# quasiperfect number

If there exists an abundant number $n$ with divisors^{} ${d}_{1},\mathrm{\dots},{d}_{k}$, such that

$$\sum _{i=1}^{k}{d}_{i}=2n+1,$$ |

that number would be called a quasiperfect number. Such a number would be $n>{10}^{35}$ and have $\omega (n)>6$ (where $\omega $ is the number of distinct prime factors function).

A quasiperfect number would thus overshoot the mark for being a perfect number by a margin of just 1. (The powers of 2 are short of perfection by a margin of 1).

Title | quasiperfect number |
---|---|

Canonical name | QuasiperfectNumber |

Date of creation | 2013-03-22 16:05:51 |

Last modified on | 2013-03-22 16:05:51 |

Owner | CompositeFan (12809) |

Last modified by | CompositeFan (12809) |

Numerical id | 6 |

Author | CompositeFan (12809) |

Entry type | Definition |

Classification | msc 11A05 |

Related topic | AlmostPerfectNumber |