|
%I #7 Apr 05 2017 04:47:19
%S 1,3,5,8,11,18,22,31,39,53,64,87,104,134,165,205,248,310,368,455,545,
%T 659,784,947,1117,1337,1579,1872,2197,2604,3036,3570,4168,4866,5661,
%U 6599,7633,8859,10236,11831,13625,15715,18036,20728,23761,27211,31106,35560,40533,46221,52596,59813,67912,77090,87343
%N Expansion of Sum_{i>=1} mu(i)^2*x^i/(1 - x^i) * Product_{j=1..i} 1/(1 - mu(j)^2*x^j), where mu() is the Moebius function (A008683).
%C Total number of largest parts in all partitions of n into 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..i} 1/(1 - mu(j)^2*x^j).
%e a(5) = 11 because we have [5], [3, 2], [3, 1, 1], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1] and 1 + 1 + 1 + 2 + 1 + 5 = 11.
%t nmax = 55; Rest[CoefficientList[Series[Sum[MoebiusMu[i]^2 x^i/(1 - x^i) Product[1/(1 - MoebiusMu[j]^2 x^j), {j, 1, i}], {i, 1, nmax}], {x, 0, nmax}], x]]
%o (PARI) x='x+O('x^56); Vec(sum(i=1, 56, moebius(i)^2*x^i/(1 - x^i) * prod(j=1, i, 1/(1 - moebius(j)^2*x^j)))) \\ _Indranil Ghosh_, Apr 04 2017
%Y Cf. A005117, A008683, A046746, A073576, A092311, A281572, A284829.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Apr 03 2017
|
