Hardy-Ramanujan Theorem

Let omega(n) be the number of distinct prime factors of n. If Psi(x) tends steadily to infinity with x, then


for almost all numbers n<x. "almost all" means here the frequency of those integers n in the interval 1<=n<=x for which


approaches 0 as x->infty.

See also

Distinct Prime Factors, Erdős-Kac Theorem

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Hardy-Ramanujan Theorem." From MathWorld--A Wolfram Web Resource.

Subject classifications