On the non-monotonicity of the denominator of generalized harmonic sums

Wouter van Doorn

Let $\sum _{i=a}^b\frac{1}{i}=\frac{u_{a,b}}{v_{a,b}}$ with $u_{a,b}$ and $v_{a,b}$ coprime. Erdős and Graham asked the following: Does there, for every fixed $a$,…