Peculiar mod

If \(n\) is a positive integer, denote \(f (n)\) to be the number of positive integers \(k\) such that \(n\) and \(k\) leave the same remainder when divided by \(2k-1\).

Find the number of positive integers \(x, 1 \leq x \leq 2014\) such that \(f (x)\) is odd.

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