Divisor Sum of 836
Jump to navigation
Jump to search
Example of Divisor Sum of Integer
- $\map {\sigma_1} {836} = 1680$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $836 = 2^2 \times 11 \times 19$
Hence:
\(\ds \map {\sigma_1} {836}\) | \(=\) | \(\ds \frac {2^3 - 1} {2 - 1} \times \paren {11 + 1} \times \paren {19 + 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac 7 1 \times 12 \times 20\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 7 \times \paren {2^2 \times 3} \times \paren {2^2 \times 5}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^4 \times 3 \times 5 \times 7\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 1680\) |
$\blacksquare$