2 problems

Connectedness conjecture. Given a superabundant number $n$, either there is a prime $p$ such that $np$ is superabundant or there is a prime $q$ such that $n/q$ is superabundant; mo…

Alaoglu–Erdős conjecture. For every superabundant number $n$, there exist primes $p,q$ such that both $np$ and $n/q$ are superabundant. Equivalently, the infinite lattice of supera…