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

dc.contributor.author | Delbourgo, Daniel | |

dc.date.accessioned | 2014-01-28T02:07:48Z | |

dc.date.available | 2014-01-28T02:07:48Z | |

dc.date.issued | 2013 | |

dc.identifier.citation | Broughtan, K. A. & Delbourgo, D. (2013). On the ratio of the sum of divisors and Euler’s Totient Function I. Journal of Integer Sequences, 16, article 13.8.8. | en_NZ |

dc.identifier.uri | https://hdl.handle.net/10289/8429 | |

dc.description.abstract | We prove that the only solutions to the equation σ(n)=2φ(n) with at most three distinct prime factors are 3, 35 and 1045. Moreover, there exist at most a finite number of solutions to σ(n)=2φ(n) with Ω(n)≤ k, and there are at most 22k+k-k squarefree solutions to φ (n)|σ(n) if ω(n)=k. Lastly the number of solutions to φ(n)|φ(n) as x→∞ is O(x exp(-½√log x)). | en_NZ |

dc.format.mimetype | application/pdf | |

dc.language.iso | en | en_NZ |

dc.relation.uri | https://cs.uwaterloo.ca/journals/JIS/VOL16/Broughan/broughan26.html | en_NZ |

dc.rights | This article has been published in the Journal of Integer Sequences. © 2013 the authors. | en_NZ |

dc.subject | mathematics | en_NZ |

dc.title | On the ratio of the sum of divisors and Euler’s Totient Function I | en_NZ |

dc.type | Journal Article | en_NZ |

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

pubs.begin-page | 1 | en_NZ |

pubs.edition | Article 13.8.8 | en_NZ |

pubs.elements-id | 38913 | |

pubs.end-page | 16 | en_NZ |

pubs.issue | 8 | en_NZ |

pubs.volume | 16 | en_NZ |