# polydivisible number

Given a base $b$ integer $n$ with $k$ digits ${d}_{1},\mathrm{\dots},{d}_{k}$, consider ${d}_{k}$ the least significant digit and ${d}_{1}$, to suit our purpose in this case. If for each $$ it is the case that

$$(\sum _{i=1}^{j}{d}_{i}{b}^{k-j-i})|j,$$ |

then $n$ is said to be a polydivisible number.

A reasonably good estimate of how many polydivisible numbers base $b$ has is

$$\sum _{i=2}^{b-1}\frac{(b-1){b}^{i-1}}{i!}.$$ |

In any given base, there is only one polydivisible number that is also a pandigital number.

Title | polydivisible number |
---|---|

Canonical name | PolydivisibleNumber |

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

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

Owner | CompositeFan (12809) |

Last modified by | CompositeFan (12809) |

Numerical id | 5 |

Author | CompositeFan (12809) |

Entry type | Definition |

Classification | msc 11A63 |