Divisor Sum of 11,025
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {11 \, 025} = 22 \, 971$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $11 \, 025 = 3^2 \times 5^2 \times 7^2$
Hence:
\(\ds \map {\sigma_1} {11 \, 025}\) | \(=\) | \(\ds \dfrac {3^3 - 1} {3 - 1} \times \dfrac {5^3 - 1} {5 - 1} \times \dfrac {7^3 - 1} {7 - 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {26} 2 \times \dfrac {124} 4 \times \dfrac {342} 6\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 13 \times 31 \times 57\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 13 \times 31 \times \paren {3 \times 19}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 22 \, 971\) |
$\blacksquare$