# $n$-full number

The concept of a squarefull number can be generalized. Let $n\in \mathbb{Z}$ with $n>1$. Then $m\in \mathbb{Z}$ is $n$-full if, for every prime $p$ dividing $m$, ${p}^{n}$ divides $m$.

Note that $m$ is $n$-full if and only if there exist ${a}_{0},\mathrm{\dots},{a}_{n-1}\in \mathbb{Z}$ such that $m={\displaystyle \prod _{j=0}^{n-1}}a_{j}{}^{n+j}$.

Title | $n$-full number |
---|---|

Canonical name | NfullNumber |

Date of creation | 2013-03-22 16:02:51 |

Last modified on | 2013-03-22 16:02:51 |

Owner | Wkbj79 (1863) |

Last modified by | Wkbj79 (1863) |

Numerical id | 6 |

Author | Wkbj79 (1863) |

Entry type | Definition |

Classification | msc 11A51 |

Related topic | SquarefullNumber |

Related topic | NFreeNumber |

Defines | cubefull |

Defines | cubefull number |

Defines | cube full |

Defines | cube full number |

Defines | cube-full |

Defines | cube-full number |