A376018 a(n) = Sum_{d|n} d^d * binomial(n/d-1,d-1).
1, 1, 1, 5, 1, 9, 1, 13, 28, 17, 1, 102, 1, 25, 163, 285, 1, 303, 1, 1061, 406, 41, 1, 3172, 3126, 49, 757, 5173, 1, 16654, 1, 9021, 1216, 65, 46876, 62546, 1, 73, 1783, 130956, 1, 282123, 1, 30805, 221208, 89, 1, 1024944, 823544, 393847, 3241, 56421, 1, 2616513
Offset: 1
Keywords
Programs
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PARI
a(n) = sumdiv(n, d, d^d*binomial(n/d-1, d-1));
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PARI
my(N=60, x='x+O('x^N)); Vec(sum(k=1, N, (k*x^k/(1-x^k))^k)) -
Python
from math import comb from itertools import takewhile from sympy import divisors def A376018(n): return sum(d**d*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 - x^k) )^k.
If p is prime, a(p) = 1.