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 2007-12-16, 18:50 #1 grandpascorpion     Jan 2005 Transdniestr 503 Posts Expected Number of Factors for numbers within a ra Hello, I was wondering if there's a simple formula to estimate the number of prime factors for a number in some range say a to b. For instance, between x=900 and x=1000, the expected number of prime factors is 3.04 ~ 3.
 2007-12-16, 22:33 #2 R. Gerbicz     "Robert Gerbicz" Oct 2005 Hungary 1,429 Posts It's very well known that the expected number of different prime factors for a large positive integer N is log(log(N))+O(1), this is also true if you write multiplicity instead of different. So the answer is also log(log(b))+O(1) for your question, supposing that b is large and a isn't very close to b. You can prove this using Merten's theorem: sumprime(p=2,n,1/p)=log(log(n))+O(1) is enough for you. Last fiddled with by R. Gerbicz on 2007-12-16 at 22:35
 2007-12-17, 13:48 #3 grandpascorpion     Jan 2005 Transdniestr 503 Posts Heh, not well enough I guess. Thanks

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