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The -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 -ary analogues of various popular functions in number theory, proving various results about the structure of the -ary divisibility relations along the way.

international journal of mathematics and mathematical sciences

Arithmetical Functions Associated with the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:math>-ary Divisors of an Integer

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