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%I #8 Mar 09 2018 08:39:19
%S 1,0,-2,-3,1,1,3,0,9,8,4,-31,-12,-13,20,-13,48,-17,74,-87,8,-143,175,
%T -174,349,-164,369,-651,520,-1004,1142,-1218,1652,-1739,3291,-3933,
%U 3546,-5743,6170,-8022,11435,-13230,17196,-18706,22958,-31884,38420,-49802,58916
%N Expansion of Product_{k>=1} (1 - x^prime(k))^prime(k).
%F G.f.: Product_{k>=1} (1 - x^A000040(k))^A000040(k).
%F G.f.: exp(-Sum_{k>=1} A005063(k)*x^k/k).
%t nmax = 48; CoefficientList[Series[Product[(1 - x^Prime[k])^Prime[k], {k, 1, nmax}], {x, 0, nmax}], x]
%t nmax = 48; CoefficientList[Series[Exp[-Sum[DivisorSum[k, Boole[PrimeQ[#]] #^2 &] x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x]
%Y Cf. A000040, A000607, A005063, A007441, A030009, A046675, A073592, A219224, A291647, A291696.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Mar 08 2018
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