# cabtaxi number

A cabtaxi number^{} for a given $n$ is the smallest positive number which can be written as ${a}^{3}+{b}^{3}$ in $n$ different ways, with either $a$ or $b$ allowed to be negative integers. For example, 91 is the 2nd cabtaxi number since it can be expressed ${(-5)}^{3}+{6}^{3}={3}^{3}+{4}^{3}=91$. The known cabtaxi numbers are 1, 91, 728, 2741256, 6017193, 1412774811, 11302198488, 137513849003496, 424910390480793000, listed in A047696 of Sloane’s OEIS. Adding the restriction^{} $a\ge b>0$ gives the definition for the taxicab numbers^{}.

Title | cabtaxi number |
---|---|

Canonical name | CabtaxiNumber |

Date of creation | 2013-03-22 17:56:08 |

Last modified on | 2013-03-22 17:56:08 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 4 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 00A08 |