A338663 a(n) = Sum_{d|n} (n/d)^n * binomial(d+n/d-1, d).
1, 9, 82, 1073, 15626, 284567, 5764802, 134874369, 3486981232, 100146490520, 3138428376722, 107039261352736, 3937376385699290, 155587085803983069, 6568409424129452048, 295158038428838854657, 14063084452067724991010, 708242105301294465144506, 37589973457545958193355602
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := DivisorSum[n, (n/#)^n * Binomial[# + n/# - 1, #] &]; Array[a, 20] (* Amiram Eldar, Apr 22 2021 *)
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PARI
a(n) = sumdiv(n, d, (n/d)^n*binomial(d+n/d-1, d));
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PARI
N=20; x='x+O('x^N); Vec(sum(k=1, N, 1/(1-(k*x)^k)^k-1))
Formula
G.f.: Sum_{k >= 1} (1/(1 - (k * x)^k)^k - 1).
If p is prime, a(p) = 1 + p^(p+1).