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arXiv · 1206.1823

On arithmetic numbers

Antonio M. Oller-Marcén
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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.

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Antonio M. Oller-Marcén. 2012-06-08. On arithmetic numbers. https://arxiv.org/abs/1206.1823

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