Arithmetic Functions

✍ Scribed by József Sándor; Krassimir Todorov Atanassov

• Publisher: Nova Science Publishers
• Year: 2021
• Tongue: English
• Leaves: 255
• Category: Library

✦ Synopsis

"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"--

✦ Table of Contents

ARITHMETIC FUNCTIONS
ARITHMETIC FUNCTIONS
Contents
Glossary of Symbols
Preface
Chapter 1 On Standard Arithmetic
Functions 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 2
Perfect 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 3 On Modifications and Extensions of the Arithmetic
Functions 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 4 Arithmetic Functions of Other
Types
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