Abstract:
Based on the famous Smarandache function S(n) and factor plot sequence {Pd(n)}, the function ∑n≤x(S(Pd(n-12d(n)P(n))2 is constructed and its mean value distribution properties are discussed. By using 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.
