Primitive Abundant Number/Examples/70

Example of Primitive Abundant Number
$70$ is a primitive abundant number:
 * $1 + 2 + 5 + 7 + 10 + 14 + 35 = 74 > 70$

Proof
From $\sigma$ of $70$, we have:
 * $\map \sigma {70} - 70 = 74$

where $\sigma$ denotes the $\sigma$ function: the sum of all divisors of $20$.

Thus, by definition, $70$ is an abundant number.

The aliquot parts of $70$ are enumerated at $\tau$ of $70$:
 * $1, 2, 5, 7, 10, 14, 35$

By inspecting the $\sigma$ values of each of these, they are seen to be deficient.

Hence the result, by definition of primitive abundant number.