  We prove the conjecture stated in F. Qi and R. Agarwal, \textit{On complete
monotonicity for several classes of functions related to ratios of gamma
functions}, J. Inequal. Appl. (2019), 1-42, that the function $1/\arctan$ is
logarithmically completely monotonic on $(0,\infty)$, but not a Stieltjes
transform.
