Rafael Jakimczuk

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 20, 2014, Number 4, Pages 77—80

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## Details

### 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 *F _{k}*(

*n*) be the number of 2 ≤

*s*≤

*n*such that

*P*(

*s*) >

*s/k*. We prove the following asymptotic formula

where

*C*is a constant defined in this article.

_{k}### 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.

## Related papers

## Cite this paper

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

ChicagoJakimczuk, Rafael. “A Note on the Greatest Common Divisor.” Notes on Number Theory and Discrete Mathematics 20, no. 4 (2014): 77-80.

MLAJakimczuk, Rafael. “A Note on the Greatest Common Divisor.” Notes on Number Theory and Discrete Mathematics 20.4 (2014): 77-80. Print.