On the small sieve. II. sifting by composite numbers

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

For any set A of natural numbers let F(x, A) denote the number of natural numbers up to x that are divisible by no element of A and let H(x, K) be the maximum of F(x, A) when A runs over the sets not containing 1 and having a sum of reciprocals not greater than K. A logarithmic asymptotic formula is given for H(x, K)-in particular it shows H(x, K) <xε for K > K0(ε)-and some related problems are discussed.

Original languageEnglish
Pages (from-to)260-268
Number of pages9
JournalJournal of Number Theory
Volume14
Issue number2
DOIs
Publication statusPublished - 1982

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Composite number
Sieve
Natural number
Divisible
Asymptotic Formula
Logarithmic
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ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On the small sieve. II. sifting by composite numbers. / Ruzsa, I.

In: Journal of Number Theory, Vol. 14, No. 2, 1982, p. 260-268.

Research output: Contribution to journalArticle

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