Middle divisors and $\sigma$-palindromic Dyck words

José Manuel Rodríguez Caballero

Given a real number $\lambda >1$, we say that $d|n$ is a $\lambda$-middle divisor of $n$ if $$\sqrt{\frac{n}{\lambda }}<d\le \sqrt{\lambda n}.$$ We will prove that there are integers having an arbitrari…