Divisor Sum of 29,295
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {29 \, 295} = 61 \, 440$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $29 \, 295 = 3^3 \times 5 \times 7 \times 31$
Hence:
\(\ds \map {\sigma_1} {29 \, 295}\) | \(=\) | \(\ds \dfrac {3^4 - 1} {3 - 1} \times \paren {5 + 1} \times \paren {7 + 1} \times \paren {31 + 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {80} 2 \times 6 \times 8 \times 32\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 40 \times 6 \times 8 \times 32\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \paren {2^3 \times 5} \times \paren {2 \times 3} \times 2^3 \times 2^5\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^{12} \times 3 \times 5\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 61 \, 440\) |
$\blacksquare$