Arithmetical functions associated with the \(k\)-ary divisors of an integer (Q1652936)

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.