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} , then Omega(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...

Search another word or see Big Omega functionon Dictionary | Thesaurus |Spanish
Copyright © 2014 Dictionary.com, LLC. All rights reserved.
  • Please Login or Sign Up to use the Recent Searches feature
FAVORITES
RECENT

;