Symbols:Greek/Tau/Tau Function

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Tau Function

$\map \tau n$

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 $n$.

The $\LaTeX$ code for \(\map \tau n\) is \map \tau n .

Linguistic Note

The name of the Greek letter $\tau$ (tau) is properly pronounced to rhyme with cow not caw.