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# aliquot sequence

For a given $m$, define the recurrence relation $a_{1}=m$, $a_{n}=\sigma(a_{{n-1}})-a_{{n-1}}$, where $\sigma(x)$ is the sum of divisors function. $a$ is then the aliquot sequence of $m$.

If $m$ is an amicable number, its aliquot sequence is periodic, alternating between the abundant and deficient member of the amicable pair. For a prime number $p$, its aliquot sequence is $p,1,0$. In other cases, the aliquot sequence reaches a fixed point upon 0, or on a perfect number.

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## Mathematics Subject Classification

11A25*no label found*

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