Question 133
Let $\sigma(n)$ denote the sum of the (positive) divisors of $n$, including $1$ and $n$ itself.
Prove that
$$
\sigma(1)+\sigma(2)+\sigma(3)+\cdots+\sigma(n) \leq n^{2}
$$
for every positive integer $n$.
Prove that
$$
\sigma(1)+\sigma(2)+\sigma(3)+\cdots+\sigma(n) \leq n^{2}
$$
for every positive integer $n$.