ON THE PERMUTATION SEQUENCE AND ITS SOME PROPERTIES

The main purpose of this paper is to prove that there is no any perfect power among the permutation sequence: 12, 1342, 135642, 13578642, 13579108642...........

A NEW SEQUENCE RELATED SMARANDACHE SEQUENCES AND ITS MEAN VALUE FORMULA

Let n be any positive integer, a(n) denotes the product of all non-zero digits in base 10

ON THE SYMMETRIC SEQUENCE AND ITS SOME PROPERTIES

The main purpose of this paper is to prove that there is only one prime among the symmetric sequence

ON THE SMARANDACHE FUNCTION AND SQUARE COMPLEMENTS

The main purpose of this paper is using the elementary method to study the mean value properties of the Smarandache function, and give an interesting asymptotic formula

Two problems related to the Smarandache function

The main purpose of this paper is to study the solvability of some equations involving the pseudo Smarandache function Z(n) and the Smarandache reciprocal function Sc(n), and propose some interesting conjectures

A NUMBER THEORETIC FUNCTION AND ITS MEAN VALUE PROPERTY

Let p be a prime, n be any positive integer, a(n,p) denotes the power of p in the factorization of n!

A NUMBER THEORETIC FUNCTION AND ITS MEAN VALUE PROPERTY

Studying the asymptotic properties of a mean value, and giving an interesting asymptotic formula for it

ON THE DIVISOR PRODUCTS AND PROPER DIVISOR PRODUCTS SEQUENCES

Let n be a positive integer, Pd(n) denotes the product of all positive divisors of n, qd(n) denotes the product of all proper divisors of n

ON A PROBLEM OF F. SMARANDACHE

The main purpose of this paper is to give two exact ca:lculating formulas for A1 (x) and A2 (x)

RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (VOL. II)

The research on Smarandache Problems plays a key role in the development of number theory. Therefore, many mathematicians show their interest in the Smarandache problems and they conduct much research on them. Under such circumstances, we published the book , Vol. I, in September, 2004. That book stimulated more Chinese mathematicians to pay attention to Smarandache conjectures, open and solved problems in number theory. The First Northwest Number Theory Conference was held in Shangluo Teacher's College, China, in March 2005. One of the sessions was dedicated to the Smarandache problems. In that session, several professors gave a talk on Smarandache problems and many participants lectured on Smarandache problems both extensively and intensively. This book includes 34 papers, most of which were written by participants of the above mentioned conference. All these papers are original and have been refereed. The themes of these papers range from the mean value or hybrid mean value of Smarandache type functions, the mean value of some famous number theoretic functions acting on the Smarandache sequences, to the convergence property of some infinite series involving the Smarandache type sequences