Definition:Divisor Function

The divisor function

$$\sigma_\alpha (n) = \sum_{m|n} m^\alpha \ $$

(meaning the sum is taken over all $$m \leq n \ $$ such that $$m \ $$ divides $$n \ $$).


 * $$\sigma_0(n) \ $$ is the number of divisors of $$n \ $$ and is frequently written $$d(n) \ $$, or $$\tau \left({n}\right)$$ as specified in the definition of the tau function.


 * $$\sigma_1(n) \ $$ is the sum of the divisors of $$n \ $$ and is frequently written $$\sigma(n) \ $$ as specified in the definition of the sigma function.