Adrian W. Dudek

activity

20152026

collaborators

3 papers

math.NT2026

An Explicit Result for the Sum of Two Almost Primes

Adrian Dudek, Lachlan Dunn

We show that every $N \geq 2$ can be written as the sum of positive integers $a$ and $b$ where $Ω (ab) \leq 40$ . The result is obtained through the direct application of an explicit…

math.NT2018

Note on the number of divisors of reducible quadratic polynomials

Adrian W. Dudek, Łukasz Pańkowski, Victor Scharaschkin

In a recent paper, Lapkova uses a Tauberian theorem to derive the asymptotic formula for the divisor sum $\sum_{n \leq x} d (n (n + v))$ where $v$ is a fixed integer and $d (n)$ denot…

math.NT2015

On the Distribution of Products of Primes and Powers

Adrian Dudek

We prove several results regarding the distribution of numbers that are the product of a prime and a $k$ -th power. First, we prove an asymptotic formula for the counting function o…