Randell Heyman

activity

20172021

collaborators

6 papers

math.NT2021

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

Randell Heyman

Let $x$ be a positive integer. We give an asymptotic result for $ω (lcm (m, n))$ summed over all positive integers $m$ and $n$ with $mn \leq x$ . This answers an open que…

math.NT2020

On certain sums of arithmetic functions involving the gcd and lcm of two positive integers

Randell Heyman, László Tóth

We obtain asymptotic formulas with remainder terms for the hyperbolic summations $\sum_{mn \leq x} f ((m, n))$ and $\sum_{mn \leq x} f ([m, n])$ , where $f$ belongs to certain classes of ar…

math.NT2020

A summation involving the number of divisors function and the GCD function

Randell Heyman

Let $N$ be a positive number. We give an asymptotic formula for the sum of $τ (g cd (a, b))$ for all $a$ and $b$ with $ab \leq N$ .

math.NT2019

Cardinality of a floor function set

Randell Heyman

Fix a positive integer X. We quantify the cardinality of the set ${⌊ X / n ⌋}_{n = 1}^{X}$ . We discuss restricting the set to those elements that are prime, semiprime or si…

math.NT2018

On a sum involving the Euler function

Olivier Bordellès, Lixia Dai, Randell Heyman +2

We obtain reasonably tight upper and lower bounds on the sum $\sum_{n ⩽ x} φ (⌊ x / n ⌋)$ , involving the Euler functions $φ$ and the integer…

math.NT2017

Tuples of polynomials over finite fields with pairwise coprimality conditions

Juan Arias de Reyna, Randell Heyman

Let $q$ be a prime power. We estimate the number of tuples of degree bounded monic polynomials $(Q_{1}, \dots, Q_{v}) \in (F_{q} [z])^{v}$ that satisfy given pairwise coprimality co…