Divisor Sum of 418
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Example of Divisor Sum of Square-Free Integer
- $\map {\sigma_1} {418} = 720$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $418 = 2 \times 11 \times 19$
Hence:
\(\ds \map {\sigma_1} {418}\) | \(=\) | \(\ds \paren {2 + 1} \paren {11 + 1} \paren {19 + 1}\) | Divisor Sum of Square-Free Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times 12 \times 20\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times \paren {2^2 \times 3} \times \paren {2^2 \times 5}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^4 \times 3^2 \times 5\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 12^3\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 720\) |
$\blacksquare$