Odd Amicable Pair/Examples/29,912,035,725-34,883,817,075
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Example of Odd Amicable Pair
$29 \, 912 \, 035 \, 725$ and $34 \, 883 \, 817 \, 075$ are an odd amicable pair:
- $\map {\sigma_1} {29 \, 912 \, 035 \, 725} = \map {\sigma_1} {34 \, 883 \, 817 \, 075} = 64 \, 795 \, 852 \, 800 = 29 \, 912 \, 035 \, 725 + 34 \, 883 \, 817 \, 075$
Proof
By definition, $m$ and $n$ form an amicable pair if and only if:
- $\map {\sigma_1} m = \map {\sigma_1} n = m + n$
where $\sigma_1$ denotes the divisor sum function.
Thus:
| \(\ds \map {\sigma_1} {29 \, 912 \, 035 \, 725}\) | \(=\) | \(\ds 64 \, 795 \, 852 \, 800\) | $\sigma_1$ of $29 \, 912 \, 035 \, 725$ | |||||||||||
| \(\ds \) | \(=\) | \(\ds 29 \, 912 \, 035 \, 725 + 34 \, 883 \, 817 \, 075\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \map {\sigma_1} {34 \, 883 \, 817 \, 075}\) | $\sigma_1$ of $34 \, 883 \, 817 \, 075$ |
$\blacksquare$
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $64,795,852,800$