Divisor Sum of Square-Free Integer/Examples/170
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Example of Divisor Sum of Square-Free Integer
- $\map {\sigma_1} {170} = 324$
where $\sigma_1$ denotes the divisor sum.
Proof
We have that:
- $170 = 2 \times 5 \times 17$
Hence:
| \(\ds \map {\sigma_1} {170}\) | \(=\) | \(\ds \paren {2 + 1} \paren {5 + 1} \paren {17 + 1}\) | Divisor Sum of Square-Free Integer | |||||||||||
| \(\ds \) | \(=\) | \(\ds 3 \times 6 \times 18\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 3 \times \paren {2 \times 3} \times \paren {2 \times 3^2}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 2^2 \times 3^4\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {2 \times 3^2}^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 18^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 324\) |
$\blacksquare$