An algorithm for counting smooth integers
- Authors: Ishmukhametov S.1, Sharifullina F.1
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Affiliations:
- Kazan Federal University
- Issue: Vol 37, No 2 (2016)
- Pages: 128-137
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/197396
- DOI: https://doi.org/10.1134/S1995080216020062
- ID: 197396
Cite item
Abstract
An integer number n > 0 is called y-smooth for y > 0 if any prime factor p of n satisfies p ≤ y. Let ψ(x, y) be the number of all y-smooth integers less or equal to x. In this paper we elaborate a new algorithm for approximate calculation of ψ(x, y) at large x and relatively small y < log x.
About the authors
S. Ishmukhametov
Kazan Federal University
Author for correspondence.
Email: ishm@nextmail.ru
Russian Federation, Kremlevskaya ul. 18, Kazan, 420111
F. Sharifullina
Kazan Federal University
Email: ishm@nextmail.ru
Russian Federation, Kremlevskaya ul. 18, Kazan, 420111