On $k$-Lehmer numbers

Antonio M. Oller-Marcén; José María Grau

On $k$-Lehmer numbers

Number Theory 2012-03-23 v2

Authors: Antonio M. Oller-Marcén , José María Grau

Abstract

Lehmer's totient problem consists of determining the set of positive integers $n$ such that $\varphi(n)|n-1$ where $\varphi$ 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 $\varphi(n)|(n-1)^k$ . 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.

Cite

@article{arxiv.1012.2337,
  title  = {On $k$-Lehmer numbers},
  author = {Antonio M. Oller-Marcén and José María Grau},
  journal= {arXiv preprint arXiv:1012.2337},
  year   = {2012}
}

On $k$-Lehmer numbers

Abstract

Cite

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