Progress towards a nonintegrality conjecture

Shanta Laishram, Daniel López-Aguayo, Carl Pomerance +1

Given $r\in \mathbb{N}$, define the function $S_r:\mathbb{N}\to \mathbb{Q}$ by $S_r(n)=\sum _{k=0}^n\frac{k}{k+r}\left(\genfrac{}{}{0ex}{}{n}{k}\right)$. In $2015$, the secon…