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:
 * $\map P n = n^{\map \tau n / 2 - 1}$

where $\map P n$ denotes the product of the proper divisors of $n$.

From Tau Function of 12:


 * $\map \tau {12} = 6$

and so:
 * $\map P {12} = 12^{6 / 2 - 1} = 12^2 = 144$