Big Omega function

Big Omega function

The notation Ω( ) has two meanings in mathematics:

* "f" = Ω("g") means that the function "f" dominates "g" in some limit, see Big O notation.

* Ω("n") is the total number of prime factors of "n", counting prime factors with multiplicity.

If

n = prod_{i=1}^{omega(n)} p_i^{alpha_i},thenOmega(n) = sum_{i=1}^{omega(n)} alpha_i.

where {omega(n)} is the number of distinct prime factors of n.

For example, 24=2^3.3^1, so: Omega(24)=3+1=4 and omega(24)=2.

Ω("n") for n = 1, 2, 3, ... is 0, 1, 1, 2, 1, 2, 1, 3, 2... OEIS|id=A001222


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