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

1,2

Comments

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

Convolution of A034444 and A073576.

Links

Table of n, a(n) for n=1..50.

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 - mu(j)^2*x^j).

Example

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

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]]

Crossrefs

Cf. A005117, A008683, A034444, A073576.

Sequence in context: A066778 A265075 A147079 * A152074 A123629 A212484

Adjacent sequences: A281569 A281570 A281571 * A281573 A281574 A281575

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 24 2017

Status

approved