Let [Formula: see text] and [Formula: see text], where [Formula: see text] is Euler’s function and [Formula: see text] is Dedekind’s arithmetic function. We obtain the maximal order of [Formula: see text], as well as the average orders of [Formula: see text] and [Formula: see text]. Furthermore, we prove a density theorem for both [Formula: see text] and [Formula: see text].
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Guo et al. (2025) studied this question.
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