Tau Function/Examples

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Examples of Tau Function

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

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

This sequence is A000005 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


$\tau$ of $1$

The value of the $\tau$ function for the integer $1$ is $1$.


$\tau$ of $3$

$\tau \left({3}\right) = 2$


$\tau$ of $12$

$\tau \left({12}\right) = 6$


$\tau$ of $60$

$\tau \left({60}\right) = 12$


$\tau$ of $105$

$\tau \left({105}\right) = 8$


$\tau$ of $108$

$\tau \left({108}\right) = 12$


$\tau$ of $110$

$\tau \left({110}\right) = 8$


$\tau$ of $120$

$\tau \left({120}\right) = 16$


Sources