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

Showing 2023Show all

3 papers · 1 filter

math.NT2023

Weighted Versions of the Arithmetic-Mean-Geometric Mean Inequality and Zaremba's Function

Tim McCormack, Joshua Zelinsky

We use the weighted version of the arithmetic-mean-geometric-mean inequality to motivate new results about Zaremba's function, $z (n) = \sum_{d ∣ n} \frac{l o g d}{d}$ . We investigate…

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.NT2023

A Note on a Result of Makowski

Luis H. Gallardo, Joshua Zelinsky

In this note, we fix a gap in a proof of the first author that 28 is the only even perfect number which is the sum of two perfect cubes. We also discuss the situation for higher po…