On the small sieve. II. sifting by composite numbers

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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 - Apr 1982

ASJC Scopus subject areas

  • Algebra and Number Theory

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