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 multiple factors multiple times.

If n = \prod_{i=1}^m p_i^{\gamma_i}, then \Omega (n) = \sum_{i=1}^m \gamma_i. For example, 24 = 23.31, so: Ω(24) = 3 + 1 = 4.

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