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A376016
a(n) = Sum_{d|n} d^(n/d) * binomial(n/d,d).
2
1, 2, 3, 8, 5, 30, 7, 104, 36, 330, 11, 1296, 13, 2702, 2445, 7440, 17, 33030, 19, 51220, 76566, 112662, 23, 699216, 3150, 639002, 1653399, 2064412, 29, 10620300, 31, 12451872, 29229288, 17825826, 1640660, 190101888, 37, 89653286, 455976417, 441305440, 41
OFFSET
1,2
LINKS
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