Primitive Abundant Number/Examples/464

Example of Primitive Abundant Number
$464$ is a primitive abundant number:
 * $1 + 2 + 4 + 8 + 16 + 29 + 58 + 116 + 232 = 466 > 464$

Proof
From :
 * $\map \sigma {464} - 464 = 466$

where $\sigma$ denotes the $\sigma$ function: the sum of all divisors of $464$.

Thus, by definition, $464$ is an abundant number.

The aliquot parts of $464$ are enumerated at :
 * $1, 2, 4, 8, 16, 29, 58, 116, 232$

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

Hence the result, by definition of primitive abundant number.