Some characterizations of totients. (English) Zbl 0846.11005

Haukkanen, Pentti

Int. J. Math. Math. Sci. 19, No. 2, 209-217 (1996).

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.

Reviewer: J.Spilker (Freiburg i.Br.)

MSC:

11A25

Arithmetic functions; related numbers; inversion formulas

Keywords:

arithmetical function; totient; completely multiplicative functions; Dirichlet convolution