

A300983


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


7



1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 2, 1, 3, 2, 2, 1, 5, 1, 5, 2, 1, 2, 7, 2, 9, 1, 4, 6, 9, 1, 11, 6, 10, 2, 14, 2, 15, 1, 2, 12, 19, 1, 18, 5, 16, 2, 26, 1, 24, 2, 23, 26, 35, 2, 39, 31, 3, 1, 40, 4, 50, 6, 49, 9, 61, 1, 67, 68, 7, 6, 70, 10, 87, 2, 1, 93, 102, 2, 107
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OFFSET

0,6


LINKS



FORMULA

a(n) = [x^n] Product_{bigomega(k) = bigomega(n)} (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`(i*(i+1)/2<n, 0, `if`(n=0, 1,
b(n, i1)+`if`(bigomega(i)=k, b(ni, min(i1, ni)), 0)))
end: b(m$2)
end:


MATHEMATICA

Table[SeriesCoefficient[Product[(1 + Boole[PrimeOmega[k] == PrimeOmega[n]] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 85}]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



