What is the percentage of integers $n$ such that $\frac{\phi_{1}(n)}{n} \geq x$ where $\phi_{1}(n)$ is the sum of all divisors of $n$? Are there any methods of improving these bounds (percentages) for certain $x$?

What is the percentage of integers $n$ such that $\frac{\sigma(n)}{n} \geq x$ where $\sigma(n)$ is the sum of all divisors of $n$? Are there any methods of improving these bounds (percentages) for certain $x$?

What are the percentage of integers $n$ such that $\frac{\phi_{1}(n)}{n} \geq x$ where $\phi_{1}(n)$ is the sum of all divisors of $n$? Are there any methods of improving these bounds (percentages) for certain $x$?

What is the percentage of integers $n$ such that $\frac{\phi_{1}(n)}{n} \geq x$ where $\phi_{1}(n)$ is the sum of all divisors of $n$? Are there any methods of improving these bounds (percentages) for certain $x$?