Primitive Abundant Number/Examples/104

Example of Primitive Abundant Number
$104$ is a primitive abundant number:
 * $1 + 2 + 4 + 8 + 13 + 26 + 52 = 106 > 104$

Proof
From, we have:
 * $\map \sigma {104} - 104 = 106$

where $\sigma$ denotes the $\sigma$ function: the sum of all divisors of $104$.

Thus, by definition, $104$ is an abundant number.

The aliquot parts of $104$ are enumerated at :
 * $1, 2, 4, 8, 13, 26, 52$

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

Hence the result, by definition of primitive abundant number.