So I am trying to generate a sequence with an equation (that I don't think exists) and it involves all the even numbers, and one way to find the sequence is to get rid of all odd prime numbers so...
$2\frac{x}{n_k}$ where $n_m$ is $x$ without any $2$'s in its prime factorization.
then I tried to make an equation for $n_k$.
$n_m=n_{m-1}(\frac{(n_{m-1}\mod{2})+1}2)$
where $n_1=x$
or
$n_m=n_{m-1}(\frac{3-\cos(\pi n_{m-1})}{4})$
where $n_1=x$
now that I have a recursive formula I was wondering if any one could make a standard formula from this (and show how you did it if you want)