The Symmetric Semidivisor Counting Function.

Written by Michael Thomas De Vlieger, St. Louis, Missouri, 2023 0216.

Abstract.

We explore properties of numbers k < n such that both share a squarefree kernel, yet k does not divide n. The smallest example of such is k = 12, n = 18. We determine the sort of prime decomposition that k and n must have so as to enjoy this rare relationship. Examination of a counting function and records transform follow. The problem touches upon odd prime p-smooth numbers and the nature of the tensor product of prime divisor power ranges bounded by n, which relates to OEIS A010846. This paper mildly relies upon concepts laid out in “Constitutive Basics”.

Click here for the PDF. Supplementary data for A360589 is here.

Concerns OEIS sequences:

A000040, A000961, A001221, A002473, A003586, A005117, A007947, A013929, A024619, A051037, A051038, A080197, A080681, A080682, A080683, A120944, A126706, A162306, A275280, A355432, A359929, A360589, A360765, A360767, A360768.

To cite:

Michael Thomas De Vlieger, The Symmetric Semidivisor Counting Function, Simple Sequence Analysis, Article 20230216.