

A286225


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


3



1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 7, 9, 13, 18, 25, 34, 46, 61, 83, 112, 153, 209, 286, 387, 526, 713, 969, 1317, 1794, 2437, 3312, 4497, 6110, 8302, 11290, 15347, 20865, 28354, 38533, 52361, 71167, 96721, 131464, 178672, 242834, 330020, 448532, 609590, 828511, 1126037, 1530418, 2079977, 2826896, 3841998
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OFFSET

0,7


LINKS

Amiram Eldar, Table of n, a(n) for n = 0..7000
Eric Weisstein's World of Mathematics, Distinct Prime Factors
Index entries for sequences related to compositions


FORMULA

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


EXAMPLE

a(8) = 4 because we have [6, 1, 1], [1, 6, 1], [1, 1, 6] and [1, 1, 1, 1, 1, 1, 1, 1].


MATHEMATICA

nmax = 53; CoefficientList[Series[1/(1  Sum[Boole[EvenQ[PrimeNu[k]]] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]


CROSSREFS

Cf. A030231, A285798, A286221, A286224.
Sequence in context: A320316 A236166 A017834 * A239048 A219898 A263360
Adjacent sequences: A286222 A286223 A286224 * A286226 A286227 A286228


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, May 04 2017


STATUS

approved



