

A286227


Number of compositions (ordered partitions) of n into parts with an even number of prime divisors (counted with multiplicity).


2



1, 1, 1, 1, 2, 3, 5, 7, 10, 15, 24, 36, 53, 78, 118, 179, 271, 405, 605, 907, 1366, 2055, 3086, 4628, 6948, 10440, 15689, 23560, 35371, 53110, 79771, 119821, 179958, 270243, 405833, 609495, 915394, 1374780, 2064647, 3100680, 4656676, 6993575, 10503180, 15773877, 23689467, 35577360
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OFFSET

0,5


LINKS

Amiram Eldar, Table of n, a(n) for n = 0..5000
Eric Weisstein's World of Mathematics, Prime Factor
Index entries for sequences related to compositions


FORMULA

G.f.: 1/(1  Sum_{k>=1} x^A028260(k)).


EXAMPLE

a(6) = 5 because we have [6], [4, 1, 1], [1, 4, 1], [1, 1, 4] and [1, 1, 1, 1, 1, 1].


MATHEMATICA

nmax = 45; CoefficientList[Series[1/(1  Sum[Boole[EvenQ[PrimeOmega[k]]] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]


CROSSREFS

Cf. A028260, A286219, A286223, A286225, A286226.
Sequence in context: A018133 A261081 A116975 * A134792 A300795 A033068
Adjacent sequences: A286224 A286225 A286226 * A286228 A286229 A286230


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, May 04 2017


STATUS

approved



