When the Large Divisors of a Natural Number Are in Arithmetic Progression

Abstract

Iannucci considered the positive divisors of a natural number $n$ that do not exceed the square root of $n$ and found all numbers whose such divisors are in arithmetic progression. Continuing the work, we define large divisors to be divisors at least $\sqrt{n}$ and find all numbers whose large divisors are in arithmetic progression. The asymptotic formula for the count of these numbers up to a bound $x$ is observed to be $\frac{x\log\log x}{\log x}$.