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Number of partitions of n into squarefree parts where every part appears at least 2 times.
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%I #4 Nov 28 2020 09:12:22

%S 1,0,1,1,2,1,4,2,5,5,8,6,13,10,17,17,24,22,36,32,47,48,64,63,90,86,

%T 116,120,154,156,208,206,265,277,344,354,448,458,566,596,720,752,920,

%U 956,1149,1217,1440,1518,1810,1900,2236,2380,2771,2937,3434,3631,4204,4487,5155,5485,6317

%N Number of partitions of n into squarefree parts where every part appears at least 2 times.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

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

%e a(6) = 4 because we have [3, 3], [2, 2, 2], [2, 2, 1, 1] and [1, 1, 1, 1, 1, 1].

%t nmax = 60; CoefficientList[Series[Product[1 + MoebiusMu[k]^2 x^(2 k)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A005117, A007690, A073576.

%K nonn

%O 0,5

%A _Ilya Gutkovskiy_, Nov 27 2020