Divisor Sum of 36
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {36} = 91$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $36 = 2^2 \times 3^2$
Hence:
\(\ds \map {\sigma_1} {36}\) | \(=\) | \(\ds \frac {2^3 - 1} {2 - 1} \times \frac {3^3 - 1} {3 - 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac {8 - 1} 1 \times \frac {27 - 1} 2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 7 \times 13\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 91\) |
$\blacksquare$