Divisor Sum of 31,815
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {31 \, 815} = 63 \, 648$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $31 \, 815 = 3^2 \times 5 \times 7 \times 101$
Hence:
\(\ds \map {\sigma_1} {31 \, 815}\) | \(=\) | \(\ds \dfrac {3^3 - 1} {3 - 1} \times \paren {5 + 1} \times \paren {7 + 1} \times \paren {101 + 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {26} 2 \times 6 \times 8 \times 102\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 13 \times 6 \times 8 \times 102\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 13 \times \paren {2 \times 3} \times 2^3 \times \paren {2 \times 3 \times 17}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^5 \times 3^2 \times 13 \times 17\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 63 \, 648\) |
$\blacksquare$