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Found problems: 1

2009 Argentina Team Selection Test, 2
Tags: inequalities , clevermath
Let $ a_1, a_2, ..., a_{300}$ be nonnegative real numbers, with $ \sum_{i\equal{}1}^{300} a_i \equal{} 1$. Find the maximum possible value of $ \sum_{i \neq j, i|j} a_ia_j$.