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 √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 √n (when n is a square). Surprisingly, the length of our arithmetic progression cannot exceed 5.