English

On arithmetic numbers

Number Theory 2012-06-11 v1

Abstract

An integer nn is said to be \textit{arithmetic} if the arithmetic mean of its divisors is an integer. In this paper, using properties of the factorization of values of cyclotomic polynomials, we characterize arithmetic numbers. As an application, in Section 2, we give an interesting characterization of Mersenne numbers.

Keywords

Cite

@article{arxiv.1206.1823,
  title  = {On arithmetic numbers},
  author = {Antonio M. Oller-Marcén},
  journal= {arXiv preprint arXiv:1206.1823},
  year   = {2012}
}
R2 v1 2026-06-21T21:16:29.293Z