×

Some characterizations of totients. (English) Zbl 0846.11005

An arithmetical function \(f\) is a totient if it has the form \(f = g*h^{-1}\) with completely multiplicative functions \(g,h\) (star is Dirichlet convolution). A typical example is Euler’s function \(\varphi = \text{id}* e^{-1}\). The author gives several characterizations of totients and proves their properties. The proofs are elementary.

MSC:

11A25 Arithmetic functions; related numbers; inversion formulas
PDF BibTeX XML Cite
Full Text: DOI EuDML