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 $\sigma$ of $88$, we have:
 * $\sigma \left({88}\right) - 88 = 92$

where $\sigma$ denotes the $\sigma$ function: the sum of all divisors of $88$.

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

The aliquot parts of $88$ are enumerated at $\tau$ of $88$:
 * $1, 2, 4, 8, 11, 22, 44$

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

Hence the result, by definition of primitive abundant number.