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 $\sigma_1$ of $550$, we have:

$\map {\sigma_1} {550} - 550 = 566$

where $\sigma_1$ denotes the divisor sum function,

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

The aliquot parts of $550$ are enumerated at $\sigma_0$ of $550$:

$1, 2, 5, 10, 11, 22, 25, 50, 55, 110, 275$

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

Hence the result, by definition of primitive abundant number.

$\blacksquare$