关于新Smarandache函数的部分数列

On the New of Smarandache Factorial Par Series

对任意正整数n,设Sp(x)表示不小于素数p的x幂的最大m阶乘部分,Sp*(x)表示不超过素数p的x幂的最小m阶乘部分。利用初等方法研究了{Sp(x)}和{Sp*(x)}这两个数列的性质,并给出由两个数列构成的行列式的一些特殊性质。

Let n be a positive integer,ak（n）be the largest m factorial number greater than or equal to p of the m-th power,and bk（n）be the smallest m factorial number less than or equal to p of the m-th power.The main purpose is using the elementary method to study the convergent property of an infinite series involving the inferior and superior factorial part sequences,and give two sufficient condition of the convergent property of the series.