Set of all densities of exponentially S-numbers
Abstract
Let G be the set of all finite or infinite increasing sequences of positive integers beginning with 1. For a sequence S=\s(n)\, n≥1, from G, a positive number N is called an exponentially S-number (N∈ E(S)), if all exponents in its prime power factorization are in S. The author 2 proved that, for every sequence S∈ G, the sequence of exponentially S-numbers has a density h=h(E(S))∈ [6π2, 1]. In this paper we study the set \h(E(S)\ of all such densities.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.