Arithmetic Functions

"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 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