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arXiv · 1912.11587

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

Hung Viet Chu
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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 $\frac{x\log\log x}{\log x}$.

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Hung Viet Chu. 2019-12-25. When the Large Divisors of a Natural Number Are in Arithmetic Progression. https://arxiv.org/abs/1912.11587

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