Table of Contents
Journal of Numbers
Volume 2014, Article ID 537606, 6 pages
Research Article

On the Distribution of -Tuples of -Free Numbers

Department of Mathematics, Northwest University, Xi’an, Shaanxi 710069, China

Received 24 January 2014; Accepted 27 March 2014; Published 13 April 2014

Academic Editor: Andrej Dujella

Copyright © 2014 Ting Zhang and Huaning Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For k, being a fixed integer ≥2, a positive integer n is called k-free number if n is not divisible by the kth power of any integer >1. In this paper, we studied the distribution of r-tuples of k-free numbers and derived an asymptotic formula.