一个F.Smarandache函数与最大素因子函数的均值计算

摘要

Based on the famous Smarandache function S (n) and factor plot sequence qd (n) . the function ∑n≤x (S(qd(n))-(1/2d(n)-1)p(n))2 is constructed and its mean value distribution properties are discussed. Byusing the elementary method and the prime theorem, the hybrid mean value involving an arithmetical function and the greatest prime divisor function is proved, and a sharp asymptotic formula is also given.%在F.Smarandache函数S(n)及真因子序列｛qd(n)｝的基础上,构造并研究了∑n≤x(S(qd(n))-(1—2d(n)-1)p(n))2的一种均值性质,利用初等方法和素数定理证明了关于一个算术函数与最大素因子函数的混合均值问题,并给出了它的一个较强的渐进公式.