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

Department of Mathematics

University of Illinois at Urbana-Champaign

Champaign, IL 61820

USA

**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 √*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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