Joshua Zelinsky

activity

20172025

most citedAn improvement of an inequality of Ochem and Rao concerning odd perfect numbers

2 citations · 2 across the 4 of their papers we have counts for

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6 papers · 1 filter

math.NT2025

Kullback-Leibler divergence and primitive non-deficient numbers

Joshua Zelinsky, Kyle Zhang

Let $H (n) = \prod_{p ∣ n} \frac{p}{p - 1}$ where $p$ ranges over the primes which divide $n$ . It is well known that if $n$ is a primitive non-deficient number, then $H (n) > 2$ . We exami…

math.NT2023

On 2-Near Perfect Numbers

Vedant Aryan, Dev Madhavani, Savan Parikh +2

Let $σ (n)$ be the sum of the positive divisors of $n$ . A number $n$ is said to be 2-near perfect if $σ (n) = 2 n + d_{1} + d_{2}$ , where $d_{1}$ and $d_{2}$ are distinct positive divisors of…

math.NT2022

Upper Bounds on Integer Complexity

Joshua Zelinsky

Define $∣∣ n ∣∣$ to be the \emph{complexity} of $n$ , which is the smallest number of $1$ s needed to write $n$ using an arbitrary combination of addition and multiplication. John Self…

math.NT2018

On the number of total prime factors of an odd perfect number

Joshua Zelinsky

Let $N$ be an odd perfect number. Let $ω (N)$ be the number of distinct prime factors of $N$ and let $Ω (N)$ be the total number of prime factors of $N$ . We prove that if $(3, N) = 1$ ,…

math.NT2018

Upper bounds on the second largest prime factor of an odd perfect number

Joshua Zelinsky

Acquaah and Konyagin showed that if $N$ is an odd perfect number where $N = p_{1}^{a_{1}} p_{2}^{a_{2}} \dots p_{k}^{a_{k}}$ where $p_{1} < p_{2} \dots < p_{k}$ then one must have $p_k < 3^{1/3}N^{1…

math.NT2017★ 2 cited

An improvement of an inequality of Ochem and Rao concerning odd perfect numbers

Joshua Zelinsky

Let $Ω (n)$ denote the total number of prime divisors of $n$ (counting multiplicity) and let $ω (n)$ denote the number of distinct prime divisors of $n$ . Various inequalities have be…