A301332 Number of compositions (ordered partitions) of n into parts having the same number of distinct prime divisors as n.

1, 1, 1, 1, 2, 3, 1, 8, 11, 19, 1, 47, 2, 116, 1, 1, 460, 724, 4, 1820, 4, 3, 6, 11482, 10, 28821, 11, 72338, 16, 181549, 1, 455647, 721847, 18, 44, 14, 67, 7203907, 82, 49, 119, 45380392, 1, 113898439, 223, 141, 326, 717490903, 472, 1800800888, 614, 407, 884, 11343951113, 1268, 790, 1692, 1185

Offset

0,5

Links

Table of n, a(n) for n=0..57.

Index entries for sequences related to compositions

Formula

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

Example

a(18) = 4 because we have [18], [12, 6], [6, 12] and [6, 6, 6], where 18, 12 and 6 are numbers that are divisible by exactly 2 different primes.

Mathematica

Table[SeriesCoefficient[1/(1 - Sum[Boole[PrimeNu[k] == PrimeNu[n]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 57}]

Crossrefs

Cf. A001221, A300979, A300980, A301331, A301333.

Sequence in context: A106033 A121634 A006015 * A110292 A138672 A103749

Adjacent sequences: A301329 A301330 A301331 * A301333 A301334 A301335

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 18 2018

Status

approved