# examples of smooth numbers

If a number is $k$-smooth, it is also a smooth number for smaller $k$. So, to give just a handful of examples of smooth numbers for a few different values of $k$, the following table only goes up to 100, and for $k>2$, only those numbers not already listed for smaller $k$ are given. Also, the $k$ have been limited to prime numbers^{}. Obviously the 2-smooth numbers are the powers of two.

2 | 1, 2, 4, 8, 16, 32, 64 |
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3 | 3, 6, 9, 12, 18, 24, 27, 36, 48, 54, 64, 72, 81, 96 |

5 | 5, 10, 15, 20, 25, 30, 40, 45, 50, 60, 75, 80, 90, 100 |

7 | 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 84, 98 |

11 | 11, 22, 33, 44, 55, 66, 77, 88, 99 |

13 | 13, 26, 39, 52, 65, 78, 91 |

17 | 17, 34, 51, 68, 85 |

19 | 19, 38, 57, 57, 76, 95 |

Title | examples of smooth numbers |
---|---|

Canonical name | ExamplesOfSmoothNumbers |

Date of creation | 2013-03-22 18:10:25 |

Last modified on | 2013-03-22 18:10:25 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 4 |

Author | PrimeFan (13766) |

Entry type | Example |

Classification | msc 11A05 |