A344080 a(n) = Sum_{d|n} tau(d)^n, where tau(n) is the number of divisors of n.

1, 5, 9, 98, 33, 4225, 129, 72354, 20196, 1050625, 2049, 2194099186, 8193, 268468225, 1073807361, 156925970179, 131073, 101629064089930, 524289, 3657261440572306, 4398050705409, 17592194433025, 8388609, 4727105427440383342818, 847322163876, 4503599761588225

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..719

Formula

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

If p is prime, a(p) = 1 + 2^p.

Mathematica

a[n_] := DivisorSum[n, DivisorSigma[0, #]^n &]; Array[a, 26] (* Amiram Eldar, May 09 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, numdiv(d)^n);
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, (numdiv(k)*x)^k/(1-(numdiv(k)*x)^k)))

Crossrefs

Cf. A007425, A062367, A097988, A279789, A344060, A344081.

Sequence in context: A344081 A171812 A221741 * A098097 A279707 A329002

Adjacent sequences: A344077 A344078 A344079 * A344081 A344082 A344083

Keyword

nonn

Author

Seiichi Manyama, May 09 2021

Status

approved