Arithmetical Functions Associated with the k-ary Divisors of an Integer

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. © 2018 Joseph Vade Burnett et al.