On the Counting Function of Primitive Sets of Integers

Rudolf Ahlswede, Levon H. Khachatrian, András Sárközy

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Erdos has shown that for a primitive set A⊂N ∑a∈A1/(aloga)<const. This implies that A(x)<x/(loglogxlogloglogx) for infinitely many x. We prove that this is best possible apart from a factor (logloglogx)ε

Original languageEnglish
Pages (from-to)330-344
Number of pages15
JournalJournal of Number Theory
Volume79
Issue number2
DOIs
Publication statusPublished - Dec 1 1999

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Keywords

  • Primitive sets; Besicovitch construction; Sathe-Selberg sieve; normal number of prime factors

ASJC Scopus subject areas

  • Algebra and Number Theory

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