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A281904 Expansion of Sum_{i>=1} mu(i)^2*i*x^i/(1 - x^i) / Product_{j>=1} (1 - x^j), where mu() is the Moebius function (A008683). 0

%I

%S 1,4,9,16,31,58,93,144,221,343,502,733,1048,1495,2089,2881,3947,5357,

%T 7205,9618,12758,16812,22001,28623,37037,47720,61121,77973,99029,

%U 125322,157874,198205,247954,309203,384260,476116,588149,724613,890175,1090781,1333193,1625702,1977505,2400221,2906800,3513121

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

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

%C Convolution of the sequences A000041 and A048250.

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

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

%e a(4) = 16 because we have [4], [3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1] and 3 + 1 + 2 + 2 + 2 + 1 + 1 + 1 + 1 + 1 + 1 = 16.

%t nmax = 46; Rest[CoefficientList[Series[Sum[MoebiusMu[i]^2 i x^i/(1 - x^i), {i, 1, nmax}] / Product[1 - x^j, {j, 1, nmax}], {x, 0, nmax}], x]]

%Y Cf. A000041, A005117, A008683, A048250, A066186, A073118.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Feb 01 2017

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Last modified June 6 04:02 EDT 2020. Contains 334858 sequences. (Running on oeis4.)