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A281667
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).
0
1, 1, 3, 2, 3, 6, 5, 9, 10, 12, 15, 16, 20, 24, 27, 38, 41, 48, 56, 62, 78, 88, 101, 120, 131, 149, 174, 189, 221, 243, 278, 318, 349, 394, 444, 491, 556, 622, 693, 773, 849, 953, 1048, 1158, 1292, 1422, 1568, 1735, 1901, 2101, 2307, 2534, 2795, 3060, 3357, 3681, 4024, 4404, 4809, 5245, 5734, 6242, 6805, 7418
OFFSET
1,3
COMMENTS
Total number of parts in all partitions of n into distinct squarefree parts (A005117).
FORMULA
G.f.: Sum_{i>=1} mu(i)^2*x^i/(1 + x^i) * Product_{j>=1} (1 + mu(j)^2*x^j).
EXAMPLE
a(8) = 9 because we have [7, 1], [6, 2], [5, 3], [5, 2, 1] and 2 + 2 + 2 + 3 = 9.
MATHEMATICA
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]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 26 2017
STATUS
approved