Divisor Sum of 11,655
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {11 \, 655} = 23 \, 712$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $11 \, 655 = 3^2 \times 5 \times 7 \times 37$
Hence:
\(\ds \map {\sigma_1} {11 \, 655}\) | \(=\) | \(\ds \dfrac {3^3 - 1} {3 - 1} \times \paren {5 + 1} \times \paren {7 + 1} \times \paren {37 + 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {26} 2 \times 6 \times 8 \times 38\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 13 \times 6 \times 8 \times 38\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 13 \times \paren {2 \times 3} \times 2^3 \times \paren {2 \times 19}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^5 \times 3 \times 13 \times 19\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 23 \, 712\) |
$\blacksquare$