Primitive Abundant Number/Examples/20
Jump to navigation
Jump to search
Example of Primitive Abundant Number
$20$ is a primitive abundant number:
- $1 + 2 + 4 + 5 + 10 = 22 > 20$
Proof
From $\sigma_1$ of $20$, we have:
- $\map {\sigma_1} {20} - 20 = 22$
where $\sigma_1$ denotes the divisor sum function.
Thus, by definition, $20$ is abundant number.
The aliquot parts of $20$ are enumerated at $\sigma_0$ of $20$:
- $1, 2, 4, 5, 10$
By inspecting the divisor sum values of each of these, they are seen to be deficient.
Hence the result, by definition of primitive abundant number.
$\blacksquare$