OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..385
Eric Weisstein's World of Mathematics, Divisor Function
FORMULA
G.f.: Sum_{k>0} k^(k+1)*x^k/(1-(k*x)^k).
L.g.f.: -log(Product_{k>=1} (1 - (k*x)^k)) = Sum_{k>=1} a(k)*x^k/k. - Seiichi Manyama, Jun 02 2019
a(n) ~ n^(n+1). - Vaclav Kotesovec, Oct 07 2020
MATHEMATICA
Table[DivisorSigma[n + 1, n], {n, 1, 20}] (* Vaclav Kotesovec, Oct 07 2020 *)
PROG
(PARI) {a(n) = sigma(n, n+1)}
(PARI) N=66; x='x+O('x^N); Vec(sum(k=1, N, k^(k+1)*x^k/(1-(k*x)^k)))
(PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, 1-(k*x)^k)))) \\ Seiichi Manyama, Jun 02 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 05 2017
STATUS
approved