A308671 a(n) = Sum_{d|n} d^(d^2).

1, 17, 19684, 4294967313, 298023223876953126, 10314424798490535546171968756, 256923577521058878088611477224235621321608, 6277101735386680763835789423207666416102355444468329480209

Offset

1,2

Links

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

Formula

L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^(k^2-1))) = Sum_{k>=1} a(k)*x^k/k.

Mathematica

a[n_] := DivisorSum[n, #^(#^2) &]; Array[a, 8] (* Amiram Eldar, May 11 2021 *)

Prog

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

Crossrefs

Column k=2 of A308674.

Cf. A000005, A062796, A308670.

Sequence in context: A308962 A191964 A230638 * A308670 A308571 A283719

Adjacent sequences: A308668 A308669 A308670 * A308672 A308673 A308674

Keyword

nonn

Author

Seiichi Manyama, Jun 16 2019

Status

approved