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:

$\map P n = n^{\map {\sigma_0} n / 2 - 1}$

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

From $\sigma_0$ of $12$:

$\map {\sigma_0} {12} = 6$

and so:

$\map P {12} = 12^{6 / 2 - 1} = 12^2 = 144$

$\blacksquare$

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $12$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $12$