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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). 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 7 17:17 EST 2021. Contains 349582 sequences. (Running on oeis4.)