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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
OFFSET
0,3
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: A270379 A337358 A295557 * A066874 A087577 A323741
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 20 2019
STATUS
approved