Question 170
Prove that
$$
\frac{\sigma(1)}{1}+\frac{\sigma(2)}{2}+\frac{\sigma(3)}{3}+\cdots+\frac{\sigma(n)}{n} \leq 2 n
$$
for every positive integer $n$.
$$
\frac{\sigma(1)}{1}+\frac{\sigma(2)}{2}+\frac{\sigma(3)}{3}+\cdots+\frac{\sigma(n)}{n} \leq 2 n
$$
for every positive integer $n$.