Definition:Polydivisible Number/Definition 1

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Definition

A polydivisible number is a positive integer $N$ of which, for all $n$ up to the number of digits of $N$, the first $n$ digits form an integer which is divisible by $n$.


Sequence of Polydivisible Numbers

The sequence of polydivisible numbers begins:

$1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, \ldots$


Examples

$381 \, 654 \, 729$ is Polydivisible

The integer $381 \, 654 \, 729$ is the only polydivisible number which is pandigital in the sense of excluding zero.


$3 \, 608 \, 528 \, 850 \, 368 \, 400 \, 786 \, 036 \, 725$ is Polydivisible

The largest polydivisible number has $25$ digits:

$3 \, 608 \, 528 \, 850 \, 368 \, 400 \, 786 \, 036 \, 725$


Also see