Primitive Abundant Number/Examples/464

Example of Primitive Abundant Number

$464$ is a primitive abundant number:

$1 + 2 + 4 + 8 + 16 + 29 + 58 + 116 + 232 = 466 > 464$

Proof

From $\sigma_1$ of $464$:

$\map {\sigma_1} {464} - 464 = 466$

where $\sigma_1$ denotes the divisor sum function: the sum of all divisors of $464$.

Thus, by definition, $464$ is an abundant number.

The aliquot parts of $464$ are enumerated at $\sigma_0$ of $464$:

$1, 2, 4, 8, 16, 29, 58, 116, 232$

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

Hence the result, by definition of primitive abundant number.

$\blacksquare$