# extravagant number

An extravagant number or wasteful number $n$ is an integer with a base $b$ representation^{} of $k$ digits for which the prime factorization^{} uses more than $k$ digits (with repeated prime factors^{} grouped with exponents and the digits of those exponents counted whenever greater than 1). The first few extravagant numbers in base 10 are 4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, etc. (listed in A046760 of Sloane’s OEIS).

## References

- 1 D. Darling, “Economical number” in The Universal Book of Mathematics: From Abracadabra To Zeno’s paradoxes. Hoboken, New Jersey: Wiley (2004)

Title | extravagant number |
---|---|

Canonical name | ExtravagantNumber |

Date of creation | 2013-03-22 16:41:20 |

Last modified on | 2013-03-22 16:41:20 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 4 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 11A63 |

Synonym | wasteful number |

Related topic | FrugalNumber |

Related topic | EquidigitalNumber |