A281572 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).

1, 3, 6, 11, 18, 30, 45, 68, 98, 139, 192, 266, 357, 478, 632, 828, 1074, 1386, 1769, 2250, 2840, 3566, 4452, 5534, 6842, 8427, 10335, 12624, 15361, 18634, 22519, 27137, 32598, 39047, 46645, 55580, 66050, 78313, 92630, 109330, 128760, 151342, 177517, 207833, 242878, 283326, 329944, 383598, 445246, 516013

Offset: 1

Author

Ilya Gutkovskiy, Jan 24 2017

Keywords

• nonn

Comments

Total number of parts in all partitions of n into squarefree parts (A005117).

Convolution of A034444 and A073576.

Examples

			a(4) = 11 because we have [3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1] and 2 + 2 + 3 + 4 = 11.
		

Links

• Index entries for related partition-counting sequences

Crossrefs

Cf. A005117, A008683, A034444, A073576.

Programs

Mathematica

nmax = 50; 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]]

Formula

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