A376017 - OEIS

%I #17 Sep 06 2024 14:08:02

%S 1,2,3,5,5,12,7,32,10,90,11,264,13,686,105,1809,17,5166,19,11560,2856,

%T 28182,23,81456,26,159770,61263,375004,29,1122660,31,1984032,1082598,

%U 4456482,560,14486329,37,22413350,16888053,50674560,41,174582072,43,247627820,241884450

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

%H Seiichi Manyama, <a href="/A376017/b376017.txt">Table of n, a(n) for n = 1..5000</a>

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

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

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

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

%o (Python)

%o from math import comb

%o from itertools import takewhile

%o from sympy import divisors

%o 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

%Y Cf. A318636.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Sep 06 2024