Etude du graphe divisoriel 4

Pierre Mazet; Eric Saias

Etude du graphe divisoriel 4

Number Theory 2018-03-28 v1

Authors: Pierre Mazet , Eric Saias

Abstract

We show that there is a permutation $f$ of the positive integers such that for $n \geq 2,$ l.c.m. $(f(n), f(n+1)) \leq cn(\log n)^2,$ where $c$ is a positive constant. It improves previous results of Erd\"os, Freud and Hegyvari (1983), and Chen and Ji (2011).

Keywords

permutations multiplicative functions collatz conjecture

Cite

@article{arxiv.1803.10073,
  title  = {Etude du graphe divisoriel 4},
  author = {Pierre Mazet and Eric Saias},
  journal= {arXiv preprint arXiv:1803.10073},
  year   = {2018}
}

Comments

5 pages, in French

Related papers

View all related →

Combinatorics · Mathematics

A Generalisation of a Result on Monotone Arithmetic Progressions in Permutations of the Positive Integers