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A286226 Number of compositions (ordered partitions) of n into parts with an odd number of prime divisors (counted with multiplicity). 1
1, 0, 1, 1, 1, 3, 2, 6, 7, 10, 18, 22, 39, 54, 81, 127, 179, 282, 412, 620, 940, 1384, 2106, 3129, 4698, 7062, 10531, 15856, 23695, 35541, 53304, 79773, 119723, 179262, 268748, 402832, 603484, 904821, 1355652, 2031963, 3045374, 4563604, 6840316, 10250612, 15363248, 23024904, 34506390 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..46.

Eric Weisstein's World of Mathematics, Prime Factor

Index entries for sequences related to compositions

FORMULA

G.f.: 1/(1 - Sum_{k>=1} x^A026424(k)).

EXAMPLE

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

MATHEMATICA

nmax = 46; CoefficientList[Series[1/(1 - Sum[Boole[OddQ[PrimeOmega[k]]] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

CROSSREFS

Cf. A026424, A286218, A286222, A286224, A286227.

Sequence in context: A026211 A021310 A230267 * A269852 A293204 A273344

Adjacent sequences:  A286223 A286224 A286225 * A286227 A286228 A286229

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 04 2017

STATUS

approved

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Last modified April 20 03:36 EDT 2019. Contains 322294 sequences. (Running on oeis4.)