# A Peculiar Function!

Algebra Level 5

$\large{f(n) = \max \{f(j)+f(n-j)+j \} }$

Let $$f$$ be a function from the set of positive integers to the set of non-negative integers such that $$f(1)=0$$ and $$f(n)$$ is defined as of above for all $$n \geq 2$$. Determine the value of $$f(2015)$$.

Note: The maximum in the definition of $$f(n)$$ is considered over all $$j$$ such that $$1 \leq j \leq n-1$$, i.e for all $$j$$ for which $$f(n)$$ and $$f(n-j)$$ are defined.

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