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%I #5 Jan 27 2017 13:06:58
%S 1,1,3,2,3,6,5,9,10,12,15,16,20,24,27,38,41,48,56,62,78,88,101,120,
%T 131,149,174,189,221,243,278,318,349,394,444,491,556,622,693,773,849,
%U 953,1048,1158,1292,1422,1568,1735,1901,2101,2307,2534,2795,3060,3357,3681,4024,4404,4809,5245,5734,6242,6805,7418
%N Expansion of Sum_{i>=1} mu(i)^2*x^i/(1 + x^i) * Product_{j>=1} (1 + mu(j)^2*x^j), where mu() is the Moebius function (A008683).
%C Total number of parts in all partitions of n into distinct squarefree parts (A005117).
%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 + mu(j)^2*x^j).
%e a(8) = 9 because we have [7, 1], [6, 2], [5, 3], [5, 2, 1] and 2 + 2 + 2 + 3 = 9.
%t nmax = 64; Rest[CoefficientList[Series[Sum[MoebiusMu[i]^2 x^i/(1 + x^i), {i, 1, nmax}] Product[1 + MoebiusMu[j]^2 x^j, {j, 1, nmax}], {x, 0, nmax}], x]]
%Y Cf. A005117, A008683, A015723, A024938, A087188, A281572.
%K nonn
%O 1,3
%A _Ilya Gutkovskiy_, Jan 26 2017
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