The number $100$ has four perfect square divisors, namely $1,$ $4,$ $25,$ and $100.$ What is the smallest positive integer that has exactly $2$ perfect square divisors?

The smallest number that works is 16.

In the example, the divisors of 100 include 1 and 100.

Using that standard, the smallest integer would be 4

because its perfect square divisors are 1 and 4.

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