On the Distribution Properties of the Smarandache Prime Part. (17th August 2021) - Yu, Yahui; Hu, Jiayuan
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.