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:
 * $\displaystyle \tau \left({n}\right) = \sum_{d \mathop \backslash n} 1$

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

Values
The tau function for the first few positive integers is as follows:


 * $\begin{array} {r|r}

n & \tau \left({n}\right) \\ \hline 1 & 1 \\ 2 & 2 \\ 3 & 2 \\ 4 & 3 \\ 5 & 2 \\ 6 & 4 \\ 7 & 2 \\ 8 & 4 \\ 9 & 3 \\ 10 & 4 \\ 11 & 2 \\ 12 & 6 \\ 13 & 2 \\ 14 & 4 \\ 15 & 4 \\ 16 & 5 \\ \end{array}$

Also see

 * Definition:Divisor Function