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Some characterizations of totients

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  • Pentti Haukkanen

Abstract

An arithmetical function is said to be a totient if it is the Dirichlet convolution between a completely multiplicative function and the inverse of a completely multiplicative function. Euler's phi-function is a famous example of a totient. All completely multiplicative functions are also totients. There is a large number of characterizations of completely multiplicative functions in the literature, while characterizations of totients have not been widely studied in the literature. In this paper we present several arithmetical identities serving as characterizations of totients. We also introduce a new concrete example of a totient.

Suggested Citation

  • Pentti Haukkanen, 1996. "Some characterizations of totients," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 19, pages 1-9, January.
    • Handle: RePEc:hin:jijmms:129618
    DOI: 10.1155/S0161171296000312
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