2010/12/10 by Antonio M. Oller‐Marcén, Antonio M. Oller-Marcén, Oller-Marcén, Antonio M. +2
Mathematics · #11A25 #11B99 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A25 #msc:11B99
paper · pdf · doi:10.48550/arxiv.1012.2337
openalex publication_date 2010/12/10 · arxiv created 2012/03/22 · arxiv updated 2012/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Lehmer's totient problem consists of determining the set of positive integers n such that φ(n)|n-1 where φ is Euler's totient function. In this paper we introduce the concept of k-Lehmer number. A k-Lehmer number is a composite number such that φ(n)|(n-1)k. The relation between k-Lehmer numbers and Carmichael numbers leads to a new characterization of Carmichael numbers and to some conjectures related to the distribution of Carmichael numbers which are also k-Lehmer numbers.