A344060 a(n) = Sum_{d|n} sigma(d)^n.

1, 10, 65, 2483, 7777, 2990810, 2097153, 2568661988, 10604761518, 3570527751850, 743008370689, 232227195048256531, 793714773254145, 21035724521219881850, 504857283427304833025, 727429690188773950335429, 2185911559738696531969, 43567528891100073055151954340, 5242880000000000000000001

Offset

1,2

Links

Table of n, a(n) for n=1..19.

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A007429, A023887, A065018, A342471, A344044, A344047, A344061.

Sequence in context: A262342 A307144 A344047 * A140362 A159838 A269679

Adjacent sequences: A344057 A344058 A344059 * A344061 A344062 A344063

Keyword

nonn

Author

Seiichi Manyama, May 08 2021

Status

approved