

A285798


Number of partitions of n into parts with an even number of distinct prime divisors.


7



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
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OFFSET

0,7


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000
Index entries for related partitioncounting sequences


FORMULA

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


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: A029193 A308052 A005858 * A321346 A291444 A219795
Adjacent sequences: A285795 A285796 A285797 * A285799 A285800 A285801


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, Apr 26 2017


STATUS

approved



