Measuring Abundance with Abundancy Index

Abstract

A positive integer n is called perfect if σ(n) = 2n, where σ(n) denote the sum of divisors of n. In this paper we study the ratio σ(n) n . We define the function Abundancy Index I :n . Then we study different properties of 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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