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?

The best function is actually $f(n)=n+1$ which holds iff $n$ is prime.
Since there are infinitely many primes you can't expect anything better for $n$ large enough.
Ramanujan under the assumption of Riemann hypothesis has shown that $\sigma(n)<e^{\gamma}n{\log\log}n$ for $n$ sufficiently large.
Unfortunately, $\sigma(n)$ does not have a certain rate of growth.
