# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc:1910.43460

Acta Mathematica Hungarica, 144, (2), 353-366, 2014.12
We introduce an irrational factor of order <i>k</i> defined by I k ( n ) = i = 1 l p i i , where I k ( n ) = i = 1 l p i i is the factorization of <i>n</i> and $${\beta_{i} = \left\{\begin{array}{ll}\alpha_i, \quad \quad {\rm if} \quad \alpha_i &lt; k \\ \frac{1}{\alpha_i},\quad \quad {\rm if} \quad \alpha_i \geqq k \end{array}\right.}$$. It turns out that the function I k ( n ) = i = 1 l p i i well approximates the characteristic function of <i>k</i>-free integers. We also derive asymptotic formulas for I k ( n ) = i = 1 l p i i and I k ( n ) = i = 1 l p i i .
@inproceedings{dong2014irrational,
title={Irrational Factor of Order k and ITS Connections With k-Free Integers},
author={Dong Dong, and X Meng},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020175540805267989},
booktitle={Acta Mathematica Hungarica},
volume={144},
number={2},
pages={353-366},
year={2014},
}

Dong Dong, and X Meng. Irrational Factor of Order k and ITS Connections With k-Free Integers. 2014. Vol. 144. In Acta Mathematica Hungarica. pp.353-366. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020175540805267989.