Divisor Sum of 29,925
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {29 \, 925} = 64 \, 480$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $29 \, 925 = 3^2 \times 5^2 \times 7 \times 19$
Hence:
\(\ds \map {\sigma_1} {29 \, 925}\) | \(=\) | \(\ds \dfrac {3^3 - 1} {3 - 1} \times \dfrac {5^3 - 1} {5 - 1} \times \paren {7 + 1} \times \paren {19 + 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {26} 2 \times \dfrac {124} 4 \times 8 \times 20\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 13 \times 31 \times 8 \times 20\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 13 \times 31 \times 2^3 \times \paren {2^2 \times 5}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^5 \times 5 \times 13 \times 31\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 64 \, 480\) |
$\blacksquare$