# 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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