Sum of Squares of a Partition

If we have a partition $\lambda$ of an integer $n$, such that:

$$\lambda =({\lambda }_1,{\lambda }_2,\dots ,{\lambda }_k)$$

where ${\sum }_{i=1}^k{\lambda }_i=n$, then the sum of squares is defined as:

$$SSQ(\lambda )=\sum _{i=1}^k{\lambda }_i^2$$

For some fixed $k$, the minimum sum of squares happens when the partitions are as equal as possible, the maximum sum of squares happens when the partitions are as imbalanced as possible.

No comment, just thought this was interesting.