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

1,2

Comments

Total number of squarefree parts in all partitions of n.

Convolution of A000041 and A034444.

Links

Table of n, a(n) for n=1..48.

Index entries for related partition-counting sequences

Formula

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

Example

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.

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]]

Crossrefs

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

Sequence in context: A001911 A020957 A179006 * A262987 A191696 A252479

Adjacent sequences: A281570 A281571 A281572 * A281574 A281575 A281576

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 24 2017

Status

approved