

A301332


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


2



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
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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



