Self-Power Squares

How many integers $n$, between $1$ and $100$ inclusive, have the property that $n^n$ is a square number?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
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How many integers $n$, between $1$ and $100$ inclusive, have the property that $n^n$ is a square number?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.