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Let P(n) be the greatest prime factor of a positive integer n ≥ 2. Let L (n) be the number of 2 ≤ k ≤ n such that P(k) > kα, where 0 < α < 1. We prove the following asymptotic formula
where ρ(α) is the Dickman’s function.
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Cite this paperAPA
Jakimczuk, R. (2013). A note on the density of the Greatest Prime Factor. Notes on Number Theory and Discrete Mathematics, 19(1), 55-58.Chicago
Jakimczuk, Rafael. “A Note on the Density of the Greatest Prime Factor.” Notes on Number Theory and Discrete Mathematics 19, no. 1 (2013): 55-58.MLA
Jakimczuk, Rafael. “A Note on the Density of the Greatest Prime Factor.” Notes on Number Theory and Discrete Mathematics 19.1 (2013): 55-58. Print.