What are the applications of Sigma Function? I read about the Sigma Function today.It tells that- 

The $\sigma(n)$ is the sum of all the positive divisors of $n$.

But I had no idea how they can be useful.What are the practical applications or uses of the sigma function? Are there some seemingly big mathematical problems that can be solved in seconds by applying the Sigma Function?
Thanks for any reply!!

a general relationship between how n's prime factorization effects (n+1) prime factorization would offer a proof to the reiman hypothesis, collatz conjecture,  and more conjectures then I can count. 
