# 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.

Title aliquot sequence AliquotSequence 2013-03-22 16:07:14 2013-03-22 16:07:14 PrimeFan (13766) PrimeFan (13766) 5 PrimeFan (13766) Definition msc 11A25