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A positive number $n$ is called nice if it has at least $3$ proper divisor and it is equal to the sum of its three largest proper divisor. For example, $6$ is a nice number because its three largest proper divisors are $1,2,3$ and $6=1+2+3$. Find the number of nice integers not greater than $6000$. 


Source: BdMO 2021


Number Theory

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