When the Nontrivial, Small Divisors of a Natural Number are in Arithmetic Progression

Abstract

Iannucci considered the positive divisors of a natural number $n$ that do not exceed $\sqrt{n}$ and found all forms of numbers whose such divisors are in arithmetic progression. In this paper, we generalize Iannucci's result by excluding the trivial divisors $1$ and $\sqrt{n}$ (when $n$ is a square). Surprisingly, the length of our arithmetic progression cannot exceed $5$.

arXiv comment8 pages. Edited according to anonymous referees' suggestions. To appear in Quaestiones Mathematicae