Primitive Abundant Number/Examples/304

Example of Primitive Abundant Number

$304$ is a primitive abundant number:

$1 + 2 + 4 + 8 + 16 + 19 + 38 + 76 + 152 = 316 > 304$

Proof

From $\sigma_1$ of $304$, we have:

$\map {\sigma_1} {304} - 304 = 316$

where $\sigma_1$ denotes the divisor sum function: the sum of all divisors of $304$.

Thus, by definition, $304$ is an abundant number.

The aliquot parts of $304$ are enumerated at $\sigma_0$ of $304$:

$1, 2, 4, 8, 16, 19, 38, 76, 152$

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

Hence the result, by definition of primitive abundant number.

$\blacksquare$