digits in the product of the first n numbers not divisible by 5.
A356862 (program): Numbers with a unique largest prime exponent.
A356868 (program): a(n) = n^2 * prime(n).
A356869 (program): Decimal expansion of 4 / sqrt(5).
A356874 (program): Write n as Sum_{i in S} 2^(i-1), where S is a set of positive integers, then a(n) = Sum_{i in S} F_i, where F_i is the i-th Fibonacci number, A000045(i).
A356875 (program): Square array, n >= 0, k >= 0, read by descending antidiagonals. A(n,k) = A022341(n)*2^k.
A356876 (program): Binary weight of the composite numbers (A002808).
A356880 (program): Squares that can be expressed as the sum of two powers of two (2^x + 2^y).
A356888 (program): a(n) = ((n-1)^2 + 2)*2^(n-2).
A356889 (program): a(n) = (n^2 + 3*n + 10/3)*4^(n-3) - 1/3.
A356891 (program): a(n) = a(n-1) * a(n-2) + 1 if n is even, otherwise a(n) = a(n-3) + 1, with a(0) = a(1) = 1.
A356894 (program): a(n) is the number of 0’s in the maximal tribonacci representation of n (A352103).
A356895 (program): a(n) is the length of the maximal tribonacci representation of n (A352103).
A356896 (program): Nonnegative numbers whose maximal tribonacci representation (A352103) ends in an even number of 1’s.
A356897 (program): Nonnegative numbers whose maximal tribonacci representation (A352103) ends in an odd number of 1’s.
A356898 (program): a(n) is the number of trailing 1’s in the maximal tribonacci representation of n (A352103).
A356900 (program): a(n) = P(n, 1/2) where P(n, x) = x^(-n)*Sum_{k=0..n} A241171(n, k)*x^k.
A356901 (program): a(n) = (2*n)! * [x^(2*n)] arctan(x / sqrt(2))^2.
A356907 (program): Expansion of 1 / (1 + Sum_{k>=1} lambda(k)*x^k), where lambda() is the Liouville function (A008836).
A356929 (program): Integers with an even number of even digits.
A356935 (program): Numbers whose prime indices all have odd bigomega (number of prime factors with multiplicity). Products of primes indexed by elements of A026424. MM-numbers of finite multisets of finite odd-length multisets of positive integers.
A356936 (program): Number of multiset partitions of the multiset of prime indices of n into intervals. Number of factorizations of n into members of A073485.
A356982 (program): Fixed point of the morphism 0->010, 1->000.
A356988 (program): a(n) = n - a^2 with a(1) = 1, where a^2 = a(a(n)) and a^3 = a(a(a(n))).
A356989 (program): a(n) = n - a^3 with a(1) = 1, where a^3 = a(a(a(n))) and a^4 = a(a(a(a(n)))).
A356990 (program): a(n) = n - a^4 with a(1) = 1, where a^4 = a(a(a(a(n)))) and a^5 = a(a(a(a(a(n))))).
A356999 (program): a(n) = 2*A356988(n) - n.
A357012 (program): Triangle read by rows. T(n, k) = x^k.
A357013 (program): Triangle read by rows. T(n, k) = ((2*n)! * k!) / (n + k)!.
A357014 (program): Numbers whose sum of exponential divisors (A051377) is odd.
A357030 (program): a(n) is the number of integers in 0..n having nonincreasing digits.
A357042 (program): The sum of the numbers of the central diamond of the multiplication table [1..k] X [1..k] for k=2*n-1.
A357056 (program): Integers k such that k^k + k^2 + 2*k + 1 is prime.
A357057 (program): a(n) = A356886(2^n+1)/A356886(2^n-1).
A357070 (program): Number of partitions of n into at most 2 distinct positive triangular numbers.
A357073 (program): For n >= 1, a(n) = A003714(n) mod n.
A357074 (program): Numbers sandwiched between a pair of numbers each with exactly two prime factors (counted without multiplicity).
A357075 (program): Numbers sandwiched between numbers with exactly three distinct prime factors.
A357081 (program): Leader at step n of the THROWBACK procedure (see definition in comments).
A357100 (program): Decimal expansion of the real root of x^3 + x^2 - 3.
A357101 (program): Decimal expansion of the real root of x^3 - 2*x^2 - 2.
A357102 (program): Decimal expansion of the real root of x^3 + 2*x - 2.
A357103 (program): Decimal expansion of the real root of x^3 - 3*x - 3.
A357104 (program): Decimal expansion of the real root of x^3 + 3*x - 1.
A357105 (program): Decimal expansion of the real root of 2*x^3 - x^2 - 2.
A357106 (program): Decimal expansion of the real root of 2*x^3 + x^2 - 2.
A357107 (program): Decimal expansion of the real root of 2*x^3 - x - 2.
A357108 (program): Decimal expansion of the real root of 2*x^3 + x - 2.
A357109 (program): Decimal expansion of the real root of 2*x^3 - 2*x^2 - 1.
A357111 (program): For n >= 1, a(n) = n / A076775(n).
A357112 (program): a(n) = A035019(n)/6 for n > 0.
A357127 (program): a(n) = A081257(n) if A081257(n) > n, otherwise a(n) = 1.
A357130 (program): a(n) = 2*n - (-1)^n*(1+(n mod 2)).
A357136 (program): Triangle read by rows where T(n,k) is the number of integer compositions of n with alternating sum k = 0..n. Part of the full triangle A097805.
A357137 (program): Maximal run-length of the n-th composition in standard order; a(0) = 0.
A357146 (program): a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^(2*k)/(n - 2*k)!.
A357171 (program): a(n) is the number of divisors of n whose digits are in strictly increasing order (A009993).
A357178 (program): First differences of cubes of triangular numbers.
A357180 (program): First run-length of the n-th composition in standard order.
A357181 (program): Last run-length of the n-th composition in standard order.
A357186 (program): Take the k-th composition in standard order for each part k of the n-th composition in standard order, then add up everything.
A357187 (program): First differences A357186 = “Take the k-th composition in standard order for each part k of the n-th composition in standard order, then add up everything.”
A357195 (program): a(n) is the smallest palindrome of the form k*(2*n+k-1)/2 where k is a positive integer.
A357210 (program): a(n) = Sum_{k=1..n} prime(k/gcd(n,k)).
A357213 (program): Triangular array read by rows: T(n, k) = number of subsets s of {1, 2, …, n} such max(s) - min(s) = k, for n >= 1, 0 <= k <= n-1.
A357214 (program): a(n) = number of subsets S of {1, 2,…, n} such that every number in S is a composite.
A357215 (program): a(n) = number of nonempty subsets S of {1, 2, …, n} that contain only primes.
A357218 (program): Primes p such that T(p) - 2 is prime, where T(p) is the triangular number (A000217) with index p.
A357219 (program): Primes of the form T(p) - 2 where T(p) is the triangular number (A000217) with prime index p in A357218.
A357238 (program): Inverse Moebius transform of tribonacci numbers (A000073).
A357239 (program): Inverse Moebius transform of tetranacci number (A000078).
A357242 (program): Number of n node tournaments that have exactly two circular triads.
A357251 (program): a(n) = Sum_{1<=i<=j<=n} prime(i)*prime(j)
A357253 (program): a(n) is the largest prime < 6*n.
A357255 (program): Triangular array: row n gives the recurrence coefficients for the sequence (c(k) = number of subsets of {1,2,…,n} that have at least k-1 elements) for k >= 1.
A357259 (program): a(n) is the number of 2 X 2 Euclid-reduced matrices having determinant n.
A357270 (program): a(n) = s(n) mod prime(n+1), where s = A143293.
A357277 (program): Largest side c of primitive triples, in nondecreasing order, for integer-sided triangles with angles A < B < C = 2*Pi/3 = 120 degrees.
A357281 (program): The numbers of a square spiral with 1 in the center, lying at integer points of the right branch of the parabola y=n^2.
A357282 (program): a(n) = number of subsets S of {1,2,…,n} having more than 1 element such that (difference between least two elements of S) = difference between greatest two elements of S.
A357283 (program): a(n) = number of subsets S of {1,2,…,n} having more than 1 element such that (sum of least two elements of S) < max(S).
A357284 (program): a(n) = (1/2)*A357283(n).
A357290 (program): a(n) = number of subsets S of {1,2,…,n} having more than 2 elements such that (sum of least two elements of S) > difference between greatest two elements of S.
A357291 (program): a(n) = number of subsets S of {1,2,…,n} having more than 2 elements such that (sum of least two elements of S) < difference between greatest two elements of S.
A357292 (program): a(n) = number of subsets S of {1,2,…,n} having more than 2 elements such that (sum of least two elements of S) = difference between greatest two elements of S.
A357308 (program): a(0) = a(1) = 0, a(2) = 1; a(n) = a(n-1) + Sum_{k=0..n-3} a(k) * a(n-k-3).
A357367 (program): Triangle read by rows. T(n, k) = Sum_{m=0..k} ((-1)^(m + k) * binomial(n + k, n + m) * L(n + m, m), where L denotes the unsigned Lah numbers A271703.
A357372 (program): Square array A(n, k), n, k > 0, read by antidiagonals; A(n, k) is the numerator of 1/n + 1/k.
A357380 (program): Expansion of Product_{k>=1} (1 - x^Fibonacci(k)).
A357392 (program): E.g.f. satisfies A(x) = -log(1 - x * exp(2 * A(x))).
A357393 (program): E.g.f. satisfies A(x) = -log(1 - x * exp(3 * A(x))).
A357394 (program): E.g.f. satisfies A(x) = exp(x * exp(2 * A(x))) - 1.
A357395 (program): E.g.f. satisfies A(x) = exp(x * exp(3 * A(x))) - 1.
A357407 (program): Coefficients a(n) of x^n, n >= 0, in A(x) = exp( Sum_{n>=1} A183204(n)*x^n/n ), where A183204 equals the central terms of triangle A181544.
A357408 (program): a(n) is the least sum n + y such that 1/n + 1/y = 1/z with gcd(n,y,z) = 1, for some integers y and z.
A357417 (program): Row sums of the triangular array A357431.
A357440 (program): Possible half-lengths of self-similar sequences over a finite alphabet that are invariant under retrograde inversion.
A357448 (program): Fixed point starting with 0 of the two-block substitution 00->010, 01->010, 10->101, 11->101.
A357454 (program): Number of partitions of n into pentanacci numbers 1,2,4,8,16,31, … (A001591).
A357455 (program): Number of compositions (ordered partitions) of n into pentanacci numbers 1,2,4,8,16,31, … (A001591).
A357456 (program): Number of partitions of n into two or more odd parts.
A357458 (program): First differences of A325033 = “Sum of sums of the multiset of prime indices of each prime index of n.”
A357463 (program): Decimal expansion of the real root of 2*x^3 + 2*x - 1.
A357464 (program): Decimal expansion of the real root of 3*x^3 + x^2 - 1.
A357465 (program): Decimal expansion of the real root of 3*x^3 - x^2 - 1.
A357466 (program): Decimal expansion of the real root of 3*x^3 - x - 1.
A357467 (program): Decimal expansion of the real root of 3*x^3 + x - 1.
A357468 (program): Decimal expansion of the real root of x^3 + x^2 + x - 2.
A357469 (program): Decimal expansion of the real root of x^3 - x^2 + x - 2.
A357470 (program): Decimal expansion of the real root of x^3 - x^2 - 2*x - 1.
A357471 (program): Decimal expansion of the real root of x^3 - x^2 + 2*x - 1.
A357472 (program): Decimal expansion of the real root of x^3 + x^2 + 2*x - 1.
A357476 (program): Number of partitions of n into two or more powers of 2.
A357479 (program): a(n) = (n!/6) * Sum_{k=0..n-3} 1/k!.
A357480 (program): a(n) = (n!/24) * Sum_{k=0..n-4} 1/k!.
A357483 (program): Decimal expansion of sum of squares of reciprocals of primes whose distance to the next prime is equal to 6, Sum_{j>=1} 1/A031924(j)^2.
A357484 (program): Number of linearity regions of a max-pooling function with a 3 by n input and 2 by 2 pooling windows.
A357502 (program): a(n) = ((1 + sqrt(n))^n - (1 - sqrt(n))^n)/(2*sqrt(n)).
A357504 (program): Numbers that are the sum of two distinct triangular numbers.
A357505 (program): Numbers that are not sum of two distinct triangular numbers.
A357508 (program): a(n) = binomial(4*n,2*n) - 2*binomial(4*n,n).
A357509 (program): a(n) = 2*binomial(3*n,n) - 9*binomial(2*n,n).
A357510 (program): a(n) = Sum_{k = 0..n} k * binomial(n,k)^2 * binomial(n+k,k)^2.
A357512 (program): a(n) = Sum_{k = 0..n} k^5 * binomial(n,k)^2 * binomial(n+k,k)^2
A357518 (program): Unique fixed point of the two-block substitution 00->111, 01->110, 10->101, 11->100.
A357519 (program): Number of compositions (ordered partitions) of n into Jacobsthal numbers 1,3,5,11,21,43, … (A001045).
A357529 (program): Triangular numbers k such that 2*k cannot be expressed as a sum of two distinct triangular numbers.
A357531 (program): Final value obtained by traveling clockwise around a circular array with positions numbered clockwise from 1 to n. Each move consists of traveling clockwise k places, where k is the position at the beginning of the move. The first move begins at position 1. a(n) is the position at the end of the n-th move.
A357532 (program): a(n) = Sum_{k=0..floor(n/3)} (n-2*k)!/(n-3*k)!.
A357533 (program): a(n) = Sum_{k=0..floor(n/4)} (n-3*k)!/(n-4*k)!.
A357534 (program): Number of compositions (ordered partitions) of n into two or more powers of 2.
A357543 (program): a(n) = (3*n+1)!/(3^n*n!) * Product_{k=1..n} (3*k - 2), for n >= 0.
A357552 (program): a(n) = sigma(n) * binomial(2*n-1,n), for n >= 1.
A357553 (program): a(n) = A000045(n)*A000045(n+1) mod A000032(n).
A357555 (program): a(n) is the numerator of Sum_{d|n} (-1)^(d+1) / d^2.
A357556 (program): a(n) is the denominator of Sum_{d|n} (-1)^(d+1) / d^2.
A357558 (program): a(n) = Sum_{k = 0..n} (-1)^(n+k)*k*binomial(n,k)*binomial(n+k,k)^2.
A357559 (program): a(n) = Sum_{k = 0..n} (-1)^(n+k)*k^3*binomial(n,k)*binomial(n+k,k)^2.
A357562 (program): a(n) = n - 2*b(b(n)) for n >= 2, where b(n) = A356988(n).
A357564 (program): a(n) = n - 2*b(b(n)) for n >= 2, where b(n) = A006165(n).
A357569 (program): a(n) = binomial(3*n,n)^2 - 27*binomial(2*n,n).
A357570 (program): a(n) = Sum_{k=0..floor(n/5)} (n-4*k)!/(n-5*k)!.
A357572 (program): Expansion of e.g.f. sinh(sqrt(3) * (exp(x)-1)) / sqrt(3).
A357574 (program): a(n) is the number of pairs that add to a power of 2 in a set of n consecutive positive or negative odd numbers including A357409(n) positive numbers.
A357580 (program): a(n) = ((1 + sqrt(n))^n - (1 - sqrt(n))^n)/(2*n*sqrt(n)).
A357587 (program): If k > 1 and k divides DedekindPsi(k) then A358015(k)/2 is a term of this sequence.
A357589 (program): a(n) = n - A130312(n).
A357593 (program): Number of faces of the Minkowski sum of n simplices with vertices e_(i+1), e_(i+2), e_(i+3) for i=0,…,n-1, where e_i is a standard basis vector.
A357598 (program): Expansion of e.g.f. sinh(2 * (exp(x)-1)) / 2.
A357599 (program): Expansion of e.g.f. sinh(2 * log(1+x)) / 2.
A357604 (program): Number of prime powers in the sequence of the floor of n/k for k <= n, A010766.
A357613 (program): Triangle read by rows T(n, k) = binomial(2 * n, k) * binomial(3 * n - k, 2 * n)
A357615 (program): Expansion of e.g.f. cosh(sqrt(3) * (exp(x) - 1)).
A357617 (program): Expansion of e.g.f. sinh( (exp(4*x) - 1)/4 ).
A357618 (program): a(n) = sum of lengths of partitions of more than one consecutive positive integer adding up to n.
A357621 (program): Half-alternating sum of the n-th composition in standard order.
A357622 (program): Half-alternating sum of the reversed n-th composition in standard order.
A357623 (program): Skew-alternating sum of the n-th composition in standard order.
A357624 (program): Skew-alternating sum of the reversed n-th composition in standard order.
A357625 (program): Numbers k such that the k-th composition in standard order has half-alternating sum 0.
A357626 (program): Numbers k such that the reversed k-th composition in standard order has half-alternating sum 0.
A357627 (program): Numbers k such that the k-th composition in standard order has skew-alternating sum 0.
A357628 (program): Numbers k such that the reversed k-th composition in standard order has skew-alternating sum 0.
A357642 (program): Number of even-length integer compositions of 2n whose half-alternating sum is 0.
A357650 (program): Expansion of e.g.f. cosh( (exp(4*x) - 1)/4 ).
A357654 (program): Number of lattice paths from (0,0) to (i,n-2*i) that do not go above the diagonal x=y using steps in {(1,0), (0,1)}.
A357655 (program): Total number of nodes summed over all lattice paths from (0,0) to (i,n-2*i) that do not go above the diagonal x=y using steps in {(1,0), (0,1)}.
A357661 (program): Expansion of e.g.f. cosh( (exp(2*x) - 1)/sqrt(2) ).
A357663 (program): Expansion of e.g.f. cosh( (exp(4*x) - 1)/2 ).
A357664 (program): Expansion of e.g.f. sinh( (exp(2*x) - 1)/sqrt(2) )/sqrt(2).
A357666 (program): Expansion of e.g.f. sinh( (exp(4*x) - 1)/2 )/2.
A357667 (program): Expansion of e.g.f. cosh( 3 * (exp(x) - 1) ).
A357668 (program): Expansion of e.g.f. sinh( 3 * (exp(x) - 1) )/3.
A357669 (program): a(n) is the number of divisors of the powerful part of n.
A357671 (program): a(n) = Sum_{k = 0..n} ( binomial(n+k-1,k) + binomial(n+k-1,k)^2 ).
A357672 (program): a(n) = Sum_{k = 0..n} binomial(n+k-1,k) * Sum_{k = 0..n} binomial(n+k-1,k)^2.
A357679 (program): a(n) = prime(n)*(prime(n-1) + prime(n+1)).
A357683 (program): a(n) = Sum_{k=0..floor(n/2)} n^k * |Stirling1(n,2*k)|.
A357684 (program): The squarefree part (A007913) of numbers whose squarefree part is a unitary divisor (A335275).
A357686 (program): Nonsquarefree numbers k such that A293228(k) > k.
A357689 (program): a(n) = n/A204455(n), where A204455(n) is the product of odd noncomposite divisors of n.
A357693 (program): Expansion of e.g.f. cos( sqrt(2) * log(1+x) ).
A357698 (program): a(n) is the sum of the aliquot divisors of n that are cubefree.
A357703 (program): Expansion of e.g.f. cosh( sqrt(3) * log(1-x) ).
A357711 (program): Expansion of e.g.f. cosh( 2 * log(1-x) ).
A357715 (program): Decimal expansion of sqrt(16 + 32 / sqrt(5)).
A357718 (program): Expansion of e.g.f. cos( sqrt(3) * log(1+x) ).
A357719 (program): Expansion of e.g.f. cos( 2 * log(1+x) ).
A357721 (program): a(n) = Sum_{k=0..floor(n/2)} (-n)^k * Stirling1(n,2*k).
A357725 (program): Expansion of e.g.f. cos( sqrt(2) * (exp(x) - 1) ).
A357726 (program): Expansion of e.g.f. cos( sqrt(3) * (exp(x) - 1) ).
A357727 (program): Expansion of e.g.f. cos( 2 * (exp(x) - 1) ).
A357731 (program): Number of partitions of n into 2 distinct positive Fibonacci numbers (with a single type of 1).
A357736 (program): Expansion of e.g.f. sin( sqrt(2) * (exp(x) - 1) )/sqrt(2).
A357737 (program): Expansion of e.g.f. sin( sqrt(3) * (exp(x) - 1) )/sqrt(3).
A357738 (program): Expansion of e.g.f. sin( 2 * (exp(x) - 1) )/2.
A357753 (program): a(n) is the least square with n binary digits.
A357754 (program): a(n) is the largest square with n binary digits.
A357761 (program): a(n) = A227872(n) - A356018(n).
A357770 (program): Number of 2n-step closed paths on quasi-regular rhombic (rhombille) lattice starting from a degree-3 node.
A357771 (program): Number of 2n-step closed paths on quasi-regular rhombic (rhombille) lattice starting from a degree-6 node.
A357773 (program): Odd numbers with two zeros in their binary expansion.
A357774 (program): Binary expansions of odd numbers with two zeros in their binary expansion.
A357775 (program): Numbers k with the property that the symmetric representation of sigma(k) has seven parts.
A357778 (program): Maximum number of edges in a 5-degenerate graph with n vertices.
A357779 (program): Maximum number of edges in a 6-degenerate graph with n vertices.
A357812 (program): Number of subsets of [n] in which exactly half of the elements are powers of 2.
A357817 (program): Partial alternating sums of the Dedekind psi function (A001615): a(n) = Sum_{k=1..n} (-1)^(k+1) * psi(k).
A357825 (program): Total number of n-tuples of semi-Dyck paths from (0,0) to (n,n-2*j) for j=0..floor(n/2).
A357828 (program): a(n) = Sum_{k=0..floor(n/3)} |Stirling1(n,3*k)|.
A357829 (program): a(n) = Sum_{k=0..floor((n-1)/3)} |Stirling1(n,3*k+1)|.
A357830 (program): a(n) = Sum_{k=0..floor((n-2)/3)} |Stirling1(n,3*k+2)|.
A357831 (program): a(n) = Sum_{k=0..floor(n/3)} 2^k * |Stirling1(n,3*k)|.
A357832 (program): a(n) = Sum_{k=0..floor((n-1)/3)} 2^k * |Stirling1(n,3*k+1)|.
A357833 (program): a(n) = Sum_{k=0..floor((n-2)/3)} 2^k * |Stirling1(n,3*k+2)|.
A357834 (program): a(n) = Sum_{k=0..floor(n/3)} Stirling1(n,3*k).
A357835 (program): a(n) = Sum_{k=0..floor((n-1)/3)} Stirling1(n,3*k+1).
A357836 (program): a(n) = Sum_{k=0..floor((n-2)/3)} Stirling1(n,3*k+2).
A357837 (program): a(n) is the sum of the lengths of all the segments used to draw a square of side n representing a fishbone pattern using symmetric L-shaped tiles with side length 2.
A357847 (program): Number of integer compositions of n whose length is twice their alternating sum.
A357852 (program): Replace prime(k) with prime(k+2) in the prime factorization of n.
A357866 (program): a(n) is the greatest remainder of n divided by its sum of digits in any base > 1.
A357892 (program): T(n,k) are the values of a variant of the Chebyshev polynomials P(n,x) of order n evaluated at x = k, where T(n,k), n >= 0, k <= n is a triangle read by rows. P(0,x) = 1, P(1,x) = x, P(n,x) = x*P(n-1,x) - P(n-2,x).
A357905 (program): a(n) = log_3(A060839(n)).
A357906 (program): a(n) = log_2(A073103(n)).
A357928 (program): a(n) is the smallest c for which (s+c)^2-n is a square, where s = floor(sqrt(n)), or -1 if no such c exists.
A357938 (program): Inverse Moebius transform of n * 2^omega(n).
A357948 (program): Expansion of e.g.f. exp( x * exp(-x^2) ).
A357949 (program): a(n) = Sum_{k=0..floor(n/4)} (n-3*k)!/k!.
A357966 (program): Expansion of e.g.f. exp( x * (exp(x^2) - 1) ).
A357984 (program): Replace prime(k) with A000720(k) in the prime factorization of n.
A358012 (program): Minimal number of coins needed to pay n cents using coins of denominations 1 and 5 cents.
A358013 (program): Expansion of e.g.f. 1/(1 - x^2 * (exp(x) - 1)).
A358016 (program): a(n) is the largest k <= n-2 such that k^2 == 1 (mod n).
A358027 (program): Expansion of g.f.: (1 + x - 2*x^2 + 2*x^4)/((1-x)*(1-3*x^2)).
A358035 (program): a(n) = (8*n^3 + 12*n^2 + 4*n - 9)/3.
A358039 (program): a(n) is the Euler totient function phi applied to the n-th cubefree number.
A358040 (program): a(n) is the number of divisors of the n-th cubefree number.
A358042 (program): Partial sums of A071619.
A358043 (program): Numbers k such that phi(k) is a multiple of 8.
A358061 (program): a(n) = phi(n) mod tau(n).
A358064 (program): Expansion of e.g.f. 1/(1 - x * exp(x^2)).
A358065 (program): Expansion of e.g.f. 1/(1 - x * exp(x^3)).
A358072 (program): a(n) is the number of “merger histories” of n elements (see A256006) where at most 3 elements can merge at the same time.
A358080 (program): Expansion of e.g.f. 1/(1 - x^2 * exp(x)).
A358088 (program): Number of pairs (s,t) with s and t squarefree, 1 <= s < t <= n and s | t.
A358089 (program): First differences of A126706.
A358092 (program): Row sums of the convolution triangle of the Motzkin numbers (A202710).
A358093 (program): a(n) = n for 1 <= n <= 2; thereafter a(n) is the least unused m such that rad(m) = rad(rad(a(n-1)) + rad(a(n-2))), where rad(m) = A007947(m).
A358106 (program): Quotient of the n-th divisible pair, where pairs are ordered first by sum and then by denominator.
A358108 (program): a(n) = 16^n * Sum_{k=0..n} binomial(-1/2, k)^2 * binomial(n, k).
A358114 (program): a(n) = [x^n] (16*x*(32*x - 3) + 1)^(-1/2).
A358115 (program): a(n) = 64^n * hypergeometric([1/2, 1/2, 1/2, -n], [1, 1, 1], 1).
A358116 (program): a(n) = 64^n * hypergeometric([1/2, 1/2, 1/2, -n], [1, 1, 1], -1).
A358131 (program): Triangle T(n,k) read by rows, where each row lists the value of n coins, in cents, using k dimes (10 cents) and n-k quarters (25 cents).
A358135 (program): Difference of first and last parts of the n-th composition in standard order.
A358137 (program): Heinz number of the partial sums of the prime indices of n.
A358145 (program): a(n) = Sum_{k=0..n} binomial(n*k,k) * binomial(n*(n-k),n-k).
A358146 (program): Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} binomial(k*j,j).
A358181 (program): Decimal expansion of the real root of x^3 - 2*x^2 - x - 1.
A358182 (program): Decimal expansion of the real root of 2*x^3 - x^2 - x - 1.
A358183 (program): Decimal expansion of the real root of 2*x^3 + x^2 - x - 1.
A358184 (program): Decimal expansion of the real root of 2*x^3 - x^2 + x - 1.
A358185 (program): Coefficients of x^n/n! in the expansion of (1 - x)*log(1 - x).
A358206 (program): Number of ways of making change for n cents using coins of 1, 2, 4, 10 and 20 cents.
A358215 (program): Numbers k for which there are no such prime p that p^p would divide the arithmetic derivative of k, A003415(k).
A358217 (program): Number of prime factors (with multiplicity) in A319627(n).
A358218 (program): Number of prime factors (with multiplicity) in A328478(n).
A358220 (program): a(n) = 1 if A276086(n) is a multiple of A003415(n), with a(0) = a(1) = 0. Here A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
A358221 (program): Numbers k such that A003415(k) divides A276086(k), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
A358224 (program): Parity of A328386(n), where A328386(n) = A276086(n) mod n, and A276086 is the primorial base exp-function.
A358225 (program): Numbers k such that A276086(k) mod k is an odd number, where A276086 is the primorial base exp-function.
A358226 (program): Numbers k such that A276086(k) mod k is an even number, where A276086 is the primorial base exp-function.
A358227 (program): Parity of A328382(n), where A328382(n) = A276086(n) mod A003415(n), with A003415 the arithmetic derivative and A276086 the primorial base exp-function.
A358228 (program): Numbers k such that A276086(k) mod A003415(k) is an odd number, where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.
A358229 (program): Numbers k such that A276086(k) mod A003415(k) is an even number, where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.
A358243 (program): Number of n-regular, N_0-weighted pseudographs on 2 vertices with total edge weight 3, up to isomorphism.
A358260 (program): a(n) is the number of infinitary square divisors of n.
A358271 (program): Product of the digits of 3^n.
A358279 (program): a(n) = Sum_{d|n} (d-1)! * d^(n/d).
A358280 (program): a(n) = Sum_{d|n} (d-1)!.
A358319 (program): Multiplicative sequence a(n) with a(p^e) = ((p-2) - (p-1) * e) * p^(e-1) for prime p and e > 0.
A358333 (program): By concatenating the standard compositions for each part of the n-th standard composition, we get a sequence of length a(n). Row-lengths of A357135.
A358345 (program): a(n) is the number of even square divisors of n.
A358346 (program): a(n) is the sum of the unitary divisors of n that are exponentially odd (A268335).
A358347 (program): a(n) is the sum of the unitary divisors of n that are squares.
A358350 (program): Numbers that can be written as (m + sum of digits of m + product of digits of m) for some m.
A358351 (program): Number of values of m such that m + (sum of digits of m) + (product of digits of m) is n.
A358360 (program): The 3-adic valuation of the central Delannoy numbers (sequence A001850).
A358364 (program): a(n) = 16^n * Sum_{k=0..n} binomial(1/2, k)^2.
A358365 (program): a(n) = 16^n * Sum_{k=0..n} binomial(-1/2, k)^2.
A358367 (program): a(n) = 8^n * binomial(n * 3/2, n).
A358368 (program): a(n) = Sum_{k=0..n} C(n)^2 * binomial(n + k, k), where C(n) is the n-th Catalan number.
A358370 (program): a(n) is the size of the largest 3-independent set in the cyclic group Zn.
A358371 (program): Number of leaves in the n-th standard ordered rooted tree.
A358372 (program): Number of nodes in the n-th standard ordered rooted tree.
A358379 (program): Edge-height (or depth) of the n-th standard ordered rooted tree.
A358389 (program): a(n) = n * Sum_{d|n} (d + n/d - 2)!/d!.
A358410 (program): a(n) = Sum_{d|n} (d + n/d - 2)!/(d - 1)!.
A358411 (program): a(n) = Sum_{d|n} (d + n/d - 1)!/(d - 1)!.
A358435 (program): Row sums of the triangular array A357498.
A358436 (program): a(n) = Sum_{j=0..n} C(n)*C(n-j), where C(n) is the n-th Catalan number.
A358437 (program): a(n) = Sum_{j=0..n} binomial(n, j)*C(n)*C(n-j), where C(n) is the n-th Catalan number.
A358439 (program): a(n) is the total number of holes in all positive n-digit integers, assuming 4 has no hole.
A358440 (program): a(n) is the largest prime that divides any two successive terms of the sequence b(m) = m^2 + n with m >= 1.
A358446 (program): a(n) = n! * Sum_{k=0..floor(n/2)} 1/binomial(n-k, k).
A358491 (program): a(n) = n!*Sum_{m=0..floor((n-1)/2)} 1/(n-m)/binomial(n-m-1,m).
A358493 (program): a(n) = Sum_{k=0..floor(n/3)} (n-2*k)!/k!.
A358494 (program): a(n) = Sum_{k=0..floor(n/5)} (n-4*k)!/k!.
A358495 (program): a(n) = Sum_{k=0..n} binomial(binomial(n, k), n).
A358496 (program): a(n) = Sum_{k=0..n} binomial(binomial(n, k), k).
A358498 (program): a(n) = Sum_{k=0..floor(n/3)} (n-3*k)!.
A358499 (program): a(n) = Sum_{k=0..floor(n/4)} (n-4*k)!.
A358500 (program): a(n) = Sum_{k=0..floor(n/5)} (n-5*k)!.
A358504 (program): Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 3 children down to the generation of M.
A358509 (program): Sum of decimal digits of (3^n - 1)/2 (A003462).
A358528 (program): a(n) = n-th prime p(k) such that p(k) - p(k-1) > p(k-1) - p(k-2).
A358529 (program): Indices of the primes in A35828.
A358530 (program): a(n) = n-th prime p(k) such that p(k) - p(k-1) < p(k-1) - p(k-2).
A358531 (program): Indices of the primes in A358530.
A358547 (program): a(n) = Sum_{k=0..floor(n/3)} (n-k)!/(n-3*k)!.
A358548 (program): a(n) = A003627(n+1) - A003627(n).
A358550 (program): Depth of the ordered rooted tree with binary encoding A014486(n).
A358551 (program): Number of nodes in the ordered rooted tree with binary encoding A014486(n).
A358552 (program): Node-height of the rooted tree with Matula-Goebel number n. Number of nodes in the longest path from root to leaf.
A358560 (program): a(n) = Sum_{k=0..floor(n/3)} (n-k)!/(k! * (n-3*k)!).
A358585 (program): Number of ordered rooted trees with n nodes, most of which are leaves.
A358586 (program): Number of ordered rooted trees with n nodes, at least half of which are leaves.
A358587 (program): Number of n-node rooted trees of height equal to the number of internal (non-leaf) nodes.
A358588 (program): Number of n-node ordered rooted trees of height equal to the number of internal (non-leaf) nodes.
A358598 (program): Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 4 children down to the generation of M.
A358603 (program): a(n) = Sum_{k=0..floor(n/2)} (-1)^k * (n-k)!/(n-2*k)!.
A358604 (program): a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (n-2*k)!/(n-3*k)!.
A358605 (program): a(n) = Sum_{k=0..floor(n/4)} (-1)^k * (n-3*k)!/(n-4*k)!.
A358606 (program): a(n) = Sum_{k=0..floor(n/5)} (-1)^k * (n-4*k)!/(n-5*k)!.
A358607 (program): a(n) = Sum_{k=0..floor(n/2)} (-1)^k * (n-2*k)!.
A358608 (program): a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (n-3*k)!.
A358609 (program): a(n) = Sum_{k=0..floor(n/4)} (-1)^k * (n-4*k)!.
A358611 (program): a(n) = Sum_{k=0..floor(n/5)} (-1)^k * (n-5*k)!.
A358613 (program): a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (n-k)!/(k! * (n-3*k)!).
A358620 (program): Number of nonzero digits needed to write all nonnegative n-digit integers.
A358632 (program): Coordination sequence for the faces of the uniform infinite surface that is formed from congruent regular pentagons and from which there is a continuous function that maps the faces 1:1 to regular pentagons in the plane.
A358682 (program): Numbers k such that 8*k^2 + 8*k - 7 is a square.
A358687 (program): a(n) = n! * Sum_{k=0..n} k^(3 * (n-k)) / (n-k)!.
A358688 (program): a(n) = n! * Sum_{k=0..n} k^(k * (n-k)) / (n-k)!.
A358691 (program): Gilbreath transform of primes p(2k-1); see Comments.
A358692 (program): Gilbreath transform of primes p(2k) with 2 prefixed; see Comments.
A358714 (program): a(n) = phi(n)^3.
A358738 (program): Expansion of Sum_{k>=0} k! * ( x/(1 - k*x) )^k.
A358740 (program): Expansion of Sum_{k>=0} k! * ( k * x/(1 - k*x) )^k.
A358741 (program): Expansion of Sum_{k>=0} k! * ( k * x/(1 - x) )^k.
A358769 (program): a(n) = 1 if n is of the form p * m^2, where p is a prime and m is a natural number >= 1, otherwise 0.
A358772 (program): Numbers whose arithmetic derivative is of the form 4k+1, cf. A003415.
A358791 (program): a(n) = n!*Sum_{m=0..floor(n/2)} binomial(n,2m)^(-1).

License Info