四川师范大学学报（自然科学版）2017，Vol.40Issue(1)：1-10,10.DOI:10.3969/j.issn.1001-8395.2017.01.001
Smarandache函数的准确计算公式以及相关数论方程的求解
The Explicit Formula for the Smarandache Functionand Solutions of Related Equations
摘要
Abstract
Let φ(n) and S(n) be the Euler function and Smarandache function for a positive integer n,respectively.By using elementary methods and techniques,the explicit formula for S(pα) is obtained,where p is a prime and α is a positive integer.As a corollary,some properties for positive integer solutions of the equations φ(n)=S(nk) or σ(2αq)/S(2αq) are given,where q is an odd prime and σ(n) is the sum of different positive factors for n.关键词
Smarandache函数/欧拉函数/高斯函数/完全数Key words
Smarandache function/Euler function/Gauss function/perfect number分类
数理科学引用本文复制引用
廖群英,罗文力..Smarandache函数的准确计算公式以及相关数论方程的求解[J].四川师范大学学报（自然科学版）,2017,40(1):1-10,10.基金项目
This work is supported by National Natural Science Foundation of China (No.11401408) and Project of Science and TechnologyDepartment of Sichuan Province (No.2016JY0134) （No.11401408）
国家自然科学基金(11401408)和四川省科技厅研究项目(2016JY0134) （11401408）
