# divisor sum of an arithmetic function

Given an arithmetic function^{} $f:{\mathbb{Z}}^{+}\to \u2102$, the *divisor sum* $F$ of $f$ is defined by

$$F(n)=\sum _{d\mid n}f(d)\text{,}$$ | (1) |

where the summation runs over all positive divisors^{} $d$ of $n$.

Title | divisor sum of an arithmetic function |
---|---|

Canonical name | DivisorSumOfAnArithmeticFunction |

Date of creation | 2013-03-22 17:07:31 |

Last modified on | 2013-03-22 17:07:31 |

Owner | azdbacks4234 (14155) |

Last modified by | azdbacks4234 (14155) |

Numerical id | 10 |

Author | azdbacks4234 (14155) |

Entry type | Definition |

Classification | msc 11A25 |

Related topic | Divisibility |

Related topic | ArithmeticFunction |

Related topic | MultiplicativeFunction |

Defines | divisor sum |