Suppose you divide all non-prime numbers in two categories, those which (a) have a prime factor greater than the square root of the number, and those which (b) don't, and all prime factors are less or equal than the square root.(adsbygoogle = window.adsbygoogle || []).push({});

Let Ca and Cb be the count of numbers in categories (a) and (b), resp. As you collect more numbers, a quick&dirty survey seems to indicate that the ratio Ca/Cb keeps growing (I don't know if converging), from 1.4 to 1.9 to 2.3... (Funny, actually I kind of imagined Cb to be bigger than Ca.)

What kind of math knowledge in number theory (or not) applies to the study of this? Any pointer, please?

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# Numbers with a prime factor > sqrt

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