## 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
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