For the numbers $1, \ldots, N$, how many ways can I arrange them such that either:

- The number at $i$ is evenly divisible by $i$, or
- $i$ is evenly divisible by the number at $i$.

Example: for $N = 2$, we have:

$\{1, 2\}$

- number at $i = 1$ is $1$ and is evenly divisible by $i = 1$.
- number at $i = 2$ is $2$ and $i = 2$ is evenly divisible by $2$.

$\{2, 1\}$

- number at $i = 1$ is $2$ and is evenly divisible by $i = 1$.
- number at $i = 2$ is $1$ and $i = 1$ is evenly divisible by $1$.

so there are two such arrangements for $N = 2$.