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A281904 Expansion of Sum_{i>=1} mu(i)^2*i*x^i/(1 - x^i) / Product_{j>=1} (1 - x^j), where mu() is the Moebius function (A008683). 0
1, 4, 9, 16, 31, 58, 93, 144, 221, 343, 502, 733, 1048, 1495, 2089, 2881, 3947, 5357, 7205, 9618, 12758, 16812, 22001, 28623, 37037, 47720, 61121, 77973, 99029, 125322, 157874, 198205, 247954, 309203, 384260, 476116, 588149, 724613, 890175, 1090781, 1333193, 1625702, 1977505, 2400221, 2906800, 3513121 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Total sum of squarefree parts in all partitions of n.

Convolution of the sequences A000041 and A048250.

LINKS

Table of n, a(n) for n=1..46.

Index entries for related partition-counting sequences

FORMULA

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

EXAMPLE

a(4) = 16 because we have [4], [3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1] and 3 + 1 + 2 + 2 + 2 + 1 + 1 + 1 + 1 + 1 + 1 = 16.

MATHEMATICA

nmax = 46; Rest[CoefficientList[Series[Sum[MoebiusMu[i]^2 i x^i/(1 - x^i), {i, 1, nmax}] / Product[1 - x^j, {j, 1, nmax}], {x, 0, nmax}], x]]

CROSSREFS

Cf. A000041, A005117, A008683, A048250, A066186, A073118.

Sequence in context: A138992 A199936 A326958 * A007679 A239870 A068037

Adjacent sequences:  A281901 A281902 A281903 * A281905 A281906 A281907

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 01 2017

STATUS

approved

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Last modified April 6 21:24 EDT 2020. Contains 333286 sequences. (Running on oeis4.)