Caution! Radiation

Algebra Level pending

Say a positive integer n is radioactive if one of its prime factors is strictly greater than √ n. For example, 2012 = 22 · 503, 2013 = 3 · 11 · 61 and 2014 = 2 · 19 · 53 are all radioactive, but 2015 = 5 · 13 · 31 is not. How many radioactive numbers have all prime factors less than 30?

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