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

Abstract EN

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.