Divisor Sum of 19,845
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {19 \, 845} = 41 \, 382$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $19 \, 845 = 3^4 \times 5 \times 7^2$
Hence:
\(\ds \map {\sigma_1} {19 \, 845}\) | \(=\) | \(\ds \dfrac {3^5 - 1} {3 - 1} \times \paren {5 + 1} \times \dfrac {7^3 - 1} {7 - 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {242} 2 \times 6 \times \dfrac {342} 6\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 121 \times 6 \times 57\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 11^2 \times \paren {2 \times 3} \times \paren {3 \times 19}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2 \times 3^2 \times 11^2 \times 19\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 41 \, 382\) |
$\blacksquare$