A294645 a(n) = Sum_{d|n} d^(n+1).

1, 9, 82, 1057, 15626, 282252, 5764802, 134480385, 3486843451, 100048830174, 3138428376722, 107006334784468, 3937376385699290, 155572843119354936, 6568408508343827972, 295150156996346511361, 14063084452067724991010, 708236696816416252145973

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

Column k=1 of A308504.

Cf. A023882, A023887, A082245, A158095, A292312.

Sequence in context: A045741 A283498 A294956 * A338663 A308668 A308481

Adjacent sequences: A294642 A294643 A294644 * A294646 A294647 A294648

Keyword

nonn

Author

Seiichi Manyama, Nov 05 2017

Status

approved