Primitive Abundant Number/Examples/368

Example of Primitive Abundant Number
$368$ is a primitive abundant number:
 * $1 + 2 + 4 + 8 + 16 + 23 + 46 + 92 + 184 = 376 > 368$

Proof
From $\sigma$ of $368$, we have:
 * $\sigma \left({368}\right) - 368 = 376$

where $\sigma$ denotes the $\sigma$ function: the sum of all divisors of $368$.

Thus, by definition, $368$ is an abundant number.

The aliquot parts of $368$ are enumerated at $\tau$ of $368$:
 * $1, 2, 4, 8, 16, 23, 46, 92, 184$

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

Hence the result, by definition of primitive abundant number.