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:

$\sigma \left({29 \, 912 \, 035 \, 725}\right) = \sigma \left({34 \, 883 \, 817 \, 075}\right) = 64 \, 795 \, 852 \, 800 = 29 \, 912 \, 035 \, 725 + 34 \, 883 \, 817 \, 075$


Proof

By definition, $m$ and $n$ form an amicable pair if and only if:

$\sigma \left({m}\right) = \sigma \left({n}\right) = m + n$

where $\sigma \left({n}\right)$ denotes the $\sigma$ function.


Thus:

\(\displaystyle \sigma \left({29 \, 912 \, 035 \, 725}\right)\) \(=\) \(\displaystyle 64 \, 795 \, 852 \, 800\) $\sigma$ of $29 \, 912 \, 035 \, 725$
\(\displaystyle \) \(=\) \(\displaystyle 29 \, 912 \, 035 \, 725 + 34 \, 883 \, 817 \, 075\)
\(\displaystyle \) \(=\) \(\displaystyle \sigma \left({34 \, 883 \, 817 \, 075}\right)\) $\sigma$ of $34 \, 883 \, 817 \, 075$

$\blacksquare$


Sources