A376018 - OEIS

%I #14 Sep 06 2024 14:08:24

%S 1,1,1,5,1,9,1,13,28,17,1,102,1,25,163,285,1,303,1,1061,406,41,1,3172,

%T 3126,49,757,5173,1,16654,1,9021,1216,65,46876,62546,1,73,1783,130956,

%U 1,282123,1,30805,221208,89,1,1024944,823544,393847,3241,56421,1,2616513

%N a(n) = Sum_{d|n} d^d * binomial(n/d-1,d-1).

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

%F If p is prime, a(p) = 1.

%o (PARI) a(n) = sumdiv(n, d, d^d*binomial(n/d-1, d-1));

%o (PARI) my(N=60, x='x+O('x^N)); Vec(sum(k=1, N, (k*x^k/(1-x^k))^k))

%o (Python)

%o from math import comb

%o from itertools import takewhile

%o from sympy import divisors

%o def A376018(n): return sum(d**d*comb(n//d-1,d-1) for d in takewhile(lambda d:d**2<=n,divisors(n))) # _Chai Wah Wu_, Sep 06 2024

%Y Cf. A143862, A376014.

%K nonn

%O 1,4

%A _Seiichi Manyama_, Sep 06 2024