Show that sum of divisors of a composite number $n$ is $> n+ \sqrt{n}$ The hint says to use :  When $1\lt d\lt n$, $1 \lt n/d \lt n$. If $d\le \sqrt{n}$, then $n/d \ge \sqrt{n}$
My try :
Since there will be atleast half divisors $> \sqrt{n}$,
the sum of divisors will be atleast $\dfrac{\tau (n)}{2}\sqrt{n}$
Not sure how to proceed further. Any help ?

Use the hint to prove that there exists a divisor $\sqrt{n} \leq d <n$. 
Then $n$ and $d$ are divisors of $n$ and their sum is....
