Divisor Sum of 2205
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {2205} = 4446$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $2205 = 3^2 \times 5 \times 7^2$
Hence:
\(\ds \map {\sigma_1} {2205}\) | \(=\) | \(\ds \dfrac {3^3 - 1} {3 - 1} \times \paren {5 + 1} \times \dfrac {7^3 - 1} {7 - 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {26} 2 \times 6 \times \dfrac {342} 6\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 13 \times 6 \times 57\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 13 \times \paren {2 \times 3} \times \paren {3 \times 19}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2 \times 3^2 \times 13 \times 19\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 4446\) |
$\blacksquare$