Divisor Sum of 81,081
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {81 \, 081} = 162 \, 624$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $81 \, 081 = 3^4 \times 7 \times 11 \times 13$
Hence:
\(\ds \map {\sigma_1} {81 \, 081}\) | \(=\) | \(\ds \dfrac {3^5 - 1} {3 - 1} \times \paren {7 + 1} \times \paren {11 + 1} \times \paren {13 + 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {242} 2 \times 8 \times 12 \times 14\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 121 \times 8 \times 12 \times 14\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 11^2 \times 2^3 \times \paren {2^2 \times 3} \times \paren {2 \times 7}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^6 \times 3 \times 7 \times 11^2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 162 \, 624\) |
$\blacksquare$