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 $\sigma_1$ of $572$, we have:

$\map {\sigma_1} {572} - 572 = 604$

where $\sigma_1$ denotes the divisor sum function.

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

The aliquot parts of $572$ are enumerated at $\sigma_0$ of $572$:

$1, 2, 4, 11, 13, 22, 26, 44, 52, 143, 286$

By inspecting the divisor sums of each of these, they are seen to be deficient.

Hence the result, by definition of primitive abundant number.

$\blacksquare$