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G.f. A(x) satisfies: 1 / (1 - x) = Product_{i>=1, j>=1} A(x^(i*j)).
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%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