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
Keywords
Programs
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PARI
a(n) = sumdiv(n, d, d^n*binomial(n/d-1, d-1));
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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
Formula
G.f.: Sum_{k>=1} ( (k*x)^k / (1 - (k*x)^k) )^k.
If p is prime, a(p) = 1.