Sequences relating Ω(n), ω(n), and rad(n).

A205959, A363923, and S20230712, sequences of Peter Luschny.
Written by Michael Thomas De Vlieger, St. Louis, Missouri, 2023 0501.

Abstract.

We examine related sequences that raise n to a power and dividing by squarefree kernel, where the power is the either number of distinct primes p dividing n, or those p | n with multiplicity. These sequences exhibit behavior that excludes numbers that belong to certain easily defined subsets of the natural numbers.

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Concerns OEIS sequences:

A000040, A001221, A001222, A001694, A005117, A006881, A007947, A013929, A024619, A120944, A126706, A151821, A246547, A286708, A350352, A363919, A363923.

To cite:

Michael Thomas De Vlieger, Sequences relating Ω(n), ω(n), and rad(n), Simple Sequence Analysis, Article 20230711.