Lower bound on the sum of divisor function It there a lower bound on the sum of divisors function? More specifically is there a "simple" function  $f(n)$  such that $\sigma(n) \ge f(n)$ for all $n$ large enough?

I think I can prove, that for $n>1$ we have:
$\sigma(n) \ge \sqrt{\frac{2\sum_{d<e,d|n,e|n}{de}}{\sum{p|n,p \text{ prime }}{\frac{p \log(p)}{p-1}-\log(p-1)}}}$
Although this formula is not "simple" it seems to be true and a good lower bound if the number $n$ is "highly composed" (better than $n+1$).
