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A376018 a(n) = Sum_{d|n} d^d * binomial(n/d-1,d-1).

%I A376018 #14 Sep 06 2024 14:08:24
%S A376018 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 A376018 3126,49,757,5173,1,16654,1,9021,1216,65,46876,62546,1,73,1783,130956,
%U A376018 1,282123,1,30805,221208,89,1,1024944,823544,393847,3241,56421,1,2616513
%N A376018 a(n) = Sum_{d|n} d^d * binomial(n/d-1,d-1).
%F A376018 G.f.: Sum_{k>=1} ( k*x^k / (1 - x^k) )^k.
%F A376018 If p is prime, a(p) = 1.
%o A376018 (PARI) a(n) = sumdiv(n, d, d^d*binomial(n/d-1, d-1));
%o A376018 (PARI) my(N=60, x='x+O('x^N)); Vec(sum(k=1, N, (k*x^k/(1-x^k))^k))
%o A376018 (Python)
%o A376018 from math import comb
%o A376018 from itertools import takewhile
%o A376018 from sympy import divisors
%o A376018 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 A376018 Cf. A143862, A376014.
%K A376018 nonn
%O A376018 1,4
%A A376018 _Seiichi Manyama_, Sep 06 2024