标题:On the smooth values of shifted almost-primes
作者:Lu, Xiaodong; Wang, Zhiwei; Chen, Bin
作者机构:[Lu, Xiaodong] Yangzhou Univ, Sch Math Sci, Yangzhou 225002, Jiangsu, Peoples R China.; [Wang, Zhiwei; Chen, Bin] Shandong Univ, Sch Math, Jinan 250 更多
通讯作者:Wang, ZW;Wang, ZW
通讯作者地址:[Wang, ZW]Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China;[Wang, ZW]Univ Lorraine, Inst Elie Cartan Lorraine, BP 70239, F-54506 Vando 更多
来源:INTERNATIONAL JOURNAL OF NUMBER THEORY
出版年:2019
卷:15
期:1
页码:1-9
DOI:10.1142/S1793042118501683
关键词:Shifted almost-primes; friable numbers; largest prime factor; sieve; methods
摘要:Denote by P+ (n) (respectively, P- (n)) the largest (respectively, the smallest) prime factor of the integer n >= 1. In this paper, we prove a lower bound of almost-primes n <= x with P- (n) > x(1/v),v > 4 such that P+ (n - a) <= x(1/u) for 1 <= u << 1,a is an element of Z, a not equal 0. As an application, we study two patterns on the largest prime factors of consecutive integers with one of which without small prime factor.
收录类别:SCOPUS;SCIE
资源类型:期刊论文
原文链接:https://www.scopus.com/inward/record.uri?eid=2-s2.0-85053003497&doi=10.1142%2fS1793042118501683&partnerID=40&md5=87de2836cf0d07fca1eb411e979f0704
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