%I #6 Feb 10 2022 11:46:36
%S 1,1,-1,-3,-1,1,4,2,-2,-5,4,2,-2,-10,3,10,21,-15,-26,-23,34,28,25,-54,
%T -18,2,67,-48,-22,-55,116,44,37,-227,-10,32,295,-85,-76,-336,254,74,
%U 250,-451,59,-127,672,-294,-69,-761,740,77,657,-1208,59,-450,1700,-487,241,-1892,1202
%N G.f. A(x) satisfies: 1 / (1 - x) = Product_{i>=1, j>=1} A(x^(i*j)).
%C Euler transform of A007427.
%F G.f. A(x) satisfies: 1 / (1 - x) = Product_{k>=1} A(x^k)^A000005(k).
%F G.f.: Product_{k>=1} 1 / (1 - x^k)^A007427(k).
%F G.f.: exp( Sum_{k>=1} A101035(k) * x^k / k ).
%F a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} A101035(k) * a(n-k).
%t nmax = 60; A007427[n_] := Sum[MoebiusMu[d] MoebiusMu[n/d], {d, Divisors[n]}]; CoefficientList[Series[Product[1/(1 - x^k)^A007427[k], {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A000005, A006171, A007427, A101035, A117209, A351403.
%K sign
%O 0,4
%A _Ilya Gutkovskiy_, Feb 10 2022