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ISI2011-PCB-A-1

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Let $D = \{d_1, d_2, \dots, d_k\}$ be the set of distinct divisors of a positive integer $n$ ($D$ includes 1 and $n$). Then show that
$\Sigma_{i=1}^k \sin^{-1} \sqrt{\log_nd_i}=\frac{\pi}{4} \times k$.
hint: $\sin^{−1} x + \sin^{−1} \sqrt{1-x^2} = \frac{\pi}{2}$
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