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A directed graph is strongly connected if it is possible to reach any vertex starting from any other vertex.
A directed graph is called aperiodic if the greatest common divisor of the lengths of its cycles is one.
`a(n)` is the number of strongly connected aperiodic graphs of `n` vertice up to isomorphism. In this problem, graphs are simple graphs, that is, no loops or multiple edges are allowed.
For example, it is easy to see `G_1`, `G_2` and `G_3` are strongly connected. `G_1` has cycles of length `\{2,3\}`, `G_2` has cycles of length `\{2,2,3\}` and `G_3` has cycles of length `\{2,4\}`. Therefore, `G_1` and `G_2` are aperiodic while `G_3` is periodic.
Find `a(n)`.