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A286218 Number of partitions of n into parts with an odd number of prime divisors (counted with multiplicity). 4
1, 0, 1, 1, 1, 2, 2, 3, 4, 4, 6, 7, 9, 11, 13, 16, 19, 23, 28, 33, 40, 46, 55, 65, 76, 89, 104, 121, 141, 163, 190, 219, 253, 290, 334, 383, 439, 502, 573, 653, 744, 845, 961, 1089, 1234, 1395, 1576, 1780, 2007, 2259, 2544, 2856, 3209, 3598, 4033, 4516, 5051, 5644, 6304, 7033, 7843 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Prime Factor

Index entries for related partition-counting sequences

FORMULA

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

EXAMPLE

a(8) = 4 because we have [8], [5, 3], [3, 3, 2] and [2, 2, 2, 2].

MAPLE

with(numtheory):

a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*add(

      `if`(bigomega(d)::odd, d, 0), d=divisors(j)), j=1..n)/n)

    end:

seq(a(n), n=0..80);  # Alois P. Heinz, May 04 2017

MATHEMATICA

nmax = 60; CoefficientList[Series[Product[1/(1 - Boole[OddQ[PrimeOmega[k]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A001156, A026424, A285799, A286219.

Sequence in context: A029040 A053281 A228117 * A094997 A173673 A018125

Adjacent sequences:  A286215 A286216 A286217 * A286219 A286220 A286221

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 04 2017

STATUS

approved

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Last modified May 19 08:25 EDT 2019. Contains 323389 sequences. (Running on oeis4.)