Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897117 | Journal of Number Theory | 2018 | 23 Pages |
Abstract
There is a large literature on the asymptotic distribution of numbers free of large prime factors, so-called smooth or friable numbers. But there is very little known about this distribution that is numerically explicit. In this paper we follow the general plan for the saddle point argument of Hildebrand and Tenenbaum, giving explicit and fairly tight intervals in which the true count lies. We give two numerical examples of our method, and with the larger one, our interval is so tight we can exclude the famous Dickman-de Bruijn asymptotic estimate as too small and the Hildebrand-Tenenbaum main term as too large.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jared D. Lichtman, Carl Pomerance,