Divisor Sum of 282
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Example of Divisor Sum of Square-Free Integer
- $\map {\sigma_1} {282} = 576$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $282 = 2 \times 3 \times 47$
Hence:
| \(\ds \map {\sigma_1} {282}\) | \(=\) | \(\ds \paren {2 + 1} \paren {3 + 1} \paren {47 + 1}\) | Divisor Sum of Square-Free Integer | |||||||||||
| \(\ds \) | \(=\) | \(\ds 3 \times 4 \times 48\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 3 \times 2^2 \times \paren {2^4 \times 3}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 2^6 \times 3^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {2^3 \times 3}^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 24^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 576\) |
$\blacksquare$