Divisor Sum of 714
Jump to navigation
Jump to search
Example of Divisor Sum of Square-Free Integer
- $\map {\sigma_1} {714} = 1728$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $714 = 2 \times 3 \times 7 \times 17$
Hence:
\(\ds \map {\sigma_1} {714}\) | \(=\) | \(\ds \paren {2 + 1} \paren {3 + 1} \paren {7 + 1} \paren {17 + 1}\) | Divisor Sum of Square-Free Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times 4 \times 8 \times 18\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times 2^2 \times 2^3 \times \paren {2 \times 3^2}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^6 \times 3^2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \paren {2^2 \times 3}^3\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 12^3\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 1728\) |
$\blacksquare$