# refactorable number

A refactorable number^{} or tau number is an integer $n$ that is divisible by the count of its divisors^{}, or to put it algebraically, $n$ is such that $\tau (n)|n$, with $\tau (n)$ being the divisor function^{}. The first few refactorable numbers are listed in the OEIS A033950 are 1, 2, 8, 9, 12, 18, 24, 36, 40, 56, 60, 72, 80, 84, 88, 96. The equation $\mathrm{gcd}(n,x)=\tau (n)$ has solutions only if $n$ is a refactorable number.

Title | refactorable number |
---|---|

Canonical name | RefactorableNumber |

Date of creation | 2013-03-22 17:40:41 |

Last modified on | 2013-03-22 17:40:41 |

Owner | CompositeFan (12809) |

Last modified by | CompositeFan (12809) |

Numerical id | 4 |

Author | CompositeFan (12809) |

Entry type | Definition |

Classification | msc 11A25 |