Question 77
Let $\sigma(n)$ denote the sum of the positive divisors of $n$. We say $n$ is perfect if $\sigma(n)=2 n$. If $n$ is a positive integer such that
$$
\frac{\sigma(n)}{n}=\frac{5}{3}
$$
show that $5 n$ is an odd perfect number.
$$
\frac{\sigma(n)}{n}=\frac{5}{3}
$$
show that $5 n$ is an odd perfect number.