Divisor Sum of Non-Square Semiprime/Examples/119
< Divisor Sum of Non-Square Semiprime | Examples(Redirected from Divisor Sum of 119)
Jump to navigation
Jump to search
Example of Divisor Sum of Non-Square Semiprime
- $\map {\sigma_1} {119} = 144$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $119 = 7 \times 17$
Hence:
| \(\ds \map {\sigma_1} {119}\) | \(=\) | \(\ds \paren {7 + 1} \paren {17 + 1}\) | Divisor Sum of Non-Square Semiprime | |||||||||||
| \(\ds \) | \(=\) | \(\ds 8 \times 18\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 2^3 \times \paren {2 \times 3^2}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 2^4 \times 3^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {2^2 \times 3}^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 12^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 144\) |
$\blacksquare$