Erdős Problem #770

declared status 'open'. Formalized: yes. Let $h(n)$ be minimal such that $2^n-1,3^n-1,\ldots,h(n)^n-1$ are mutually coprime. Does, for every prime $p$, the density $\delta_p$ of integers with $h(n)=p$ exist? Does $\liminf h(n)=\infty$? Is it true that if $p$ is the greatest prime such that $p-1\mid n$ and $p>n^\epsilon$ then $h(n)=p$? Prize: no. OEIS: A263647. Tags: number theory.

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