The Semitotative Counting Function and Species.

A243823, A360480, A360543.
Written by Michael Thomas De Vlieger, St. Louis, Missouri, 2023 0308.

Abstract.

Consider k, n ∈ ℕ and define n-semicoprime k to be such that sets of prime divisors of k and that of n meet, yet p | k but does not divide n. It is clear that semicoprimality requires both k and n composite. We consider k < n, thus k a semitotative of n. We describe symmetric and nonsymmetric varieties of the semitotative. This paper expands on an earlier work regarding symmetric semitotatives.

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Concerns OEIS sequences:

A000005, A000010, A000040, A000961, A001221, A003557, A006881, A007947, A010846, A013929, A024619, A045763, A051953, A053211, A120944, A126706, A133995, A162306, A243823, A246547, A272618, A272619, A334151, A355432, A360480, A360543, A360765, A360767, A360768, A360769, A361235.

To cite:

Michael Thomas De Vlieger, The semitotative counting function and species, Simple Sequence Analysis, Article 20230225.