The Study Of Some Problems Involving The Mean Value Of The Smarandache Function

It is well known that the problems of the mean value on arithmetical function playan important role in the study of number theory. At home and abroad, some scholars andresearchers had studied them deeply, and obtained a lot of very meaningful results，andpromoting the subject of number theory advancing all the time.In1991, Professor Florentin Smaradache who is an American Romania famousmathematician, proposed105unsolved problems and conjectures about specialsequences, arithmetic function in his book“Only Problems, Not Solutions”.Based on theinterest of the Smarandache function, the dissertation makes researches on the propertiesand some equations about the Smrandache functions by using the elementary andanalytic ways. The main achievements contained in this dissertation are as follows:1. Studying the asymptotic properties of the Smarandache square complementsfunctions relate to simple numbers;2. Studying the hybrid mean values of the Smarandache square complementsfunctions and SL(n)﹑SM(n);3. Studying the solutions of the equation about the Smarandache squarecomplements functions and SL(n);4. Studying the hybrid mean values of the largest triangle number less than or equalto n and SSC(n)﹑SM(n).