2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142227In this paper, we introduce some explicit approximations for the summation $\sum_{k\leq n}Ω(k)$, where $Ω(k)$ is the total number of prime factors of $k$.Project Report. Accepted for publication in the Sarajevo Journal of MathematicsNumber TheoryGeneral Mathematics05A10, 11A41, 26D15, 26D20text