The Mean Value Problems Of Some Functions And All Solutions Of The Equation

In this paper,the properties of Smarandache original functions are studied by using elementary and analytical method.And the Sp*(x) of Smarandache simple func-tion,LCM fractional number sequence,the mean value problem of square root se-quence are include. Also some related indential equation and asymptotic formula are given.The main content are as follows:1.The relationship between Euler function and Smarandache function is stud-ied by using elementary and analytical method.And the solutions to corresponding equation is given.2.The mean value of square root sequence is studied by using analytical method,and the asymptotic formula is given.3.The LCM fractional number sequence is studied by using elementary method,and the formula of general term is given.4.The Sp*(x) of Smarandache simple function is by using analytical method,and the asymptotic formula is obtained.The solution of these problems helps the study to other arithmatical problems and produces some references,and makes some contributions to the research of mean value and function.