Find the dissimilar number from the following:
$$16,256,64,624,1024$$

Let's check the mathematical properties of each number:
* $16=4^2$ (Perfect square)
* $256=16^2$ (Perfect square)
* $64=8^2$ (Perfect square, also $4^3$)
* $1024=32^2$ (Perfect square)
* $624$ is not a perfect square (Since $25^2=625$, so $624=25^2-1$).

All numbers except $624$ are perfect squares. Therefore, $624$ is the dissimilar number.