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Arithmetical functions associated with the \(k\)-ary divisors of an integer. (English) Zbl 1486.11007

Summary: The \(k\)-ary divisibility relations are a class of recursively defined relations beginning with standard divisibility and culminating in the so-called infinitary divisibility relation. We examine the summatory functions corresponding to the \(k\)-ary analogues of various popular functions in number theory, proving various results about the structure of the \(k\)-ary divisibility relations along the way.

MSC:

11A25 Arithmetic functions; related numbers; inversion formulas
11N37 Asymptotic results on arithmetic functions
11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses
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