A356323 a(n) = n! * Sum_{k=1..n} sigma_3(k)/k.

1, 11, 89, 794, 6994, 72204, 753108, 8973264, 111281616, 1524322080, 21601104480, 340803192960, 5483287025280, 96044874750720, 1748238132614400, 34093033838438400, 682396164763084800, 14706429413353574400, 323342442475011993600, 7585740483060676608000

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Formula

E.g.f.: (1/(1-x)) * Sum_{k>0} x^k * (1 + x^k)/(k * (1 - x^k)^3).

E.g.f.: -(1/(1-x)) * Sum_{k>0} k^2 * log(1 - x^k).

a(n) ~ n! * Pi^4 * n^3 / 270. - Vaclav Kotesovec, Aug 07 2022

Mathematica

Table[n! * Sum[DivisorSigma[3, k]/k, {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Aug 07 2022 *)

Prog

(PARI) a(n) = n!*sum(k=1, n, sigma(k, 3)/k);
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k*(1+x^k)/(k*(1-x^k)^3))/(1-x)))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, k^2*log(1-x^k))/(1-x)))

Crossrefs

Cf. A001158, A064603, A356010, A356297, A356298.

Sequence in context: A226854 A037580 A155607 * A110252 A199394 A171470

Adjacent sequences: A356320 A356321 A356322 * A356324 A356325 A356326

Keyword

nonn

Author

Seiichi Manyama, Aug 03 2022

Status

approved