On the Distribution Properties of the Smarandache Prime Part. (17th August 2021)

• Record Type: Journal Article
• Authors: Yu, Yahui; Hu, Jiayuan
• Other Names: Shabbir Ghulam Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2021(2021)
• Publication Date: 2021-08-17
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2021/9937647
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : For each integer n, denote by p p n the largest prime ≤ n and by P p n the smallest prime ≥ n, called as the Smarandache inferior prime part and superior prime part of n, respectively. Define I n ≔ 1 / n ∑ m ≤ n p p m and S n ≔ 1 / n ∑ m ≤ n P p m . In this short note, we proved some estimates on I n − S n and I n / S n, answering a question proposed by Kashihara and improving a result of Yan.