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arXiv · 2609.06332

Normal Behavior and Periodic Points of a Pseudo-Aliquot Map Associated with the Dedekind Psi Function

Aimin Guo
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Abstract

We study the iteration of (T(n)=\psi(n)-n), where (\psi) is the Dedekind psi function. We show that, for almost all integers, successive iterates satisfy strong asymptotic growth relations governed by (T(n)/n). As an application, we prove that for every fixed (\ell\ge1), the set of integers satisfying (T^{(\ell)}(n)=n) has asymptotic density zero, and hence so does the set of periodic points of any fixed period.

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Aimin Guo. 2026-09-06. Normal Behavior and Periodic Points of a Pseudo-Aliquot Map Associated with the Dedekind Psi Function. https://arxiv.org/abs/2609.06332

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