

A286222


Number of partitions of n into distinct parts with an odd number of prime divisors (counted with multiplicity).


3



1, 0, 1, 1, 0, 2, 0, 2, 2, 1, 3, 2, 3, 4, 3, 5, 4, 5, 7, 6, 10, 8, 10, 12, 10, 15, 14, 16, 20, 18, 25, 25, 28, 32, 31, 38, 38, 44, 49, 51, 59, 61, 68, 75, 79, 89, 93, 103, 113, 120, 137, 141, 157, 168, 176, 200, 205, 229, 245, 260, 289, 303, 332, 356, 376, 411, 433, 470, 507, 535, 587
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OFFSET

0,6


LINKS

Amiram Eldar, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Prime Factor
Index entries for related partitioncounting sequences


FORMULA

G.f.: Product_{k>=1} (1 + x^A026424(k)).


EXAMPLE

a(10) = 3 because we have [8, 2], [7, 3] and [5, 3, 2].


MATHEMATICA

nmax = 70; CoefficientList[Series[Product[1 + Boole[OddQ[PrimeOmega[k]]] x^k, {k, 1, nmax}], {x, 0, nmax}], x]


CROSSREFS

Cf. A026424, A286218, A286220, A286223.
Sequence in context: A003823 A059451 A083817 * A029273 A117963 A321594
Adjacent sequences: A286219 A286220 A286221 * A286223 A286224 A286225


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, May 04 2017


STATUS

approved



