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

Number Theory 2019-12-30 v1

Abstract

Iannucci considered the positive divisors of a natural number nn that do not exceed the square root of nn and found all numbers whose such divisors are in arithmetic progression. Continuing the work, we define large divisors to be divisors at least n\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 xx is observed to be xloglogxlogx\frac{x\log\log x}{\log x}.

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Cite

@article{arxiv.1912.11587,
  title  = {When the Large Divisors of a Natural Number Are in Arithmetic Progression},
  author = {Hung Viet Chu},
  journal= {arXiv preprint arXiv:1912.11587},
  year   = {2019}
}

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6 pages