aliquot sequence

For a given m, define the recurrence relation a1=m, an=σ(an-1)-an-1, where σ(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 numberMathworldPlanetmath p, its aliquot sequence is p,1,0. In other cases, the aliquot sequence reaches a fixed pointPlanetmathPlanetmath 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