关于正整数的k次方根数列均值

k-th Root Sequence Average Value Asymptotic Formula

设n是正整数,bk(n)表示n的k次方根取整,即正整数的k次方根部分数列.研究了数列{bk(n)}的均值性质,利用初等方法,给出了包含这个数列{bk(n)}和广义Mandoldt函数的2个有趣的渐近公式.

Let bk(n) be positive integer(n=1,2,…),that is the k-th root part.The main purpose of this paper is to study the asymptotic properties of the sequence {bk(n)}.Using the elementary method,two interesting hybrid asymptotic formulas involving this sequence {bk(n)} and the generalized Mangoldt function are given.