On the counting function of primitive sets of integers

被引：6
|
作者：
Ahlswede, R
Khachatrian, LH
Sárközy, A
机构：
[1] Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany
[2] Eotvos Lorand Univ, Dept Algebra & Number Theory, H-1088 Budapest, Hungary
来源：
JOURNAL OF NUMBER THEORY | 1999年 / 79卷 / 02期
基金：
匈牙利科学研究基金会;
关键词：
primitive sets; Besicovitch construction; Sathe-Selberg sieve; normal number of prime factors;
D O I：
10.1006/jnth.1999.2427
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Erdos has shown that for a primitive set A subset of N Sigma(a is an element of A) 1/(a log a) < const. This implies that A(x) <x/(log log x log log log x) for infinitely many x. We prove that this is best possible apart from a factor (log log log x)(epsilon). (C) 1999 Academic Press
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页码：330 / 344
页数：15
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