Polydivisible Number/Examples/381,654,729/Mistake

Source Work

 * The Dictionary
 * $381,654,729$
 * $381,654,729$

Mistake

 * The unique integer such that the number formed by the first $n$ digits is divisible by the digit $n$.

That should read:
 * The unique pandigital integer (in the sense that zero is excluded) such that the number formed by the first $n$ digits is divisible by the digit $n$.

It is a trivial task to create a $9$-digit integer with this property that is not pandigital. Straight off the top of my head:
 * $222 \, 456 \, 564$

It is also worth pointing out that $3 \, 816 \, 547 \, 290$ is also pandigital (but in the sense that zero is included) and also has the same property -- although $10$ is not a digit as such.

Numbers with this property are referred to as polydivisible.