一个数论函数均值余项的改进

Improvement of the Error Term on the Mean Value of an Arithmetical Function

设p为素数,ep(n)表示的标准分解式中p的指数,设d(n)为Dirichlet除数函数。应用初等方法得到了n≤xep(n)d(n)的一个更加精确的均值公式,从而改进了相关文献中的对应结果。

Let be a prime, denote the large exponent of power which divides. Then let be the divisor function. Using elementary method the precise mean value formala of ∑n≤xep（n）d（n） was obtained, the results of the referenee were improved.