Product of Proper Divisors/Examples/20
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Example of Product of Proper Divisors
The product of the proper divisors of $20$ is $400 = 20^2$.
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 $20$:
- $\map {\sigma_0} {20} = 6$
and so:
- $\map P {20} = 20^{6 / 2 - 1} = 20^2 = 144$
$\blacksquare$
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $400$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $400$