Primitive Abundant Number/Examples/20

Example of Primitive Abundant Number
$20$ is a primitive abundant number:
 * $1 + 2 + 4 + 5 + 10 = 22 > 20$

Proof
From $\sigma$ of $20$, we have:
 * $\sigma \left({20}\right) - 20 = 22$

where $\sigma$ denotes the $\sigma$ function: the sum of all divisors of $20$.

Thus, by definition, $20$ is abundant number.

The aliquot parts of $20$ are enumerated at $\tau$ of $20$:
 * $1, 2, 4, 5, 10$

By inspecting the $\sigma$ values of each of these, they are seen to be deficient.

Hence the result, by definition of primitive abundant number.