Global Numerical Bounds for the Number-Theoretic Omega Functions.

We obtain global explicit numerical bounds, with best possible constants, for the differences 1 n ∑ k ⩽ n ω (k) - log log n and 1 n ∑ k ⩽ n Ω (k) - log log n , where ω (k) and Ω (k) refer to the number of distinct prime divisors, and the total number of prime divisors of k, respectively. [ABSTRACT FROM AUTHOR]