Divisor Sum of 642
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {642} = 1296$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $642 = 2 \times 3 \times 107$
Hence:
\(\ds \map {\sigma_1} {642}\) | \(=\) | \(\ds \paren {2 + 1} \paren {3 + 1} \paren {107 + 1}\) | Divisor Sum of Square-Free Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times 4 \times 108\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times 2^2 \times \paren {2^2 \times 3^3}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^4 \times 3^4\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \paren {2^2 \times 3^2}^2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 1296\) |
$\blacksquare$