Online Math tools

Online Divisor function calculator

Compute $\sigma_k(n)$ with: $$\sigma_k(n)=\sum_{d|n}d^k$$

What is Divisor function?

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 : $$\sigma_0(n) = \prod_{\substack{p |n \\ \text{p prime}}} (v_p(n)+1)$$
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