Product of Proper Divisors/Examples/12

Example of Product of Proper Divisors
The product of the proper divisors of $12$ is $144 = 12^2$.

Proof
From Product of Proper Divisors:
 * $P \left({n}\right) = n^{\tau \left({n}\right) / 2 - 1}$

where $P \left({n}\right)$ denotes the product of the proper divisors of $n$.

From Tau Function of 12:


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

and so:
 * $P \left({12}\right) = 12^{6 / 2 - 1} = 12^2 = 144$