Guai Lists X45171

We say that a list $f$ is $n$-guai if all the elements in $f$ that are in positions multiples of $n$ are themselves multiples of $n$. For example, $f = [0,1,2,3,4,5,10,10,10,10,25,11]$ is 5-guai, because in positions 0, 5 and 10 (which are multiples of 5) the elements $f[0] = 0$, $f[5] = 5$, and $f[10] = 25$, are also multiples of 5. Instead, $f = [0,1,2,3,4,8]$ is not 5-guai because in position 5 which is multiple of 5 there is an 8 that is not multiple of 5.

Implement the function @is_n_guai (f, n)@ that given a list $f$ of non-negative integers and an integer $n$ greater than zero returns boolean True if $f$ is $n$-guai and False otherwise.

Sample session