Abstract.
We deduce new properties of the orbicyclic function
E of several variables investigated in a recent paper by
V. A. Liskovets. We point out that the function
E and its
connection to the number of solutions of certain linear congruences
occur in the literature in a slightly different form. We investigate
another similar function considered by Deitmar, Koyama and Kurokawa
by studying analytic properties of some zeta functions of Igusa
type. Simple number-theoretic proofs for some known properties are
also given.


















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