Big Omega function
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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
, then .
where ω(n) is the number of distinct prime factors of n.
For example, 24 = 23.31, so: Ω(24) = 3 + 1 = 4 and ω(24) = 2.
Ω(n) for n = 1, 2, 3, ... is 0, 1, 1, 2, 1, 2, 1, 3, 2... (sequence A001222 in OEIS)