A356437 a(n) = n! * Sum_{k=1..n} sigma_k(k)/k.

1, 7, 77, 1946, 84754, 6202524, 636369348, 89979720144, 16431405256656, 3796658174518560, 1077102230236529760, 368915006390671969920, 149873555740938949215360, 71297150722148582901815040, 39244301012876892023553235200

Offset

1,2

Links

Table of n, a(n) for n=1..15.

Formula

E.g.f.: -(1/(1-x)) * Sum_{k>0} log(1 - (k*x)^k)/k.

a(n) ~ n! * n^(n-1). - Vaclav Kotesovec, Aug 07 2022

Mathematica

Table[n! * Sum[DivisorSigma[k, k]/k, {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Aug 07 2022 *)

Prog

(PARI) a(n) = n!*sum(k=1, n, sigma(k, k)/k);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-(k*x)^k)/k)/(1-x)))

Crossrefs

Cf. A023887, A356297, A356436, A356440.

Sequence in context: A080492 A342347 A082782 * A107047 A210413 A045485

Adjacent sequences: A356434 A356435 A356436 * A356438 A356439 A356440

Keyword

nonn

Author

Seiichi Manyama, Aug 07 2022

Status

approved