An Arithmetic Function and the k-th Power Part of a Positive Integer

被引：0

作者：

Wang, Mingjun ^{[1
]}

机构：

[1] Weinan Teachers Univ, Dept Math & Informat Sci, Weinan 714000, Shannxi, Peoples R China

来源：

MECHATRONICS AND INTELLIGENT MATERIALS II, PTS 1-6 | 2012年 / 490-495卷

关键词：

Arithmetic function; Mean value; Asymptotic formula; k-th power;

D O I：

10.4028/www.scientific.net/AMR.490-495.1941

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

For any positive integer n,a(n) denotes the largest k-th: power less than or equal ton,and b(n) denotes the smallest k-th power greater than or equal ton. Let p be a prime, e(p)(n) denotes the large exponent of power p which divides n. In this paper we use elementary method to study the mean value properties of e(p)(a(n)) and e(p)(b(n)),and give two interesting asymptotic formulas.

引用

页码：1941 / 1944

页数：4