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

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3 papers · 1 filter

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…

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

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