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A327641 Number of partitions of n into divisors d of n such that n/d is squarefree. 0
1, 1, 2, 2, 2, 2, 8, 2, 2, 2, 11, 2, 8, 2, 14, 14, 2, 2, 8, 2, 11, 18, 20, 2, 8, 2, 23, 2, 14, 2, 742, 2, 2, 26, 29, 26, 8, 2, 32, 30, 11, 2, 1654, 2, 20, 14, 38, 2, 8, 2, 11, 38, 23, 2, 8, 38, 14, 42, 47, 2, 742, 2, 50, 18, 2, 44, 5257, 2, 29, 50, 5066, 2, 8, 2, 59, 14 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..75.

FORMULA

a(n) = [x^n] Product_{d|n} 1 / (1 - mu(n/d)^2 * x^d).

MATHEMATICA

a[n_] := SeriesCoefficient[Product[1/(1 - MoebiusMu[n/d]^2 x^d), {d, Divisors[n]}], {x, 0, n}]; Table[a[n], {n, 0, 75}]

PROG

(MAGMA) [1] cat [#RestrictedPartitions(n, {d:d in Divisors(n)|IsSquarefree(n div d)}):n in [1..75]]; // Marius A. Burtea, Sep 20 2019

CROSSREFS

Cf. A008683, A018818, A225244, A225245, A246655 (positions of 2's).

Sequence in context: A054083 A270379 A295557 * A066874 A087577 A323741

Adjacent sequences:  A327638 A327639 A327640 * A327642 A327643 A327644

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Sep 20 2019

STATUS

approved

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Last modified February 23 06:13 EST 2020. Contains 332159 sequences. (Running on oeis4.)