Research On Smarandache Function And Its Related Function

The number theoretic function is an important part of number theory.Wherein,Smarandache question is a hot topic in recent years on study of number theory,Smarandache problem not only Smarandache function, but also extends the concept of a pseudo-Smarandache function and the like;Dedekind function as a special number theoretic function,but few scholars to study.Therefore, this article focuses on some of the arithmetic properties of some number theoretic function were studied, it can be summarized as the following main aspects:1.Using the elementary methods to study under the Smarandache function in a special series ofp pa ?b Bound estimate, get a good asymptotic formula.2. Using the elementary and analytical techniques to study the pseudo-Smarandache function on a number of columns andp pa +b get the lower bound estimate; hybrid mean pseudo Smarandache function and the divisor function; construct the equation of the pseudo Smarandache function and Euler function constituted and get two more interesting asymptotic formula is given for all positive odd solution to the equation.3.Using multiplicative function definition, perron formula and analytical skills to research multiplicative function ??n? on the function complex multiplier three can mean, and obtained by calculating three more meaningful asymptotic formula.