Rafael Jakimczuk
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 20, 2014, Number 4, Pages 77—80
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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
where Ck is a constant defined in this article.
Keywords
- Greatest prime factor
- Distribution
AMS Classification
- 11A99
- 11B99
References
- 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.