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A skew brace is a triplet(A,⋅,∘)(A,{\cdot}\,,\circ), where(A,⋅)(A,{\cdot}\,)and(A,∘)(A,\circ)are groups such that the brace relationx∘(y⋅z)=(x∘y)⋅x-1⋅(x∘z)x\circ(y\cdot z)=(x\circ y)\cdot x^{-1}\cdot(x\circ z)holds for allx,y,z∈Ax,y,z\in A. In this paper, we study the number of finite skew braces(A,⋅,∘)(A,{\cdot}\,,\circ), up to isomorphism, such that(A,⋅)(A,{\cdot}\,)and(A,∘)(A,\circ)are both isomorphic toTnT^{n}with  non-abelian simple andn∈Nn\in\mathbb{N}. We prove that it is equal to the number of unlabeled directed graphs onn+1n+1vertices, with one distinguished vertex, and whose underlying undirected graph is a tree. In particular, it depends only on  and is independent of .

Finite skew braces with isomorphic non-abelian characteristically simple additive and circle groups