A379742 a(n) is the number of divisors of A000178(n).

1, 1, 2, 6, 18, 72, 234, 1088, 3600, 10416, 28080, 124080, 387828, 1921024, 6926400, 20941344, 54934880, 251328000, 810152280, 4254092800, 15266200950, 46208448000, 129674387920, 640501862400, 2197261252368, 6404827161600, 17436935577600, 43314231340800, 101062601640000, 436914124416000, 1355859833328000, 7074064925491200

Offset

0,3

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Formula

a(n) = A000005(A000178(n)).

a(n) = Product_{primes p <= n} (1 + (n*(n+1)/2 - 1 - Sum_{i=2..n} s_p(i))/(p-1)), where s_p(i) is the sum of digits of i in base p. - Amiram Eldar, Jan 15 2025

Mathematica

DivisorSigma[0, FoldList[Times, Range[0, 30]!]] (* Paolo Xausa, Jan 06 2025 *)

Prog

(PARI) a(n)=numdiv(prod(k=1, n, k!));
vector(30, n, a(n-1)) \\ Joerg Arndt, Jan 02 2025
(PARI) a(n) = {my(prd = 1); forprime(p = 2, n, prd *= (1 + (n*(n+1)/2 - 1 - sum(i = 2, n, sumdigits(i, p)))/(p-1))); prd; } \\ Amiram Eldar, Jan 15 2025

Crossrefs

Cf. A000005, A000178, A027423.

Sequence in context: A264036 A261994 A177472 * A364849 A194088 A022491

Adjacent sequences: A379739 A379740 A379741 * A379743 A379744 A379745

Keyword

nonn

Author

Tsuyoshi Hanatate, Dec 31 2024

Status

approved