

A301333


Number of compositions (ordered partitions) of n into parts having the same number of prime divisors (counted with multiplicity) as n.


2



1, 1, 1, 1, 1, 3, 1, 6, 1, 1, 3, 20, 1, 46, 6, 3, 1, 232, 1, 501, 3, 10, 23, 2352, 1, 34, 52, 1, 6, 24442, 3, 53243, 1, 234, 330, 352, 1, 550863, 804, 909, 3, 2616338, 10, 5701553, 23, 3, 4622, 27077005, 1, 8811, 34, 13864, 52, 280237217, 1, 34262, 6, 54290, 68915, 2900328380, 3, 6320545915, 169615
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OFFSET

0,6


LINKS

Table of n, a(n) for n=0..62.
Index entries for sequences related to compositions


FORMULA

a(n) = [x^n] 1/(1  Sum_{bigomega(k) = bigomega(n)} x^k).


EXAMPLE

a(20) = 3 because we have [20], [12, 8] and [8, 12], where 20, 12 and 8 are numbers that are the product of exactly 3 (not necessarily distinct) primes.


MATHEMATICA

Table[SeriesCoefficient[1/(1  Sum[Boole[PrimeOmega[k] == PrimeOmega[n]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 62}]


CROSSREFS

Cf. A001222, A300982, A300983, A301331, A301332.
Sequence in context: A117782 A317855 A301331 * A213670 A116609 A124846
Adjacent sequences: A301330 A301331 A301332 * A301334 A301335 A301336


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, Mar 18 2018


STATUS

approved



