OFFSET
1,2
FORMULA
E.g.f.: (1/(1-x)) * Sum_{k>0} x^k/(k * (1 - x^k)^2).
E.g.f.: -(1/(1-x)) * Sum_{k>0} k * log(1 - x^k).
a(n) ~ n! * zeta(3) * n^2 / 2. - Vaclav Kotesovec, Aug 07 2022
MATHEMATICA
Table[n! * Sum[DivisorSigma[2, k]/k, {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Aug 07 2022 *)
PROG
(PARI) a(n) = n!*sum(k=1, n, sigma(k, 2)/k);
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/(k*(1-x^k)^2))/(1-x)))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, k*log(1-x^k))/(1-x)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 03 2022
STATUS
approved