You're right, those two functors \\(F\\) and \\(F'\\) are not isomorphisms, but they are *related* by an isomorphism: \\(F' = F \circ S\\), where \\(S: \mathbf{M}\to\mathbf{M}\\) is the functor represented by the sequence \\((3, 2, 5, 7, 11, 13, \dots)\\), which is its own inverse. What I think is true is that two functors \\(F_1, F_2\\) are "equivalent" in the sense you describe, having the same image, just reordered, exactly when \\(F_1=F_2\circ S\\) for some invertible functor \\(S\\).