Measuring Abundance with Abundancy Index
Kalpok Guha, Sourangshu Ghosh

TL;DR
This paper explores the properties of the Abundancy Index, introduces superabundant numbers, and investigates their potential link to the Riemann Hypothesis, advancing understanding of number classification and divisor functions.
Contribution
It defines the Abundancy Index, studies its properties, introduces superabundant numbers, and examines their connection to the Riemann Hypothesis, offering new insights into divisor ratios.
Findings
Properties of the Abundancy Index analyzed
Superabundant numbers characterized and defined
Connections between superabundant numbers and Riemann Hypothesis explored
Abstract
A positive integer is called perfect if , where denote the sum of divisors of . In this paper we study the ratio . We define the function Abundancy Index with . Then we study different properties of the Abundancy Index and discuss the set of Abundancy Index. Using this function we define a new class of numbers known as superabundant numbers. Finally, we study superabundant numbers and their connection with Riemann Hypothesis.
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