Primitive Abundant Number/Examples/70

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Example of Primitive Abundant Number

$70$ is a primitive abundant number:

$1 + 2 + 5 + 7 + 10 + 14 + 35 = 74 > 70$


Proof

From $\sigma_1$ of $70$, we have:

$\map {\sigma_1} {70} - 70 = 74$

where $\sigma_1$ denotes the divisor sum.

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


The aliquot parts of $70$ are enumerated at $\sigma_0$ of $70$:

$1, 2, 5, 7, 10, 14, 35$

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

Hence the result, by definition of primitive abundant number.

$\blacksquare$