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arXiv · 1211.2147

Superabundant numbers, their subsequences and the Riemann hypothesis

Sadegh Nazardonyavi·Semyon Yakubovich
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Abstract

Let σ(n) be the sum of divisors of a positive integer n. Robin's theorem states that the Riemann hypothesis is equivalent to the inequality σ(n) 5040 (γis Euler's constant). It is a natural question in this direction to find a first integer, if exists, which violates this inequality. Following this process, we introduce a new sequence of numbers and call it as extremely abundant numbers. In this paper we show that the Riemann hypothesis is true, if and only if, there are infinitely many of these numbers. Moreover, we investigate some of their properties together with superabundant and colossally abundant numbers.

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Sadegh Nazardonyavi, Semyon Yakubovich. 2013-02-26. Superabundant numbers, their subsequences and the Riemann hypothesis. https://arxiv.org/abs/1211.2147

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