A308753 a(n) = Sum_{d|n} d^(2*(d-1)).

1, 5, 82, 4101, 390626, 60466262, 13841287202, 4398046515205, 1853020188851923, 1000000000000390630, 672749994932560009202, 552061438912436478063702, 542800770374370512771595362, 629983141281877223617054459942

Offset: 1

Author

Seiichi Manyama, Jun 22 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..215

Crossrefs

Column k=2 of A308701.

Cf. A283533, A308692, A308696, A308755, A308756.

Programs

Mathematica

a[n_] := DivisorSum[n, #^(2*(# - 1)) &]; Array[a, 14] (* Amiram Eldar, May 08 2021 *)

PARI

{a(n) = sumdiv(n, d, d^(2*(d-1)))}

PARI

N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^k^(2*k-3)))))

PARI

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

Formula

L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^(2*k-3))) = Sum_{k>=1} a(k)*x^k/k.

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