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

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

SMARANDACHE FUNCTION JOURNAL, 6

This journal is yearly published (in the Spring or Fall) in a 300-400 pages volume, and 800-1000 copies. SNJ is a referred journal: reviewed, indexed, cited, concerning any of Smarandache type functions, numbers, sequences, integer algorithms, paradoxes, Non-Euclidean geometries, etc

ERDOS-SMARANDACHE NUMBERS

The starting point of this article is represented by a recent work of Finch [2000]. Based on two asymptotic results concerning the Erdos function, he proposed some interesting equations concerning the moments of the· Smarandache function. The aim of this note is give a bit modified proof and to show some computation results for one of the Finch equation. We will call the numbers obtained from computation 'the Erdos-Smarandache Numbers'. The ErdosSmarandache number of order 1 is obtained to be the Golomb-Dickman constant

On the Smarandache reciprocal function and its mean value

The main purpose of this paper is using the elementary and analytic methods to study the mean value distribution properties of Sc(n), and give two interesting mean value formulas for it

SMARANDACHE FUNCTION JOURNAL, 4-5

This journal is yearly published (in the Spring or Fall) in a 300-400 pages volume, and 800-1000 copies. SNJ is a referred journal: reviewed, indexed, cited, concerning any of Smarandache type functions, numbers, sequences, integer algorithms, paradoxes, Non-Euclidean geometries, etc

On the mean value of SSMP(n) and SIMP(n)1

The main purpose of this paper it to studied the mean value properties of the Smarandache Superior m-th power part sequence SSMP(n) and the Smarandache Inferior m-th power part sequence SIMP(n), and give several interesting asymptotic formula for them