# polydivisible number

Given a base $b$ integer $n$ with $k$ digits $d_{1},\ldots,d_{k}$, consider $d_{k}$ the least significant digit and $d_{1}$, to suit our purpose in this case. If for each $1 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 PolydivisibleNumber 2013-03-22 16:22:20 2013-03-22 16:22:20 CompositeFan (12809) CompositeFan (12809) 5 CompositeFan (12809) Definition msc 11A63