A308670 a(n) = Sum_{d|n} d^(d*n).

1, 17, 19684, 4294967553, 298023223876953126, 10314424798490535546559373642, 256923577521058878088611477224235621321608, 6277101735386680763835789423207666416120802188537744130049

Offset: 1

Author

Seiichi Manyama, Jun 16 2019

Keywords

• nonn

Crossrefs

Column k=2 of A308676.

Cf. A023887, A062796, A308571, A308671, A308675.

Programs

Mathematica

a[n_] := DivisorSum[n, #^(#*n) &]; Array[a, 8] (* Amiram Eldar, May 11 2021 *)

PARI

{a(n) = sumdiv(n, d, d^(d*n))}

PARI

N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-(k^k*x)^k)^(1/k)))))

Formula

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