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 $\sigma_1$ of $104$, we have:

$\map {\sigma_1} {104} - 104 = 106$

where $\sigma_1$ denotes the divisor sum function.

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

The aliquot parts of $104$ are enumerated at $\sigma_0$ of $104$:

$1, 2, 4, 8, 13, 26, 52$

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

Hence the result, by definition of primitive abundant number.

$\blacksquare$