OFFSET
0,5
LINKS
FORMULA
a(n) = [x^n] Product_{omega(k) = omega(n)} 1/(1 - x^k).
EXAMPLE
a(18) = 3 because we have [18], [12, 6] and [6, 6, 6], where 18, 12 and 6 are numbers that are divisible by exactly 2 different primes.
MAPLE
with(numtheory):
a:= proc(m) option remember; local k, b; k, b:= nops(factorset(m)),
proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1)+`if`(nops(factorset(i))=k, b(n-i, min(i, n-i)), 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[PrimeNu[k] == PrimeNu[n]] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 70}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 17 2018
STATUS
approved