For any positive integer n,the new function W(n) is defined as the smallest positive integer k such thatn≤k(3k+1). That is W(n)=min {k:n≤k(3k+1) ,k ∈N}. The main purpose of this paper is to study the mean valueproperties of the composite function S(W(n)),and to give a sharper asymptotic formula by the elementary and analyticmethods.%对任意的正整数n,定义数论函数W(n)为最小的正整数k,使得n≤k (3k+1),即W(n)=min {k:n≤k(3k+1),k∈N}.利用初等及解析的方法研究复合函数S(W(n))的均值分布,并获得了较强的均值分布的渐近公式.
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