ROUGH INTEGERS WITH A DIVISOR IN A GIVEN INTERVAL

被引：3

作者：

Ford, Kevin ^{[1
]}

机构：

[1] Univ Illinois, Dept Math, 1409 West Green St, Urbana, IL 61801 USA

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2021年 / 111卷 / 01期

基金：

美国国家科学基金会;

关键词：

divisors; Farey fractions;

D O I：

10.1017/S1446788719000442

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We determine, up to multiplicative constants, the number of integers n <= x that have a divisor in (y, 2y] and no prime factor <= w. Our estimate is uniform in x, y, w. We apply this to determine the order of the number of distinct integers in the N x N multiplication table, which are free of prime factors <= w, and the number of distinct fractions of the form (a(1)a(2))=(b(1)b(2)) with 1 <= a(1) <= b(1) <= N and 1 <= a(2) <= b(2) <= N.

引用

页码：17 / 36

页数：20