The sequence of middle divisors is unbounded

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• 作者：Jon Eivind Vatne ^{jon.eivind.vatne@hib.no" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 11B83 ; secondary ; 11T55
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：172
• 期：Complete
• 页码：413-415
• 全文大小：183 K

文摘

The sequence of middle divisors is shown to be unbounded. For a given number n  , a_n,0$a_{n,0}$ is the number of divisors of n   between $\sqrt{n/2}$ and $\sqrt{2n}$. We explicitly construct a sequence of numbers n(i)$n(i)$ and a list of divisors in the interesting range, so that the length of the list goes to infinity as i increases.

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