Odd Amicable Pair/Examples/32,129,958,525-32,665,894,275
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Example of Odd Amicable Pair
$32 \, 129 \, 958 \, 525$ and $32 \, 665 \, 894 \, 275$ are an odd amicable pair:
- $\map {\sigma_1} {32 \, 129 \, 958 \, 525} = \map {\sigma_1} {32 \, 665 \, 894 \, 275} = 64 \, 795 \, 852 \, 800 = 32 \, 129 \, 958 \, 525 + 32 \, 665 \, 894 \, 275$
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 $\map {\sigma_1} n$ denotes the divisor sum function.
Thus:
\(\ds \map {\sigma_1} {32 \, 129 \, 958 \, 525}\) | \(=\) | \(\ds 64 \, 795 \, 852 \, 800\) | $\sigma_1$ of $32 \, 129 \, 958 \, 525$ | |||||||||||
\(\ds \) | \(=\) | \(\ds 32 \, 129 \, 958 \, 525 + 32 \, 665 \, 894 \, 275\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \map {\sigma_1} {32 \, 665 \, 894 \, 275}\) | $\sigma_1$ of $32 \, 665 \, 894 \, 275$ |
$\blacksquare$
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $64,795,852,800$