Divisor Sum of 32,665,894,275
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {32 \, 665 \, 894 \, 275} = 64 \, 795 \, 852 \, 800$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $32 \, 665 \, 894 \, 275 = 3 \times 5^2 \times 7 \times 31 \times 59 \times 34 \, 019$
Hence from Divisor Sum of Integer:
\(\ds \map {\sigma_1} {32 \, 665 \, 894 \, 275}\) | \(=\) | \(\ds \paren {3 + 1} \times \frac {5^3 - 1} {5 - 1} \times \paren {7 + 1} \times \paren {31 + 1} \times \paren {59 + 1} \times \paren {34 \, 019 + 1}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 4 \times \frac {124} 4 \times 8 \times 32 \times 60 \times 34 \, 020\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 4 \times 31 \times 8 \times 32 \times 60 \times 34 \, 020\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^2 \times 31 \times 2^3 \times 2^5 \times \paren {2^2 \times 3 \times 5} \times \paren {2^2 \times 3^5 \times 5 \times 7}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^{14} \times 3^6 \times 5^2 \times 7 \times 31\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 64 \, 795 \, 852 \, 800\) |
$\blacksquare$