A301333 Number of compositions (ordered partitions) of n into parts having the same number of prime divisors (counted with multiplicity) as n.

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

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 * A347231 A213670 A116609

Adjacent sequences: A301330 A301331 A301332 * A301334 A301335 A301336

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 18 2018

Status

approved