Divisor Sum of Integer/Examples/12
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {12} = 28$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $12 = 2^2 \times 3$
Hence:
| \(\ds \map {\sigma_1} {12}\) | \(=\) | \(\ds \frac {2^3 - 1} {2 - 1} \times \paren {3 + 1}\) | Divisor Sum of Integer | |||||||||||
| \(\ds \) | \(=\) | \(\ds \frac 7 1 \times 4\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 7 \times 4\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 28\) |
$\blacksquare$