MathNet 2015-part-02 — 191 problems (EN–VI) Question 141

Denote the number of all positive divisors of a positive integer $n$ by $\delta(n)$ and the sum of all positive divisors of a positive integer $n$ by $\sigma(n)$. Prove that $\sigma(n) \gt \frac{\delta(n)^2}{2}$.