Joshua Zelinsky

activity

20122026

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

2 citations · 2 across the 16 of their papers we have counts for

collaborators

20 papers

math.NT2026

Strongly Pseudoperfect Numbers

Audrey Wang, Joshua Zelinsky

A positive integer $n$ is said to be strongly pseudoperfect if there is a subset $S$ of the positive divisors of $n$ such that $d \in S$ if and only if $n / d \in S$ , and $\sum_{d \i…

math.GM2026

On odd perfect numbers with exactly one even exponent greater than 2

Pascal Ochem, Joshua Zelinsky

We show that if all the even exponents of an odd perfect number N are equal to 2 except for one, then $3^{23, 000, 000, 000}$ divides N .

math.NT2025

Complete characterization of $2$ -near perfect numbers with exactly 2 prime factors

Richard Fearon, Henry Foushee, Benjamin Porosoff +3

A positive integer $n$ is \emph{ $2$ -near perfect} if $σ (n) = 2 n + d_{1} + d_{2}$ for two distinct positive divisors $d_{1}, d_{2}$ of $n$ . We give a complete classification of $2$ -near perfect nu…

math.NT2025

On near superperfect numbers, the Goormaghtigh conjecture, and Mertens' theorem

Satvik Beri, Joshua Zelinsky

Let $σ (n)$ be the sum of the divisors of $n$ . Kalita and Saikia defined a number $n$ to be near superperfect if $2 n + d = σ (σ (n))$ for some positive divisor $d$ of $n$ . We extend some…

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.CO2024

Dots and Boxes on Certain Families of Graphs

Vedant Aryan, Alana Palmer, Alexander Skula +2

We investigate the Dots and Boxes game, also known as ``Strings and Coins,'' for certain specific families of graphs. These include complete graphs, wheel graphs, and friendship gr…

Strongly Pseudoperfect Numbers

On odd perfect numbers with exactly one even exponent greater than 2

Complete characterization of 2-near perfect numbers with exactly 2 prime factors

On near superperfect numbers, the Goormaghtigh conjecture, and Mertens' theorem

Kullback-Leibler divergence and primitive non-deficient numbers

Dots and Boxes on Certain Families of Graphs

Complete characterization of $2$ -near perfect numbers with exactly 2 prime factors