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%I #19 May 09 2021 13:34:32
%S 1,5,10,29,26,123,50,305,352,668,122,3844,170,2593,9704,13825,290,
%T 41598,362,118259,107986,33047,530,929102,394376,130744,1203580,
%U 2737415,842,9910225,962,13315073,14199222,2404670,33547310,136502007,1370,10555795,168405072,548460064,1682
%N a(n) = Sum_{d|n} (n/d)^d * binomial(d+n/d-1, d).
%H Seiichi Manyama, <a href="/A338662/b338662.txt">Table of n, a(n) for n = 1..5000</a>
%F G.f.: Sum_{k >= 1} (1/(1 - k * x^k)^k - 1).
%F If p is prime, a(p) = 1 + p^2.
%t a[n_] := DivisorSum[n, (n/#)^# * Binomial[# + n/# - 1, #] &]; Array[a, 40] (* _Amiram Eldar_, Apr 22 2021 *)
%o (PARI) a(n) = sumdiv(n, d, (n/d)^d*binomial(d+n/d-1, d));
%o (PARI) N=66; x='x+O('x^N); Vec(sum(k=1, N, 1/(1-k*x^k)^k-1))
%Y Cf. A081543, A338663, A343574.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Apr 22 2021