Kiriti's sum

Consider the sequence \( \{ a_n\} \) defined by \(a_1 = 2^{2013}\) and the recurrence relation

\[ \frac {1}{a_k} = \frac {1}{a_1} + \frac {1}{a_2} +\frac {1}{a_3}+ \cdots +\frac {1}{a_{k-1}} \mbox{ for } k>1.\]

What is the value of \(a_{2013}\)?

This problem is posed by Kiriti M.

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