A308688 a(n) = Sum_{d|n} d^(2*n/d - 1).

1, 3, 4, 13, 6, 66, 8, 201, 253, 648, 12, 5488, 14, 8550, 22824, 49681, 18, 316743, 20, 865578, 1611152, 2098506, 24, 27246276, 1953151, 33556656, 129199240, 202152908, 30, 1758141606, 32, 3223326753, 10460514288, 8589939540, 1261056768, 146050621105, 38

Offset: 1

Author

Seiichi Manyama, Jun 17 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000

Crossrefs

Column k=2 of A308690.

Cf. A087909, A308692.

Programs

Mathematica

a[n_] := DivisorSum[n, #^(2*n/# - 1) &]; Array[a, 37] (* Amiram Eldar, May 09 2021 *)

PARI

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

PARI

N=66; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-k^2*x^k)^(1/k^2)))))

Formula

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

a(p) = p+1 for prime p.

G.f.: Sum_{k>=1} k*x^k/(1 - k^2*x^k). - Ilya Gutkovskiy, Jul 25 2019