Primitive Abundant Number/Examples/368
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Example of Primitive Abundant Number
$368$ is a primitive abundant number:
- $1 + 2 + 4 + 8 + 16 + 23 + 46 + 92 + 184 = 376 > 368$
Proof
From $\sigma_1$ of $368$, we have:
- $\map {\sigma_1} {368} - 368 = 376$
where $\sigma_1$ denotes the divisor sum function.
Thus, by definition, $368$ is an abundant number.
The aliquot parts of $368$ are enumerated at $\sigma_0$ of $368$:
- $1, 2, 4, 8, 16, 23, 46, 92, 184$
By inspecting the divisor sums of each of these, they are seen to be deficient.
Hence the result, by definition of primitive abundant number.
$\blacksquare$