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.