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We study the Riesz $(a,p)$-capacity of the so called Dobi\'nski set. Wecharacterize the values of the parameters $a$ and $p$ for which the$(a,p)$-Riesz capacity of the Dobi\'nski set is positive. In particular we showthat the Dobi\'nski set has positive logarithmic capacity, thus answering aquestion of Dayan, Fernand\'ez and Gonz\'alez. We approach the problem byconsidering the dyadic analogues of the Riesz $(a,p)$-capacities which seem tobe better adapted to the problem.

Riesz capacities of a set due to Dobi\'nski