My question: what a formula for finding the number of numbers no greater than n that are divisible by all their suffixes.
e.g: 5, 25, 125, 0125, 70125 are divisors of 70125.
refinement: $\overline{0...0a_1a_2...} = \overline{a_1a_2...}$
My question: what a formula for finding the number of numbers no greater than n that are divisible by all their suffixes.
e.g: 5, 25, 125, 0125, 70125 are divisors of 70125.
refinement: $\overline{0...0a_1a_2...} = \overline{a_1a_2...}$
Here's a start. If $y \cdot 10^d + z$ is such a number (with $y \in \{1,2,\ldots,9\}$ and $1 \le z < 10^d$), then $z \mid y \cdot 10^d$.