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On arithmetic numbers
Author(s) -
OllerMarcén Antonio M.
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400085
Subject(s) - mathematics , mersenne prime , arithmetic , integer (computer science) , arithmetic progression , cyclotomic polynomial , prime factor , factorization , discrete mathematics , prime (order theory) , combinatorics , algorithm , polynomial , mathematical analysis , computer science , programming language
An integer n is said to be 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, we give an interesting characterization of Mersenne numbers.