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A344080 a(n) = Sum_{d|n} tau(d)^n, where tau(n) is the number of divisors of n. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 28 16:37 EDT 2022. Contains 354119 sequences. (Running on oeis4.)