A344081 a(n) = Sum_{d|n} tau(d)^d, where tau(n) is the number of divisors of n.

1, 5, 9, 86, 33, 4109, 129, 65622, 19692, 1048613, 2049, 2176786526, 8193, 268435589, 1073741865, 152587956247, 131073, 101559956692208, 524289, 3656158441111670, 4398046511241, 17592186046469, 8388609, 4722366482871822065758

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 - x^k).

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

Mathematica

a[n_] := DivisorSum[n, DivisorSigma[0, #]^# &]; Array[a, 24] (* Amiram Eldar, May 09 2021 *)

Prog

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

Crossrefs

Cf. A007425, A062367, A097988, A279789, A344047, A344080.

Sequence in context: A365580 A192202 A249937 * A171812 A221741 A344080

Adjacent sequences: A344078 A344079 A344080 * A344082 A344083 A344084

Keyword

nonn

Author

Seiichi Manyama, May 09 2021

Status

approved