Divisor Sum of 14,175
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {14 \, 175} = 30 \, 008$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $14 \, 175 = 3^4 \times 5^2 \times 7$
Hence:
\(\ds \map {\sigma_1} {14 \, 175}\) | \(=\) | \(\ds \dfrac {3^5 - 1} {3 - 1} \times \dfrac {5^3 - 1} {5 - 1} \times \paren {7 + 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {242} 2 \times \dfrac {124} 4 \times 8\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 121 \times 31 \times 8\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 11^2 \times 31 \times 2^3\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 30 \, 008\) |
$\blacksquare$