A positive integer $n$ is called *nice* if it has at least 3 proper divisors and it is equal to the sum of its three largest proper divisors. For example, $6$ is *nice* because its largest three proper divisors are $3, 2, 1$ and $6 = 3 + 2 + 1$. Find the number of *nice* integers not greater than $3000$.

Let's think step by step and output the final answer within \boxed{}.
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