# Peculiar mod

Number Theory Level 5

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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