Primitive Abundant Number/Examples/572

Example of Primitive Abundant Number
$572$ is a primitive abundant number:
 * $1 + 2 + 4 + 11 + 13 + 22 + 26 + 44 + 52 + 143 + 286 = 604 > 572$

Proof
From, we have:
 * $\map \sigma {572} - 572 = 604$

where $\sigma$ denotes the $\sigma$ function: the sum of all divisors of $572$.

Thus, by definition, $572$ is an abundant number.

The aliquot parts of $572$ are enumerated at :
 * $1, 2, 4, 11, 13, 22, 26, 44, 52, 143, 286$

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

Hence the result, by definition of primitive abundant number.