A308670 - OEIS

A308670

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

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

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..8.

FORMULA

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

MATHEMATICA

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

PROG

(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)))))

CROSSREFS

Column k=2 of A308676.

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

Sequence in context: A191964 A230638 A308671 * A308571 A283719 A355465

Adjacent sequences: A308667 A308668 A308669 * A308671 A308672 A308673

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jun 16 2019

STATUS

approved