# A better method than t-free for Robin's hypothesis

## TL;DR

This paper introduces a new, simpler criterion for Robin's inequality, showing that avoiding division by 17th powers of 2 suffices to satisfy the inequality, improving previous t-free conditions.

## Contribution

The paper demonstrates that the condition for Robin's inequality can be weakened to N not being divisible by 2^{17}, simplifying the verification process.

## Key findings

- N not divisible by 2^{17} implies Robin's inequality
- Simplifies previous t-free conditions for Robin's hypothesis
- Provides a new criterion for verifying Robin's inequality

## Abstract

For a positive integer t>1, an integer N is called t-free if the exponent of any prime factor of N is less than t. Some works shown if N is t-free, then N satisfies Robin's inequality, for t=5, 7, 11, 16. This article shows that the condition of t-free can be resuced to "N cannot be divided by t-th power of 2". I proved that if N cannot be divided by 17-th power of 2, then N satisfies Robin's inequality.