## On arithmetic numbers

Por • 30 jun, 2012 • Sección: Ambiente

Antonio M. Oller-Marcén

Abstract: An integer $n$ 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.

arXiv:1206.1823v1 [math.NT]