Define $(\ell,k)$-smough numbers to be numbers that have prime divisors $p$ of form either $p|\ell$ or $k<p$.

1. Given a $k$ what is the minimum $n$ such that $q(n(n+1))$ is $(6,k)$-smough where $q(x)=x(x^2-1)$?

2. Is there a fast algorithm to find such $n$ for a given $k$?