Definition:Divisor Count Function

Definition
Let $n$ be an integer such that $n \ge 1$.

The $\tau$ (tau) function is defined on $n$ as being the total number of positive integer divisors of $n$.

That is:
 * $\displaystyle \map \tau n = \sum_{d \mathop \divides n} 1$

where $\displaystyle \sum_{d \mathop \divides n}$ is the sum over all divisors of $n$.

Also known as
Some sources refer to this as the divisor function and denote it $\map d n$, but as there is a more general definition of the divisor function the more precise name tau function is preferred.

It can also be referred to as the divisor counting function.

Also see

 * Definition:Divisor Function