Divisor Sum of 15,435
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {15 \, 435} = 31 \, 200$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $15 \, 435 = 3^2 \times 5 \times 7^3$
Hence:
\(\ds \map {\sigma_1} {15 \, 435}\) | \(=\) | \(\ds \dfrac {3^3 - 1} {3 - 1} \times \paren {5 + 1} \times \dfrac {7^4 - 1} {7 - 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {26} 2 \times 6 \times \dfrac {2400} 6\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 13 \times 6 \times 400\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 13 \times \paren {2 \times 3} \times \paren {2^4 \times 5^2}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^5 \times 3 \times 5^2 \times 13\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 31 \, 200\) |
$\blacksquare$