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A285798 Number of partitions of n into parts with an even number of distinct prime divisors. 5
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 5, 5, 6, 7, 8, 8, 11, 11, 14, 16, 19, 19, 25, 26, 31, 34, 40, 41, 51, 53, 62, 68, 80, 85, 103, 107, 124, 135, 157, 166, 195, 205, 235, 256, 294, 311, 362, 383, 437, 472, 535, 568, 652, 695, 786, 847, 954, 1016, 1155, 1231, 1381, 1486, 1662, 1774, 1997, 2130, 2377, 2557, 2846 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Index entries for related partition-counting sequences

FORMULA

G.f.: Product_{k>=1} 1/(1 - x^A030231(n)).

EXAMPLE

a(10) = 3 because we have [10], [6, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

MATHEMATICA

nmax = 70; CoefficientList[Series[Product[1/(1 - Boole[EvenQ[PrimeNu[k]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A030231, A087153 (number of partitions into parts with an even number of divisors), A285799.

Sequence in context: A269333 A029193 A005858 * A291444 A219795 A082602

Adjacent sequences:  A285795 A285796 A285797 * A285799 A285800 A285801

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 26 2017

STATUS

approved

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Last modified October 16 23:12 EDT 2018. Contains 316275 sequences. (Running on oeis4.)