Conjectures involving arithmetical sequences

Abstract: We pose thirty conjectures on arithmetical sequences, most of which are about monotonicity of sequences of the form $(\root n\of{a_n}){n\ge 1}$ or the form $(\root{n+1}\of{a{n+1}}/\root n\of{a_n}){n\ge1}$, where $(a_n){n\ge 1}$ is a number-theoretic or combinatorial sequence of positive integers. This material might stimulate further research.