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A generalization of the infinitary divisibility relation: algebraic and analytic properties. (English) Zbl 1442.11010

The authors investigate a divisibility relation of positive integers generalizing the divisibility relations introduced by G. L. Cohen [Math. Comput., 54, 189, 395–411 (1990; Zbl 0689.10014)] and S. Litsyn and V. Shevelev [Integers 7, No. 1, Paper A33, 35 p. (2007; Zbl 1125.11002)]. This leads to a unique factorization theorem. The authors consider multiplicative, algebraic and asymptotic properties of arithmetic functions related to this divisibility relation. The general idea comes from the paper, [W. Narkiewicz, Colloq. Math. 10, 81–94 (1963; Zbl 0114.26502)].

MSC:

11A25 Arithmetic functions; related numbers; inversion formulas
11N37 Asymptotic results on arithmetic functions
11A51 Factorization; primality
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