Divisor Sum of 366
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Example of Divisor Sum of Square-Free Integer
- $\map {\sigma_1} {366} = 744$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $366 = 2 \times 3 \times 61$
Hence:
\(\ds \map {\sigma_1} {366}\) | \(=\) | \(\ds \paren {2 + 1} \paren {3 + 1} \paren {61 + 1}\) | Divisor Sum of Square-Free Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times 4 \times 62\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times 2^2 \times \paren {2 \times 31}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^3 \times 3 \times 31\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 744\) |
$\blacksquare$