Primitive Abundant Number/Examples/88

Example of Primitive Abundant Number

$88$ is a primitive abundant number:

$1 + 2 + 4 + 8 + 11 + 22 + 44 = 92 > 88$

Proof

From $\sigma_1$ of $88$, we have:

$\map {\sigma_1} {88} - 88 = 92$

where $\sigma_1$ denotes the divisor sum function.

Thus, by definition, $88$ is an abundant number.

The aliquot parts of $88$ are enumerated at $\sigma_0$ of $88$:

$1, 2, 4, 8, 11, 22, 44$

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

Hence the result, by definition of primitive abundant number.

$\blacksquare$