Distribution
Let denote the number of y-smooth integers less than or equal to x (the de Bruijn function).
If the smoothness bound B is fixed and small, there is a good estimate for :
where denotes the number of primes less than or equal to .
Otherwise, define the parameter u as u = log x / log y: that is, x = yu. Then,
where is the Dickman function.
Read more about this topic: Smooth Number
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