OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..5000
FORMULA
G.f.: Sum_{k>=1} (k*x^k)^k / (1 - k*x^k)^(k+1).
If p is prime, a(p) = p.
PROG
(PARI) a(n) = sumdiv(n, d, d^(n/d)*binomial(n/d, d));
(PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, (k*x^k)^k/(1-k*x^k)^(k+1)))
(Python)
from math import comb
from itertools import takewhile
from sympy import divisors
def A376016(n): return sum(d**(m:=n//d)*comb(m, d) 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