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%I #4 Oct 28 2019 20:06:00
%S 0,1,1,0,0,0,1,0,-1,-1,2,1,0,-2,0,1,3,-3,-1,-1,4,-1,-1,-4,6,2,2,-13,4,
%T 4,13,-15,-5,-5,30,-11,-7,-34,42,7,16,-78,27,18,95,-117,-21,-49,223,
%U -76,-40,-262,326,48,135,-642,242,103,752,-938,-105,-408,1826,-732,-240
%N Product_{n>=1} (1 + x^n)^a(n) = 1 + Sum_{n>=1} x^prime(n).
%C Inverse weigh transform of A010051.
%t b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[a[i], j] b[n - i j, i - 1], {j, 0, n/i}]]]; a[n_] := a[n] = Boole[PrimeQ[n]] - b[n, n - 1]; Array[a, 65]
%Y Cf. A000040, A000586, A010051, A305871, A308298.
%K sign
%O 1,11
%A _Ilya Gutkovskiy_, Oct 27 2019