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).
Full version: pdf,
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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