# $\sigma $ function

Given a positive integer $n$, the sum of the integers $$ such that $d|n$ is the value of the sum of divisors function for $n$, often symbolized by a Greek lowercase $\sigma $. Thus,

$$\sigma (n)=\sum _{d|n}d.$$ |

Sometimes this function^{} is referred to as ${\sigma}_{1}(n)$, highlighting its relation to the divisor function^{}.

Given coprime integers $m$ and $n$ (that is, $\mathrm{gcd}(m,n)=1$) then $\sigma (mn)=\sigma (m)\sigma (n)$, meaning that the sum of divisors function is a multiplicative function^{}.

Title | $\sigma $ function |
---|---|

Canonical name | sigmaFunction |

Date of creation | 2013-03-22 16:07:12 |

Last modified on | 2013-03-22 16:07:12 |

Owner | CompositeFan (12809) |

Last modified by | CompositeFan (12809) |

Numerical id | 8 |

Author | CompositeFan (12809) |

Entry type | Definition |

Classification | msc 11A25 |

Synonym | divisor sigma |

Synonym | sum of divisors function |

Synonym | ${\sigma}_{1}$ function |