Counting k between 100 and 400 with k to the k square

For how many integers $k$ with $100\le k\le 400$ is the number $k^k$ a perfect square?

$156$. If $k$ is even, $k^k=(k^{k/2})^2$, giving $151$ values. If $k$ is odd, $k^k$ is a square exactly when $k$ itself is a square; the odd squares in range are $121,169,225,289,361$, adding $5$.