A word $w$ on the alphabet $A := \{0, 1\}$ is *factorable* if
\begin{equation}
w = u^k \mbox{ where } u \in A^* \mbox{ and } k \geq 2.
\end{equation}

Let $L$ be the language of the set of factorable words on $A$ and $f(t)$ be its generating series, that is \begin{equation} f(t) := \sum_{n \geq 0} |L \cap A^n| \; t^n. \end{equation}

What is the generating function of $L$?

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