Address:
University of Tissemsilt, Faculty of Science and Technology, Algeria FIMA Laboratory, Khemis Miliana, Algeria
Khemis Miliana University (UDBKM), FIMA Laboratory, Faculty of Matter Sciences and Computer Sciences, Rue Thniet El Had, Khemis Miliana, 44225, Ain Defla Province, Algeria
E-mail: m.karras@univ-tissemsilt.dz mihoub75bouder@gmail.com
Abstract: We study the sum $\sum \limits _{abc\le x}\Omega \left( \left[ a,b,c\right] \right) $, where $\Omega (n)$ denotes the number of distinct prime divisors of $n\in \mathbb{Z}_{\ge 1}$ counted with multiplicity, and $\left[ a,b,c\right] =\operatorname{lcm}\left( a,b,c\right) $. An asymptotic formula is derived for this sum over the hyperbolic region $\left\rbrace \left( a,b,c\right) \in \mathbb{Z}_{\ge 1}^{3},\ abc\le x\right\lbrace $.
AMSclassification: primary 11A05; secondary 11A25, 11N37.
Keywords: prime divisors, hyperbolic summation, integer part.
DOI: 10.5817/AM2025-5-167