Define $\triangle_n$ to be the $n$th triangular number.
Define $$M_n=(2\triangle_n-1)2\triangle_n(2\triangle_n+1)=2\triangle_n(4\triangle_n^2-1).$$
Define $(\ell,k)$-smough numbers to be numbers that have all prime divisors $p$ of the form of either $p<\ell$ or $k<p$.
Is there an $\ell_0\geq6$ such that for every $\ell>\ell_0$ and for every $k$, there are an infinite number of $k$ for which there is always an $n$ such that $M_n$ is $(\ell,k)$-smough?
Given an $\ell$ and a $k$, how small can $n$ be such that $M_n$ is $(\ell,k)$-smough?
