Divisor Sum of 310
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Example of Divisor Sum of Square-Free Integer
- $\map {\sigma_1} {310} = 576$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $310 = 2 \times 5 \times 31$
Hence:
| \(\ds \map {\sigma_1} {310}\) | \(=\) | \(\ds \paren {2 + 1} \paren {5 + 1} \paren {31 + 1}\) | Divisor Sum of Square-Free Integer | |||||||||||
| \(\ds \) | \(=\) | \(\ds 3 \times 6 \times 32\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 3 \times \paren {2 \times 3} \times 2^5\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 2^6 \times 3^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {2^3 \times 3}^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 24^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 576\) |
$\blacksquare$