Definitions

# 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

$n = prod_\left\{i=1\right\}^\left\{omega\left(n\right)\right\} p_i^\left\{alpha_i\right\}$ , then $Omega\left(n\right) = sum_\left\{i=1\right\}^\left\{omega\left(n\right)\right\} alpha_i$.

where $\left\{omega\left(n\right)\right\}$ is the number of distinct prime factors of n.

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

Ω(n) for n = 1, 2, 3, ... is 0, 1, 1, 2, 1, 2, 1, 3, 2...

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