A308763 a(n) = Sum_{d|n} d^(n-2).

1, 2, 4, 21, 126, 1394, 16808, 266305, 4785157, 100390882, 2357947692, 61978939050, 1792160394038, 56707753666594, 1946196290656824, 72061992352890881, 2862423051509815794, 121441386937936123331, 5480386857784802185940, 262145000003883417004506

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..388

Formula

L.g.f.: -log(Product_{k>=1} (1 - (k*x)^k)^(1/k^3)) = Sum_{k>=1} a(k)*x^k/k.

G.f.: Sum_{k>=1} k^(k-2) * x^k/(1 - (k*x)^k).

Mathematica

a[n_] := DivisorSum[n, #^(n - 2) &]; Array[a, 20] (* Amiram Eldar, May 08 2021 *)

Prog

(PARI) {a(n) = sigma(n, n-2)}
(PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-(k*x)^k)^(1/k^3)))))
(PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, k^(k-2)*x^k/(1-(k*x)^k)))

Crossrefs

Cf. A023887, A082245, A294645, A294810, A308755.

Sequence in context: A107388 A233289 A296282 * A230690 A219745 A151803

Adjacent sequences: A308760 A308761 A308762 * A308764 A308765 A308766

Keyword

nonn

Author

Seiichi Manyama, Jun 23 2019

Status

approved