dc.contributor.author | Broughan, Kevin A. | |

dc.contributor.author | Zhou, Qizhi | |

dc.date.accessioned | 2010-02-19T01:59:38Z | |

dc.date.available | 2010-02-19T01:59:38Z | |

dc.date.issued | 2010 | |

dc.identifier.citation | Broughan, K. A. & Zhou, Q. (2010). Divisibility by 3 of even multiperfect numbers of abundancy 3 and 4. Journal of Integer Sequence, 13, 10.1.5 | en |

dc.identifier.uri | https://hdl.handle.net/10289/3623 | |

dc.description.abstract | We say a number is flat if it can be written as a non-trivial power of 2 times an odd squarefree number. The power is the “exponent” and the number of odd primes the “length”. Let N be flat and 4-perfect with exponent a and length m. If a ≢ 1 mod 12, then a is even. If a is even and 3 ∤ N then m is also even. If a ≡ 1 mod 12 then 3 | N and m is even. If N is flat and 3-perfect and 3 ∤ N, then if a a ≡ 1 mod 12, a is even. If
a ≡ 1 mod 12 then m is odd. If N is flat and 3 or 4-perfect then it is divisible by at least one Mersenne prime, but not all odd prime divisors are Mersenne. We also give some conditions for the divisibility by 3 of an arbitrary even 4-perfect number. | en |

dc.format.mimetype | application/pdf | |

dc.language.iso | en | |

dc.publisher | - Online | en_NZ |

dc.relation.uri | https://eudml.org/doc/224008 | en |

dc.rights | This article has been published in the journal: Journal of Integer Sequence. ©2010 K. A. Broughan & Q. Zhou. | en |

dc.subject | maths | en |

dc.title | Divisibility by 3 of even multiperfect numbers of abundancy 3 and 4 | en |

dc.type | Journal Article | en |

dc.relation.isPartOf | Journal of Integer Sequences | en_NZ |

pubs.begin-page | 1 | en_NZ |

pubs.elements-id | 34656 | |

pubs.end-page | 10 | en_NZ |

pubs.issue | 1 | en_NZ |

pubs.volume | 13 | en_NZ |