

A286221


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


4



1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 4, 4, 2, 3, 4, 4, 5, 6, 5, 5, 6, 7, 9, 10, 10, 12, 11, 11, 15, 16, 15, 17, 18, 19, 23, 26, 25, 27, 30, 33, 37, 38, 39, 46, 50, 52, 57, 59, 61, 71, 77, 78, 84, 91, 97, 107, 114, 120, 131, 139, 147, 163, 172, 180, 197
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OFFSET

0,16


LINKS

Table of n, a(n) for n=0..75.
Eric Weisstein's World of Mathematics, Distinct Prime Factors
Index entries for related partitioncounting sequences


FORMULA

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


EXAMPLE

a(21) = 4 because we have [21], [20, 1], [15, 6] and [14, 6, 1].


MATHEMATICA

nmax = 75; CoefficientList[Series[Product[1 + Boole[EvenQ[PrimeNu[k]]] x^k, {k, 1, nmax}], {x, 0, nmax}], x]


CROSSREFS

Cf. A030231, A285798, A286220.
Sequence in context: A029282 A289494 A029286 * A321347 A324383 A050333
Adjacent sequences: A286218 A286219 A286220 * A286222 A286223 A286224


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, May 04 2017


STATUS

approved



