

A300982


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


7



1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 2, 6, 1, 9, 3, 2, 1, 17, 1, 23, 2, 4, 7, 40, 1, 7, 10, 1, 3, 87, 2, 111, 1, 17, 25, 21, 1, 219, 34, 34, 2, 336, 4, 413, 7, 2, 73, 614, 1, 87, 7, 103, 10, 1083, 1, 149, 3, 176, 206, 1850, 2, 2198, 281, 7, 1, 344, 18, 3630, 25, 479, 22, 5007, 1, 5861, 725, 13
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OFFSET

0,6


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000
Index entries for sequences related to partitions


FORMULA

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


EXAMPLE

a(20) = 2 because we have [20] and [12, 8], where 20, 12 and 8 are numbers that are the product of exactly 3 (not necessarily distinct) primes.


MAPLE

with(numtheory):
a:= proc(m) option remember; local k, b; k, b:= bigomega(m),
proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i1)+`if`(bigomega(i)=k, b(ni, min(i, ni)), 0)))
end: b(m$2)
end:
seq(a(n), n=0..80); # Alois P. Heinz, Mar 17 2018


MATHEMATICA

Table[SeriesCoefficient[Product[1/(1  Boole[PrimeOmega[k] == PrimeOmega[n]] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 75}]


CROSSREFS

Cf. A001222, A300977, A300978, A300979, A300980, A300983.
Sequence in context: A297381 A051793 A065371 * A186007 A212623 A229214
Adjacent sequences: A300979 A300980 A300981 * A300983 A300984 A300985


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, Mar 17 2018


STATUS

approved



