Divisor Sum of 357
Jump to navigation
Jump to search
Example of Divisor Sum of Square-Free Integer
- $\map {\sigma_1} {357} = 576$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $357 = 3 \times 7 \times 17$
Hence:
\(\ds \map {\sigma_1} {357}\) | \(=\) | \(\ds \paren {3 + 1} \paren {7 + 1} \paren {17 + 1}\) | Divisor Sum of Square-Free Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds 4 \times 8 \times 18\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^2 \times 2^3 \times \paren {2 \times 3^2}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^6 \times 3^2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \paren {2^3 \times 3}^2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 24^2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 576\) |
$\blacksquare$