A359053 a(n) = Sum_{d|n} sigma_d(d)^(n/d).

1, 6, 29, 299, 3127, 48360, 823545, 16918164, 387462126, 10019541652, 285311670613, 8920567022545, 302875106592255, 11113363273445312, 437893951476881153, 18447309245488431653, 827240261886336764179, 39346708488214110663954, 1978419655660313589123981

Offset: 1

Author

Seiichi Manyama, Dec 14 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..386

Crossrefs

Cf. A344061, A359052, A359054.

Programs

Mathematica

a[n_] := DivisorSum[n, DivisorSigma[#, #]^(n/#) &]; Array[a, 19] (* Amiram Eldar, Aug 27 2023 *)

PARI

a(n) = sumdiv(n, d, sigma(d, d)^(n/d));

PARI

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

Formula

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

If p is prime, a(p) = 2 + p^p.