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
Famous quotes containing the word distribution:
“In this distribution of functions, the scholar is the delegated intellect. In the right state, he is, Man Thinking. In the degenerate state, when the victim of society, he tends to become a mere thinker, or, still worse, the parrot of other men’s thinking.”
—Ralph Waldo Emerson (1803–1882)
“The question for the country now is how to secure a more equal distribution of property among the people. There can be no republican institutions with vast masses of property permanently in a few hands, and large masses of voters without property.... Let no man get by inheritance, or by will, more than will produce at four per cent interest an income ... of fifteen thousand dollars] per year, or an estate of five hundred thousand dollars.”
—Rutherford Birchard Hayes (1822–1893)
“Classical and romantic: private language of a family quarrel, a dead dispute over the distribution of emphasis between man and nature.”
—Cyril Connolly (1903–1974)