A344047 a(n) = Sum_{d|n} sigma(d)^d.

1, 10, 65, 2411, 7777, 2986058, 2097153, 2562893036, 10604499438, 3570467234410, 743008370689, 232218265092200875, 793714773254145, 21035720123170684938, 504857282956046114465, 727423121747187826721517, 2185911559738696531969, 43567528752021332763809905512, 5242880000000000000000001

Offset: 1

Author

Seiichi Manyama, May 08 2021

Keywords

• nonn

Crossrefs

Cf. A065018, A342473, A344044.

Programs

Mathematica

a[n_] := DivisorSum[n, DivisorSigma[1, #]^# &]; Array[a, 19] (* Amiram Eldar, May 08 2021 *)

PARI

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

PARI

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

Formula

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

If p is prime, a(p) = 1 + (p+1)^p.