A281573 Expansion of Sum_{i>=1} mu(i)^2*x^i/(1 - x^i) / Product_{j>=1} (1 - x^j), where mu() is the Moebius function (A008683).

1, 3, 6, 11, 19, 33, 51, 79, 118, 176, 252, 362, 505, 705, 965, 1314, 1765, 2365, 3127, 4124, 5387, 7012, 9052, 11653, 14893, 18982, 24048, 30378, 38176, 47857, 59704, 74302, 92099, 113879, 140300, 172463, 211297, 258325, 314887, 383037, 464684, 562653, 679566, 819269, 985449, 1183242, 1417738, 1695886

Offset: 1

Author

Ilya Gutkovskiy, Jan 24 2017

Keywords

• nonn

Comments

Total number of squarefree parts in all partitions of n.

Convolution of A000041 and A034444.

Examples

			a(5) = 19 because we have [5], [4, 1], [3, 2], [3, 1, 1], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1] and 1 + 1 + 2 + 3 + 3 + 4 + 5 = 19.
		

Links

• Index entries for related partition-counting sequences

Crossrefs

Cf. A000041, A005117, A008683, A034444, A037032, A073335, A073336.

Programs

Mathematica

nmax = 48; Rest[CoefficientList[Series[Sum[MoebiusMu[i]^2 x^i/(1 - x^i), {i, 1, nmax}]/Product[1 - 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 - x^j).