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A376014 a(n) = Sum_{d|n} d^d * binomial(n/d,d).

%I A376014 #19 Sep 06 2024 14:08:21
%S A376014 1,2,3,8,5,18,7,32,36,50,11,180,13,98,285,384,17,702,19,1480,966,242,
%T A376014 23,5640,3150,338,2295,9352,29,22440,31,18432,4488,578,65660,85500,37,
%U A376014 722,7761,229560,41,337302,43,85448,406080,1058,47,1449360,823592,788750,18411
%N A376014 a(n) = Sum_{d|n} d^d * binomial(n/d,d).
%H A376014 Seiichi Manyama, <a href="/A376014/b376014.txt">Table of n, a(n) for n = 1..10000</a>
%F A376014 G.f.: Sum_{k>=1} (k*x^k)^k / (1 - x^k)^(k+1).
%F A376014 If p is prime, a(p) = p.
%o A376014 (PARI) a(n) = sumdiv(n, d, d^d*binomial(n/d, d));
%o A376014 (PARI) my(N=60, x='x+O('x^N)); Vec(sum(k=1, N, (k*x^k)^k/(1-x^k)^(k+1)))
%o A376014 (Python)
%o A376014 from math import comb
%o A376014 from itertools import takewhile
%o A376014 from sympy import divisors
%o A376014 def A376014(n): return sum(d**d*comb(n//d,d) for d in takewhile(lambda d:d**2<=n,divisors(n))) # _Chai Wah Wu_, Sep 06 2024
%Y A376014 Cf. A062796, A338694, A376018.
%K A376014 nonn
%O A376014 1,2
%A A376014 _Seiichi Manyama_, Sep 06 2024