与酉最小公倍数有关的和函数  

The Sum Function Related to the Least Unitary Common Multiple

作　　者：邱雨豪 

机构地区：[1]青岛大学数学与统计学院,山东 青岛

出　　处：《理论数学》2024年第12期90-94,共5页Pure Mathematics

摘　　要：最大公因数和最小公倍数问题是数论的经典问题之一,那么对任意的正整数n,若d|n且(d,nd)=1,我们就称d是n的酉除数(unitary divisor),用[ m,n ]∗表示两个数m, n的酉最小公倍数,本文主要考虑当[ m,n ]∗≤x时,满足该条件的点(m,n)的和函数的渐近公式。The greatest common divisor and the least common multiple are one of the classical problems in number theory. For any positive integer n, if d|nand (d,nd)=1, we call d is the unitary divisor of n. In this paper, using [ m,n ]∗to represent the unitary least common multiple of two numbers m, n, and this article mainly considers the asymptotic formula of the sum function of points that satisfy this condition when [ m,n ]∗≤x.

关 键 词：最小公倍数 和函数 渐近公式 酉除数 均值估计 

分 类 号：G62[文化科学—教育学]