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A327640 Number of partitions of n into divisors d of n such that n/d is odd. 0
1, 1, 1, 2, 1, 2, 2, 2, 1, 5, 2, 2, 2, 2, 2, 14, 1, 2, 5, 2, 2, 18, 2, 2, 2, 7, 2, 23, 2, 2, 14, 2, 1, 26, 2, 26, 5, 2, 2, 30, 2, 2, 18, 2, 2, 286, 2, 2, 2, 9, 7, 38, 2, 2, 23, 38, 2, 42, 2, 2, 14, 2, 2, 493, 1, 44, 26, 2, 2, 50, 26, 2, 5, 2, 2, 698, 2, 50, 30, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..80.

FORMULA

a(n) = [x^n] Product_{d|n, n/d odd} 1 / (1 - x^d).

a(2^k) = 1.

MATHEMATICA

a[n_] := SeriesCoefficient[Product[1/(1 - Boole[OddQ[n/d]] x^d), {d, Divisors[n]}], {x, 0, n}]; Table[a[n], {n, 0, 80}]

PROG

(MAGMA) [1] cat [#RestrictedPartitions(n, {d:d in Divisors(n)|IsOdd(n div d)}):n in [1..80]]; // Marius A. Burtea, Sep 20 2019

CROSSREFS

Cf. A018818, A038550 (positions of 2's), A171565.

Sequence in context: A098965 A290087 A016443 * A300648 A318450 A120256

Adjacent sequences:  A327637 A327638 A327639 * A327641 A327642 A327643

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Sep 20 2019

STATUS

approved

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Last modified February 20 16:30 EST 2020. Contains 332078 sequences. (Running on oeis4.)