The NextRegular(n) Function.

Written by Michael Thomas De Vlieger, St. Louis, Missouri, 2023 0501.

Abstract.

We introduce several related functions having to do with numbers k in an infinite sequence R_ϰ where rad(k) | ϰ, where ϰ is squarefree. These functions furnish successors and predecessors to a given number in the sequence R_ϰ. We also examine the sequence ϰR_ϰ wherein all numbers share the same squarefree kernel ϰ. Some of these functions have long existed in the OEIS and others we have proposed recently. This work merely lays out the basics about each function.

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Concerns OEIS sequences:

A007947, A013929, A024619, A065642, A079277, A120944, A126706, A162306, A360529, A360719, A362041, A362432, A362844.

To cite:

Michael Thomas De Vlieger, The NextRegular(n) Functions, Simple Sequence Analysis, Article 20230501.