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:

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


Proof

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

$\map \sigma m = \map \sigma n = m + n$

where $\map \sigma n$ denotes the $\sigma$ function of $n$.


Thus:

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

$\blacksquare$


Sources