On some floor function sets

2023/09/28 by Heyman, Randell, Miraj, MD Rahil
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2309.16072

Abstract

Let X be a positive integer and t a real number great than 1. The family of sets \\lfloor(X)/(n^t)\rfloor ~:~ 1≤ n≤ X\ have an interesting prime distribution property. We give an exact formula for the cardinality of these sets. We provide an estimate for the cardinality of the set \\lfloor(X)/(p)\rfloor ~:~ p~ prime,~ p≤ X\. For positive real X, we derive asymptotic formulas for the cardinality of the set \\lfloor f(n)\rfloor ~:~ 1≤ n≤ X\ for various sets of functions.

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