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.
$\blacksquare$