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%I #12 Apr 20 2021 22:36:45
%S 1,6,30,272,3130,46794,823550,16778544,387420768,10000018820,
%T 285311670622,8916100779324,302875106592266,11112006832146486,
%U 437893890380925960,18446744073860555680,827240261886336764194,39346408075300413088392
%N a(n) = Sum_{d|n} d^d * binomial(d+n/d-1, d).
%F G.f.: Sum_{k >= 1} (k * x)^k/(1 - x^k)^(k+1).
%F If p is prime, a(p) = p + p^p.
%t a[n_] := DivisorSum[n, #^#*Binomial[# + n/# - 1, #] &]; Array[a, 20] (* _Amiram Eldar_, Apr 20 2021 *)
%o (PARI) a(n) = sumdiv(n, d, d^d*binomial(d+n/d-1, d));
%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x)^k/(1-x^k)^(k+1)))
%Y Cf. A081543, A343568, A343573.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Apr 20 2021
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