Primitive Abundant Number/Examples/836

Example of Primitive Abundant Number

$836$ is a primitive abundant number:

$1 + 2 + 4 + 11 + 19 + 22 + 38 + 44 + 76 + 209 + 418 = 844 > 836$

Proof

From $\sigma_1$ of $836$, we have:

$\map {\sigma_1} {836} - 836 = 844$

where $\sigma_1$ denotes the divisor sum function: the sum of all divisors of $836$.

Thus, by definition, $836$ is abundant number.

The aliquot parts of $836$ are enumerated at $\sigma_0$ of $836$:

$1, 2, 4, 11, 19, 22, 38, 44, 76, 209, 418$

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

Hence the result, by definition of primitive abundant number.

$\blacksquare$