A376019 a(n) = Sum_{d|n} d^n * binomial(n/d-1,d-1).

1, 1, 1, 17, 1, 129, 1, 769, 19684, 4097, 1, 1614804, 1, 98305, 86093443, 4295426049, 1, 3876302043, 1, 4398055948289, 156905298046, 41943041, 1, 2820680971922038, 298023223876953126, 805306369, 213516729579637, 1441151884248219649, 1

Offset

1,4

Links

Table of n, a(n) for n=1..29.

Formula

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

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

Prog

(PARI) a(n) = sumdiv(n, d, d^n*binomial(n/d-1, d-1));
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, ((k*x)^k/(1-(k*x)^k))^k))
(Python)
from math import comb
from itertools import takewhile
from sympy import divisors
def A376019(n): return sum(d**n*comb(n//d-1, d-1) for d in takewhile(lambda d:d**2<=n, divisors(n))) # Chai Wah Wu, Sep 06 2024

Crossrefs

Cf. A023887, A376015.

Sequence in context: A264439 A279363 A295576 * A223519 A139804 A321259

Adjacent sequences: A376016 A376017 A376018 * A376020 A376021 A376022

Keyword

nonn

Author

Seiichi Manyama, Sep 06 2024

Status

approved