Basic Mathematics On The Study Of Some Arithmetic Function And Swquence Properties

The study of mean of number-theoretic function occupies a very important positionin the theory of number fields, and there are many famous number theoretic problems areclosely linked with it. In the1990s, American Romania famous number-theoretic expertprofessor F.Smarandache put forward105questions about number theory function,special sequence and other unresolved questions in the book Only Problems, NotSolutions, and it aroused the interest of many number-theoretic experts.This paper used elementary methods, analytical methods, etc. from four aspects toresearch on some of the properties of arithmetic functions and sequences.1. Summarizes the research background and significance.2. The author studied Dirichlet Series on the Smarandache LCM double factorialfunctionS n and it’s calculation of the mean.3. The author discussed the mean value properties of the Smarandache function andcomposite function L n in a simple set of numbers.4. The author studied the infinite sum of the swquence of Lucas inverse number, andhe gave an equality which containing Lucas sequence.