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A286224 Number of compositions (ordered partitions) of n into parts with an odd number of distinct prime divisors. 2
1, 0, 1, 1, 2, 3, 4, 8, 11, 19, 28, 47, 72, 116, 182, 289, 460, 724, 1153, 1820, 2891, 4572, 7249, 11482, 18190, 28821, 45651, 72338, 114582, 181549, 287597, 455647, 721849, 1143590, 1811753, 2870247, 4547245, 7203933, 11412922, 18080907, 28644799, 45380602, 71894401, 113899027, 180444897, 285870668 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..45.

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^A030230(k)).

EXAMPLE

a(6) = 4 because we have [4, 2], [3, 3], [2, 4] and [2, 2, 2].

MATHEMATICA

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

CROSSREFS

Cf. A030230, A285799, A286220, A286225.

Sequence in context: A046812 A269797 A280195 * A245388 A164573 A004045

Adjacent sequences:  A286221 A286222 A286223 * A286225 A286226 A286227

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 04 2017

STATUS

approved

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Last modified March 21 20:25 EDT 2019. Contains 321382 sequences. (Running on oeis4.)