%I #15 Apr 25 2021 08:51:35
%S 1,5,28,265,3126,46750,823544,16778257,387420652,10000015646,
%T 285311670612,8916100731047,302875106592254,11112006831322846,
%U 437893890380906656,18446744073843774497,827240261886336764178,39346408075300025340205
%N a(n) = Sum_{d|n} d^d * binomial(d+n/d-2, d-1).
%H Seiichi Manyama, <a href="/A343573/b343573.txt">Table of n, a(n) for n = 1..386</a>
%F G.f.: Sum_{k >= 1} (k * x/(1 - x^k))^k.
%F If p is prime, a(p) = 1 + p^p.
%t a[n_] := DivisorSum[n, #^#*Binomial[# + n/# - 2, # - 1] &]; Array[a, 20] (* _Amiram Eldar_, Apr 20 2021 *)
%o (PARI) a(n) = sumdiv(n, d, d^d*binomial(d+n/d-2, d-1));
%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x/(1-x^k))^k))
%Y Cf. A023887, A157019, A157020, A324158, A324159, A338661, A339481, A339482, A339712, A343567, A343574.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Apr 20 2021
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