The sum of positive divisors function $\sigma_k(n)$, for $(n, k)\in\mathbb{N^{*}}^{2}$, is defined as the sum of the k-th powers of the positive divisors of n.
If $k > 0$ we have : $$\sigma_k(n) = \prod_{\substack{p |n \\ \text{p prime}}} \dfrac{p^{(v_p(n)+1)k} - 1}{p^{v_p(n)} - 1}$$ Where $v_p(n)$ is the highest power of p dividing n, called also p-adic order.
If $k=0$ we have : $$\sigma_0(n) = \prod_{\substack{p |n \\ \text{p prime}}} (v_p(n)+1)$$