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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