Affiliation:
1. Center for Communications Research, Princeton, NJ, USA
2. School of Science, UNSW Canberra at ADFA, ACT 2610, Australia
Abstract
We examine oscillations in a number of sums of arithmetic functions involving [Formula: see text], the total number of prime factors of [Formula: see text], and [Formula: see text], the number of distinct prime factors of [Formula: see text]. In particular, we examine oscillations in [Formula: see text] and in [Formula: see text] for [Formula: see text], and in [Formula: see text]. We show for example that each of the inequalities [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] is true infinitely often, disproving some hypotheses of Sun.
Funder
Australian Seafood Cooperative Research Centre
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
3 articles.
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2. Oscillations in the Goldbach conjecture;Journal de théorie des nombres de Bordeaux;2022-07-07
3. Variations on criteria of Pólya and Turán for the Riemann hypothesis;Journal of Number Theory;2021-08