The Mean Value Of Smarandache Function And Some Number Theoretic Functions

The mean value problems of arithmetical functions play an important role inthe study of analytic number theory, and they relate to many famous numbertheoretic problems. In1991, American-Romanian number theorist FlorentinSmarandache published a book named”Only problems, Not solutions”, hepresented105unsolved arithmetical problems and conjectures and these functionsand sequences in it, greatly aroused the interest of scholars.With the intrest, we use elementary and analytic methods to study the meanvalue properties of Smarandache function and some arithmetical functions asfollows:1. This chapter gives the article needed to research the background andsignificance of the topic, describes the study of the status at home and abroad, andthen gives some of the major result of research for this paper has done a study onthe bedding.2. This chapter is to study the hybrid mean value of Smarandache functionsand some arithmetical functions on Simple Numbers and some asymptotic formulasare obtained.3. This chapter is to study the hybrid mean value problem involving theF.Smarandache LCM function and the prime factor sum function n, finally givesome sharper asymptotic formulas.4. This chapter defines a new function, and is to study the mean valueproperties of tow composite function that contains this function. Then, some goodresults are obtained.Graduate:Zhao Qin(Pure Mathematics)Directed by:Professor Gao Li...