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Keywords:
prime divisors; hyperbolic summation; integer part
prime divisors; hyperbolic summation; integer part
Summary:
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 $.
References:
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