Primitive Abundant Number/Examples/550

Example of Primitive Abundant Number
$550$ is a primitive abundant number:
 * $1 + 2 + 5 + 10 + 11 + 22 + 25 + 50 + 55 + 110 + 275 = 566 > 550$

Proof
From, we have:
 * $\map \sigma {550} - 550 = 566$

where $\sigma$ denotes the $\sigma$ function: the sum of all divisors of $550$.

Thus, by definition, $550$ is an abundant number.

The aliquot parts of $550$ are enumerated at :
 * $1, 2, 5, 10, 11, 22, 25, 50, 55, 110, 275$

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

Hence the result, by definition of primitive abundant number.