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%I #12 Apr 22 2021 22:05:04
%S 1,9,82,1073,15626,284567,5764802,134874369,3486981232,100146490520,
%T 3138428376722,107039261352736,3937376385699290,155587085803983069,
%U 6568409424129452048,295158038428838854657,14063084452067724991010,708242105301294465144506,37589973457545958193355602
%N a(n) = Sum_{d|n} (n/d)^n * binomial(d+n/d-1, d).
%F G.f.: Sum_{k >= 1} (1/(1 - (k * x)^k)^k - 1).
%F If p is prime, a(p) = 1 + p^(p+1).
%t a[n_] := DivisorSum[n, (n/#)^n * Binomial[# + n/# - 1, #] &]; Array[a, 20] (* _Amiram Eldar_, Apr 22 2021 *)
%o (PARI) a(n) = sumdiv(n, d, (n/d)^n*binomial(d+n/d-1, d));
%o (PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, 1/(1-(k*x)^k)^k-1))
%Y Cf. A081543, A338662.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Apr 22 2021
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