# A New Type of Abundant Numbers

## TL;DR

This paper introduces a new class of abundant numbers called LR numbers and establishes a connection between these numbers and Robin's hypothesis, showing the hypothesis holds if all LR numbers greater than 5040 satisfy Robin inequality.

## Contribution

It defines LR numbers and proves their significance in relation to Robin's hypothesis, providing a new perspective on the problem.

## Key findings

- Robin hypothesis is true iff all LR numbers > 5040 satisfy Robin inequality
- LR numbers are a new class of abundant numbers with specific properties
- The paper establishes a criterion linking LR numbers to Robin's hypothesis

## Abstract

This article defines a new type of abundant numbers, called largest rho-value (abbreviate LR) numbers, and then shows that Robin hypothesis is true if and only if all LR numbers $>5040$ satisfy Robin inequality.