Do the bare minimum

Any number can be represented as a sum of square of numbers, for example \(9\) can be represented as \(3^{2}\) or \(2^{2}+2^{2}+1^{2}\) or even \(\underset { 9\quad times }{ \underbrace { { 1 }^{ 2 }+{ 1 }^{ 2 }+\cdots +{ 1 }^{ 2 } } } \).

Let \(\varsigma (n)\) be the minimum squares of numbers needed in the representation of \(n\). What is the value of.. \[\large \sum _{ i=2 }^{ 2015 }{ \varsigma (i) } \]

Details and assumptions

As explicit examples:

\(\varsigma (100)=1 \longrightarrow 10^{2} \)

\(\varsigma (120)=3 \longrightarrow 10^{2}+4^{2}+2^{2} \)

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