A344061 a(n) = Sum_{d|n} sigma(d)^(n/d).

1, 4, 5, 17, 7, 56, 9, 146, 78, 298, 13, 1501, 15, 2276, 1265, 9219, 19, 25716, 21, 77519, 16929, 177328, 25, 739582, 7808, 1594562, 264382, 5611241, 31, 15699452, 33, 48863172, 4196081, 129140542, 312753, 447589422, 39, 1162261928, 67111665, 3771805472, 43, 10764897556, 45

Offset

1,2

Links

Table of n, a(n) for n=1..43.

Formula

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

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

Mathematica

a[n_] := DivisorSum[n, DivisorSigma[1 , #]^(n/#) &]; Array[a, 43] (* Amiram Eldar, May 08 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, sigma(d)^(n/d));
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, sigma(k)*x^k/(1-sigma(k)*x^k)))

Crossrefs

Cf. A007429, A055225, A279789, A309369, A342471, A344060.

Sequence in context: A032144 A032049 A258063 * A045680 A174352 A152021

Adjacent sequences: A344058 A344059 A344060 * A344062 A344063 A344064

Keyword

nonn

Author

Seiichi Manyama, May 08 2021

Status

approved