Second Problem, IMAR Competition 2012

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Laurențiu Ploscaru
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Second Problem, IMAR Competition 2012

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Given an integer $n\ge 2$, compute the sum $\displaystyle\sum \dfrac{1}{pq}$ where the summation is over all coprime integers $p$ and $q$ such that $1\le p < q\le n$ and $p + q > n$.
People are strange when you're a stranger,
Faces look ugly when you're alone.
Women seem wicked when you're unwanted,
Streets are uneven when you're down.
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