On The Mean Value Estimation Of Some Smarandache Sequences And Number Theory Functions

In the " Only Problems, Not Solutions " book;Professor Florentin Smarandache,a famous scholar(1954-),proposed 105 unresolved problems in the num-ber theory. The main purpose of this text is to study the several unresolved Problems of them by using elementary and analytic methods. Specifically, the main contents of this text are as follows:1,This text studies mean value properties of the Smarandache cubic part of positive integers sequence and promote in. The mean value distribution properties of the k-th part is obtained. As a result, some interesting asymptotic formulas got.2,The hybrid mean value of the Smarandache psrudo-odd sequence and number theory functions are studied and a few more meaningful asymptotic formulas are obtained.3,This section mainly studies the mean value distribution of the non-kth factor Smarandache number in the number function, then a very good mean value formula is given.4,By studying the 21th problem of " Only Problems, Not Solutions ", the general formula are found and some interesting results are obtained.