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%I #19 Apr 24 2021 09:57:02
%S 1,3,10,3,26,13,50,-177,352,-84,122,-996,170,-153,9704,-13313,290,
%T -6518,362,-2771,107986,17073,530,-805070,394376,99984,1203580,
%U 1196313,842,-4500745,962,-13313025,14199222,2316234,33547310,-19898071,1370,10418613,168405072
%N a(n) = - Sum_{d|n} (-n/d)^d * binomial(d+n/d-1, d).
%F G.f.: Sum_{k >= 1} (1 - 1/(1 + k * x^k)^k).
%F If p is prime, a(p) = (-1)^(p-1) + p^2.
%t a[n_] := -DivisorSum[n, (-n/#)^# * Binomial[# + n/# - 1, #] &]; Array[a, 40] (* _Amiram Eldar_, Apr 24 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/(1+k*x^k)^k))
%Y Cf. A327238, A338662, A338682, A338684, A338688.
%K sign
%O 1,2
%A _Seiichi Manyama_, Apr 23 2021
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