关于广义Smarandache和的均值

On the Mean Value of the Smarandache Summands

利用初等方法、解析方法和高斯取整函数的性质,研究广义Smarandache和函数S(n,m,k)的均值性质,给出一个有趣的渐近公式.

Let n,k1 are two positive integers.m≥0 is another fixed integer.The general Smarandache Summands function S（n,m,k） is defined by S（n,m,k）=∑[（n＋m）/k]i=0（n-ki）.The main purpose of this paper is using the elementary method,analytic method and the properties of the Gauss function to study the mean value properties of S（n,m,k）,and give an interesting asymptotic formula for it.