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 $\sigma_1$ of $368$, we have:

$\map {\sigma_1} {368} - 368 = 376$

where $\sigma_1$ denotes the divisor sum function.

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

The aliquot parts of $368$ are enumerated at $\sigma_0$ of $368$:

$1, 2, 4, 8, 16, 23, 46, 92, 184$

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

Hence the result, by definition of primitive abundant number.

$\blacksquare$