ARITHMETIC FUNCTIONS
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
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