Divisor Sum of 45
Jump to navigation
Jump to search
Example of Divisor Sum of Integer
- $\map {\sigma_1} {45} = 78$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $45 = 3^2 \times 5$
Hence:
\(\ds \map {\sigma_1} {45}\) | \(=\) | \(\ds \frac {3^3 - 1} {3 - 1} \times \frac {5^2 - 1} {5 - 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac {27 - 1} 2 \times \frac {25 - 1} 4\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 13 \times 6\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 78\) |
$\blacksquare$