A376017 a(n) = Sum_{d|n} d^(n/d - d) * binomial(n/d,d).

1, 2, 3, 5, 5, 12, 7, 32, 10, 90, 11, 264, 13, 686, 105, 1809, 17, 5166, 19, 11560, 2856, 28182, 23, 81456, 26, 159770, 61263, 375004, 29, 1122660, 31, 1984032, 1082598, 4456482, 560, 14486329, 37, 22413350, 16888053, 50674560, 41, 174582072, 43, 247627820, 241884450

Offset: 1

Author

Seiichi Manyama, Sep 06 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A318636.

Programs

PARI

a(n) = sumdiv(n, d, d^(n/d-d)*binomial(n/d, d));

PARI

my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, x^k^2/(1-k*x^k)^(k+1)))

Python

from math import comb
from itertools import takewhile
from sympy import divisors
def A376017(n): return sum(d**((m:=n//d)-d)*comb(m,d) for d in takewhile(lambda d:d**2<=n,divisors(n))) # Chai Wah Wu, Sep 06 2024

Formula

G.f.: Sum_{k>=1} x^(k^2) / (1 - k*x^k)^(k+1).

If p is prime, a(p) = p.