On primitive sets of squarefree integers

R. Ahlswede, L. Khachatrian, A. Sárközy

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Abstract

Let ℙN (resp. ℙ*N) be the family of the primitive subsets of {1, 2, . . . , N} (resp. the squarefree integers not exceeding N). We prove the following conjecture (even in a more general form) of Pomerance and Sárközy maxA∈ℙ*Na∈A1/a = (1 + o(1))6/π2 log N/(2π log log N)1/2 as N → ∞. In a new direction we obtain surprisingly sharp estimates for maxA∈ℙ*N |A|. As a common generalization we present conjectures about F(σ) = lim N→∞ (maxA∈ℙ*Na∈A1/aσ)/(maxA∈ℙNa∈A1/aσ).

Original languageEnglish
Pages (from-to)99-115
Number of pages17
JournalPeriodica Mathematica Hungarica
Volume42
Issue number1-2
Publication statusPublished - Dec 1 2001

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Keywords

  • Density estimates
  • Primitive sets
  • Squarefree numbers

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Ahlswede, R., Khachatrian, L., & Sárközy, A. (2001). On primitive sets of squarefree integers. Periodica Mathematica Hungarica, 42(1-2), 99-115.