A summation of the number of distinct prime divisors of the lcm

Abstract

Let $x$ be a positive integer. We give an asymptotic result for $\omega (\mathrm{lcm}(m,n))$ summed over all positive integers $m$ and $n$ with $mn\le x$. This answers an open question posed in a recent paper.

NOTE: This paper has now been incorporated in arXiv:2011.02254