On the means of Jordan's totient function (Q826589)

The author obtains the asymptotic behaviour of the geometric, as well as harmonic mean of the values of the Jordan totient function. He studies also the alternating sums of the Jordan totient, and the special values of the famous Carleman inequality for this function. {Reviewer's remark. Early results on Jordan's totient function have been proved by the reviewer in the papers: [Math. Stud. 52, No. 1--4, 91--96 (1990; Zbl 0854.11004); Note on Jordan's arithmetical function. Timişoara: Universitatea de Vest din Timişoara, Fac. Mat. (1989; Zbl 0758.11002)].}