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
Canonical name	AliquotSequence
Date of creation	2013-03-22 16:07:14
Last modified on	2013-03-22 16:07:14
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	5
Author	PrimeFan (13766)
Entry type	Definition
Classification	msc 11A25