The Biharmonic mean
Number Theory
2016-01-14 v1
Abstract
We briefly describe some well-known means and their properties, focusing on the relationship with integer sequences. In particular, the harmonic numbers, deriving from the harmonic mean, motivate the definition of a new kind of mean that we call the biharmonic mean. The biharmonic mean allows to introduce the biharmonic numbers, providing a new characterization for primes. Moreover, we highlight some interesting divisibility properties and we characterize the semi--prime biharmonic numbers showing their relationship with linear recurrent sequences that solve certain Diophantine equations.
Cite
@article{arxiv.1601.03081,
title = {The Biharmonic mean},
author = {Marco Abrate and Stefano Barbero and Umberto Cerruti and Nadir Murru},
journal= {arXiv preprint arXiv:1601.03081},
year = {2016}
}