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Expansion of Sum_{k>=1} (-1 + Product_{j>=1} 1 / (1 - x^(k*prime(j)))).
1

%I #5 Nov 13 2019 15:09:30

%S 0,1,1,2,2,4,3,5,5,8,6,12,9,14,15,19,17,27,23,35,34,42,40,61,54,70,72,

%T 92,87,121,111,143,147,175,180,232,219,268,282,340,336,419,413,499,

%U 523,598,614,752,747,879,917,1058,1083,1280,1306,1515,1576,1783,1850

%N Expansion of Sum_{k>=1} (-1 + Product_{j>=1} 1 / (1 - x^(k*prime(j)))).

%C Inverse Moebius transform of A000607.

%F G.f.: Sum_{k>=1} A000607(k) * x^k / (1 - x^k).

%F a(n) = Sum_{d|n} A000607(d).

%t nmax = 59; CoefficientList[Series[Sum[-1 + Product[1/(1 - x^(k Prime[j])), {j, 1, nmax}], {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%Y Cf. A000607, A047966, A047968, A329438.

%K nonn

%O 1,4

%A _Ilya Gutkovskiy_, Nov 13 2019