关于Smarandache函数的β次混合均值

On the β-th hybrid mean value of the Smarandache function

研究了Smarandache函数与最大素因子函数P(n)之差的β次方的值分布问题.利用初等方法给出了∑n≤x(S(n)-P(n))β的一个较强的渐近公式,其中x≥3,β>1为任意实数.

The β-th value distribution problem of Smarandache function and the biggest prime divisor function is studied.By using the elementary method,the mean value formula of ∑n≤x（S（n）-P（n））β is given,with x≥3,β1 being any real number.