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, i-1)+`if`(bigomega(i)=k, b(n-i, min(i-1, n-i)), 0)))
end: b(m$2)
end:
seq(a(n), n=0..100); # Alois P. Heinz, Mar 17 2018
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
Ilya Gutkovskiy, Mar 17 2018
STATUS
approved