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Expansion of Sum_{i>=1} mu(i)^2*x^i/(1 - x^i) / Product_{j>=1} (1 - x^j), where mu() is the Moebius function (A008683).
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%I #4 Jan 24 2017 20:29:58

%S 1,3,6,11,19,33,51,79,118,176,252,362,505,705,965,1314,1765,2365,3127,

%T 4124,5387,7012,9052,11653,14893,18982,24048,30378,38176,47857,59704,

%U 74302,92099,113879,140300,172463,211297,258325,314887,383037,464684,562653,679566,819269,985449,1183242,1417738,1695886

%N Expansion of Sum_{i>=1} mu(i)^2*x^i/(1 - x^i) / Product_{j>=1} (1 - x^j), where mu() is the Moebius function (A008683).

%C Total number of squarefree parts in all partitions of n.

%C Convolution of A000041 and A034444.

%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>

%F G.f.: Sum_{i>=1} mu(i)^2*x^i/(1 - x^i) / Product_{j>=1} (1 - x^j).

%e a(5) = 19 because we have [5], [4, 1], [3, 2], [3, 1, 1], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1] and 1 + 1 + 2 + 3 + 3 + 4 + 5 = 19.

%t nmax = 48; Rest[CoefficientList[Series[Sum[MoebiusMu[i]^2 x^i/(1 - x^i), {i, 1, nmax}]/Product[1 - x^j, {j, 1, nmax}], {x, 0, nmax}], x]]

%Y Cf. A000041, A005117, A008683, A034444, A037032, A073335, A073336.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Jan 24 2017