一个新的Smarandache函数及其均值  

A new Smarandache function and its mean value

作　　者：李梵蓓[1] 

机构地区：[1]内蒙古财经学院统计与数学学院,内蒙古呼和浩特010051

出　　处：《纯粹数学与应用数学》2008年第4期682-685,共4页Pure and Applied Mathematics

基　　金：国家自然科学基金(60472068)

摘　　要：对任意正整数n≥3,我们定义算术函数C(n)为最大的正整数m≤n-2使得n|Cnm=n!/m!·(n-m)!.即就是C(n)=max{m:m≤n-2,n|Cnm},并规定C(1)=C(2)=1.本文的主要目的是利用初等及解析方法研究这一函数的均值分布问题,并给出几个有趣的均值公式及渐近式.For any positive integer n ≥ 3, we define the arithmetical function C（n） as the largest positive integer m ≤ n - 2 such that n｜Cn^m = n!/m!（n-m）!. That is, C（n） = max{m： m ≤ n- 2, n｜Cn^m}, and C（1） = C（2） = 1. In reference [9], Jozsef Sandor introduced this function, and asked us to study the properties of C（n）. About this problem, it seems that none had studied it yet, at least we have not seen any related papers before. The main purpose of this paper is using the elementary and analytic methods to study the mean value distribution problem of C（n）, and to give several interesting mean value formula and asymptotic formula for it.

关 键 词：新的Smarandache函数 均值 渐近公式 解析方法 

分 类 号：O156.4[理学—数学]