Divisor Sum of 345
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Example of Divisor Sum of Square-Free Integer
- $\map {\sigma_1} {345} = 576$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $345 = 3 \times 5 \times 23$
Hence:
| \(\ds \map {\sigma_1} {345}\) | \(=\) | \(\ds \paren {3 + 1} \paren {5 + 1} \paren {23 + 1}\) | Divisor Sum of Square-Free Integer | |||||||||||
| \(\ds \) | \(=\) | \(\ds 4 \times 6 \times 24\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 2^2 \times \paren {2 \times 3} \times \paren {2^3 \times 3}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 2^6 \times 3^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {2^3 \times 3}^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 24^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 576\) |
$\blacksquare$