I know that the number of positive divisors of $n$ can be given by :
$\tau(n)$ = $(a_1+1)(a_2+1)\ldots(a_k+1)$ where $n = p_1^{a_1}p_2^{a_2}.... p_k^{a_k}$, where $p_1, p_2... p_k$ are the prime factors of $n$ and $a_1, a_2... a_k$ are positive integers.
And the sum of the positve divisors of $n$ can be given by :
$σ(n)$ = $\frac{p_1^{a_1+1} - 1}{p_1 - 1}$$\frac{p_2^{a_2+1} - 1}{p_2 - 1}$.....$\frac{p_k^{a_k+1} - 1}{p_k - 1}$
But is there a proof for the above two formulae?