Define $\triangle_n$ to be the $n$th triangular number.

Define $$M_n=(2\triangle_n-1)2\triangle_n(2\triangle_n+1)=2\triangle_n(2\triangle_n^2-1).$$

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

1. Is there an $\ell_0\geq6$ such that for every $\ell>\ell_0$ and for every $k$ are there infinite number of $k$ for which there is always an $n$ such that $M_n$ is $(\ell,k)$-smough?

2. Given an $\ell$ and a $k$ how small can $n$ be such that $M_n$ is $(\ell,k)$-smough?