The Research On The Mean Value Of Smarandache Functions

In recent years, many specialists groped for unsolved problems in a book named"Only problems, Notsolutions!", and they obtained many satisfying results. In thispaper,we focused on evaluating the mean values of Smarandache related functions, Thefollowing work has been done：1.Firstly, we have studied the mean value of Zω(n)，SM(n), n~k, ψ~k(n),d~k(n) onthe simple numbers;2.Secondly, we have studied the mean value distribution of the number theoreticfunctions K(n) and ω(n) in the non-kth factor sets;3.Lastly,we have studied the average variance mean value problem involving theF.Smarandache composite function,at the same time,we have studied the mean value propertiesof the average variance of SL(n)and the number theoretic function (ω|-)(n), and wehave got two mean value formulas.