关于2个算术函数的一个混合均值

A Hybrid Mean Value of Two Arithmetical Functions

设素数p,ep(n)表示整除n的p最大指数,即ep(n)=max{α∶pα|n}.对任意正整数n,k≥2为给定整数,Smarandache Ceil函数的对偶函数Sk(n)=max{x∶x N,xk|n},利用解析的方法,研究了算术函数ep(n)Sk(n)均值分布性质,并给出一个渐近公式.

In the report,let p be a prime,ep( n) denote the largest exponent of power p which divide n,ep( n) = max{ α∶ pα| n}. For any positive integer n,k be a fixed positive integer with k≥2,a dual function of Smarandache Ceil function is Sk( n) = max{ x∶ x N,xk| n}. The analytic method was used to study the mean value distribution properties of ep( n) Sk( n),and an interesting asymptotic formula was proposed.