A308756 a(n) = Sum_{d|n} d^(2*(d-2)).

1, 2, 10, 258, 15626, 1679627, 282475250, 68719476994, 22876792454971, 10000000000015627, 5559917313492231482, 3833759992447476802059, 3211838877954855105157370, 3214199700417740937033562867, 3787675244106352329254150406260

Offset: 1

Author

Seiichi Manyama, Jun 22 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..216

Crossrefs

Cf. A283533, A308696.

Programs

Mathematica

a[n_] := DivisorSum[n, #^(2*(# - 2)) &]; Array[a, 15] (* Amiram Eldar, May 08 2021 *)

PARI

{a(n) = sumdiv(n, d, d^(2*(d-2)))}

PARI

N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^k^(2*k-5)))))

PARI

N=20; x='x+O('x^N); Vec(sum(k=1, N, k^(2*(k-2))*x^k/(1-x^k)))

Formula

L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^(2*k-5))) = Sum_{k>=1} a(k)*x^k/k.

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