A308755 a(n) = Sum_{d|n} d^(d-2).

1, 2, 4, 18, 126, 1301, 16808, 262162, 4782973, 100000127, 2357947692, 61917365541, 1792160394038, 56693912392105, 1946195068359504, 72057594038190098, 2862423051509815794, 121439531096599036046, 5480386857784802185940, 262144000000000100000143

Offset: 1

Author

Seiichi Manyama, Jun 22 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..388

Crossrefs

Cf. A062796, A262843, A283498, A308753.

Programs

Mathematica

a[n_] := DivisorSum[n, #^(# - 2) &]; Array[a, 20] (* Amiram Eldar, May 08 2021 *)

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-3)))))

PARI

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

Formula

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

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