Journal of Integer Sequences, Vol. 23 (2020), Article 20.6.1

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

Hùng Việt Chu
Department of Mathematics
University of Illinois at Urbana-Champaign
Champaign, IL 61820


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 √n and find all numbers whose large divisors are in arithmetic progression. The asymptotic formula for the count of these numbers not larger than x is observed to be (x log log x)/ (log x).

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Received January 29 2020; revised version received May 10 2020; May 12 2020. Published in Journal of Integer Sequences, June 9 2020.

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