# 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 |