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I suggest 280 = 23*5*7

The 16 factors are

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280

that is 2a*5b*7c where a = 0,1,2,3; b = 0,1 and c = 0,1

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Q: What is the smallest positive integer that has exactly 16 factors and is not divisible by 6?
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