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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.
- Greatest prime factor
- Jakimczuk, R., A note on the primes in the prime factorization of an integer, International Mathematical Forum, Vol. 7, 2012, 2005–2012.
Cite this paperAPA
Jakimczuk, R. (2014). A note on the greatest common divisor. Notes on Number Theory and Discrete Mathematics, 20(4), 77-80.Chicago
Jakimczuk, Rafael. “A Note on the Greatest Common Divisor.” Notes on Number Theory and Discrete Mathematics 20, no. 4 (2014): 77-80.MLA
Jakimczuk, Rafael. “A Note on the Greatest Common Divisor.” Notes on Number Theory and Discrete Mathematics 20.4 (2014): 77-80. Print.