On the Distribution Properties of the Smarandache Prime Part

Yahui Yu, Jiayuan Hu and Ghulam Shabbir

Journal of Mathematics, 2021, vol. 2021, 1-3

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

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9937647

DOI: 10.1155/2021/9937647

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