Divisor Sum of 21,105
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {21 \, 105} = 42 \, 432$
where $\sigma_1$ denotes the Divisor sum function.
Proof
We have that:
- $21 \, 105 = 3^2 \times 5 \times 7 \times 67$
Hence:
\(\ds \map {\sigma_1} {21 \, 105}\) | \(=\) | \(\ds \dfrac {3^3 - 1} {3 - 1} \times \paren {5 + 1} \times \paren {7 + 1} \times \paren {67 + 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {26} 2 \times 6 \times 8 \times 68\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 13 \times 6 \times 8 \times 68\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 13 \times \paren {2 \times 3} \times 2^3 \times \paren {2^2 \times 17}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^6 \times 3 \times 13 \times 17\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 42 \, 432\) |
$\blacksquare$