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2011•International Journal of Mathematical ArchiveRequires access

SOME PROPERTIES OF A CERTAIN CLASS OF ARITHMETICAL FUNCTIONS

P. Sundarayya, S. Kalesha Vali

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Abstract

In this paper, we define a certain class of arithmetical multiplicative functions which are called R-multiplicative functions. Every R-multiplicative function is a multiplicative function but converse need not be true. A necessary and sufficient condition for the Dirichlet product of two R-multiplicative functions to be as R-multiplicative function is given. Some properties on R-multiplicative functions are derived.

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What this paper is about

In this paper, we define a certain class of arithmetical multiplicative functions which are called R-multiplicative functions. Every R-multiplicative function is a multiplicative function but converse need not be true. A necessary and sufficient condition for the Dirichlet product of two R-multiplicative functions to be as R-multiplicative function is given. Some properties on R-multiplicative functions are derived.

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Available abstract

In this paper, we define a certain class of arithmetical multiplicative functions which are called R-multiplicative functions. Every R-multiplicative function is a multiplicative function but converse need not be true. A necessary and sufficient condition for the Dirichlet product of two R-multiplicative functions to be as R-multiplicative function is given. Some properties on R-multiplicative functions are derived.

Key concepts: Multiplicative function, Arithmetic function, Mathematics, Converse, Class (philosophy), Function (biology), Product (mathematics), Multiplicative inverse

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