4. (16th All-Soviet Union Mathematical Olympiad, 1982) From the set of numbers $1,2,3,4, \cdots, 1982$, delete some numbers so that in the remaining numbers, no number is equal to the product of any two other numbers. How many numbers must be deleted to achieve this? How can this be done?
4. If 43 numbers: $2, 3, \cdots, 44$ are deleted, then in the remaining numbers, no number is equal to the product of any other two. If fewer than 43 numbers are deleted, then there is at least one triplet $(k, 89-k, k(89-k))$ composed of numbers that have not been deleted, where $2 \leqslant k \leqslant 43, 46 \leqslant 89-k \leqslant 87, k(89-k) \leqslant\left(\frac{89}{2}\right)^{2}=1980.25$.