Square-free values of the Carmichael function

Francesco Pappalardi, Filip Saidak, Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We obtain an asymptotic formula for the number of square-free values among p - 1, for primes p ≤ x, and we apply it to derive the following asymptotic formula for L(x), the number of square-free values of the Carmichael function λ(n) for 1 ≤ n ≤ x, L(x) = (κ + 0(1)) x/1n1-α x, where α = 0.37395... is the Artin constant, and κ = 0.80328... is another absolute constant.

Original languageEnglish
Pages (from-to)122-131
Number of pages10
JournalJournal of Number Theory
Volume103
Issue number1
DOIs
Publication statusPublished - Nov 2003

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