# amicable numbers

###### Definition.

Two natural numbers^{} $n$ and $m$ are amicable numbers (an amicable pair or simply amicable) if each is the sum of the proper divisors of the other.

###### Example.

The smallest amicable pair is $n=220$ and $m=284$. Indeed the sum of proper divisors of $220$ is:

$$1+2+4+5+10+11+20+22+44+55+110=284$$ |

and the sum of proper divisors of $284$ is:

$$1+2+4+71+142=220.$$ |

Title | amicable numbers |
---|---|

Canonical name | AmicableNumbers |

Date of creation | 2013-03-22 15:52:41 |

Last modified on | 2013-03-22 15:52:41 |

Owner | alozano (2414) |

Last modified by | alozano (2414) |

Numerical id | 6 |

Author | alozano (2414) |

Entry type | Definition |

Classification | msc 11A05 |

Synonym | amicable pair |

Synonym | amicable |

Related topic | AbundantNumber |

Related topic | DeficientNumber |