Problem 696

Erdős Problem #696: declared status 'solved'. Formalized: no. Let $h(n)$ be the largest $\ell$ such that there is a sequence of primes $p_1<\cdots < p_\ell$ all dividing $n$ with $p_{i+1}\equiv 1\pmod{p_i}$. Let $H(n)$ be the largest $u$ such that there is a sequence of integers $d_1<\cdots < d_u$ all dividing $n$ with $d_{i+1}\equiv 1\pmod{d_i}$. Estimate $h(n)$ and $H(n)$. Is it true that $H(n)/h(n)\to \infty$ for almost all $n$? Prize: no. Tags: divisors, number theory.