OFFSET
1,4
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/d)*binomial(n/d-1, d-1));
(PARI) my(N=50, 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 A376020(n): return sum(d**(m:=n//d)*comb(m-1, d-1) for d in takewhile(lambda d:d**2<=n, divisors(n))) # Chai Wah Wu, Sep 06 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 06 2024
STATUS
approved