Arithmetic functions / József Sándor and Krassimir Todorov Atanassov.

Format:

Book

Author/Creator:

Sándor, J., author.

Todorov Atanassov, Krassimir, author.

Series:

Mathematics Research Developments

Language:

English

Subjects (All):

Arithmetic functions.

Number theory.

Physical Description:

1 online resource (256 pages)

Place of Publication:

New York, New York : Nova Science Publishers, [2021]

Summary:

"This monograph is devoted to arithmetic functions, an area of number theory. Arithmetic functions are very important in many parts of theoretical and applied sciences, and many mathematicians have devoted great interest in this field. One of the interesting features of this book is the introduction and study of certain new arithmetic functions that have been considered by the authors separately or together, and their importance is shown in many connections with the classical arithmetic functions or in their applications to other problems"-- Provided by publisher.

Contents:

Intro

ARITHMETIC FUNCTIONS

Contents

Glossary of Symbols

Preface

Chapter 1On Standard ArithmeticFunctions j,y and s

1.1. A. Mullin's Inequality and Its Modification

1.2. Inequalities Related to j, y and s-Functions

1.3. A Modification of Sivaramakrishnan-Venkataraman's Inequality

1.4. On the Composition of Some Arithmetic Functions

1.5. On the Equation j(n)+d(n) = n and RelatedInequalities

Chapter 2Perfect and Related Numbers

2.1. On (m,n)-Super-Perfect Numbers

2.2. On a Modification of Perfect Numbers

2.3. On Multiplicatively Perfect Numbers

2.4. Other Modifications of the Concept of PerfectNumber

2.5. A New Point of View on Perfect and Other SimilarNumbers

2.6. On Bi-Unitary Harmonic Numbers

2.7. On Modified Hyperperfect Numbers

2.8. On Balanced Numbers

Chapter 3On Modifications andExtensions of the ArithmeticFunctions j,y and s

3.1. On an Arithmetic Function, Related to Operation"Logarithm"

3.2. Irrational Factor: Definition, Propertiesand Problems

3.3. Converse Factor: Definition, Propertiesand Problems

3.4. Restrictive Factor: Definition, Propertiesand Problems

3.5. On an Arithmetic Function, Related to Operation"Derivative"

3.6. On an Arithmetic Function Related to Function s

3.7. Extension Factor: Definition, Propertiesand Problems

3.8. Extensions of Restrictive and Extension Factors

3.8.1. First Round of Generalizations

3.8.2. Second Round of Generalizations

3.8.3. Additive Analogues

Chapter 4Arithmetic Functions of OtherTypes

4.1. A Digital Arithmetic Function

4.2. On an Inequality of Klamkin, Its ArithmeticApplications,Modifications and Extension

4.3. Some Representations Related to Arithmetic Function"Factorial"

4.4. Some Representations Concerning the Product ofDivisors of n.

4.5. A Note on Certain Euler-Mascheroni TypeSequences

4.6. On Two Conjectures by K. Kashihara on PrimeNumbers

4.7. A Generalization of J´ozsef S´andor and FlorianLuca's Theorem

References

About the Authors

Index

Blank Page.

Notes:

Description based on print version record.

Includes index.

ISBN:

1-5361-9677-0

OCLC:

1251445596