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

Hung Viet Chu

Published 2020-01-20Version 1

Iannucci considered the positive divisors of a natural number $n$ that do not exceed $\sqrt{n}$ and found all numbers whose such divisors are in arithmetic progression. In this paper, we generalize Iannucci's result by excluding the trivial divisors $1$ and $\sqrt{n}$ from consideration. In other words, we loosen the condition Iannucci put on the arithmetic progression but are still able to characterize all natural numbers whose nontrivial, small divisors are in arithmetic progression. Surprisingly, though the condition is loosened, the length of our arithmetic progression cannot exceed $5$.