A note on the greatest common divisor

Rafael Jakimczuk
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 20, 2014, Number 4, Pages 77–80
Full paper (PDF, 150 Kb)

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Authors and affiliations

Rafael Jakimczuk
División Matemática, Universidad Nacional de Luján
Buenos Aires, Argentina

Abstract

Let k ≥ 2 a fixed positive integer. Let P(n) be the greatest prime factor of a positive integer n ≥ 2. Let Fk(n) be the number of 2 ≤ s ≤ n such that P(s) > s/k. We prove the following asymptotic formula
F_k(n)\sim C_k \frac{n}{\log n},
where Ck is a constant defined in this article.

Keywords

  • Greatest prime factor
  • Distribution

AMS Classification

  • 11A99
  • 11B99

References

  1. Jakimczuk, R., A note on the primes in the prime factorization of an integer, International Mathematical Forum, Vol. 7, 2012, 2005–2012.

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Cite this paper

Jakimczuk, R. (2014). A note on the greatest common divisor. Notes on Number Theory and Discrete Mathematics, 20(4), 77-80.

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