The K-smooth integers on a Bidimensional Hilbert Curve -iteration 2- [Les entiers K-friables sur une courbe de Hilbert bidimensionnelle -itération 2- ]

The K-smooth integers on a Bidimensional Hilbert Curve -iteration 2- [Les entiers K-friables sur une courbe de Hilbert bidimensionnelle -itération 2-].




Starting from the bottom left corner of the [0,+1]x[0,+1] square, the spheres are numbered (N=2,..., 17) when following a bidimensional Hilbert curve -iteration 2-. The radius of the sphere displaying the number N is a decreasing function of the logarithm of the smoothness K of N (K being the largest prime factors of N).


Nota: the used color palette displays the parametric coordinate of the curve.


See some related pictures (including this one):

The smooth integers The smooth integers

The smooth integers: the prime factor sum of the integer numbers The smooth integers: the prime factor product -the radical function- of the integer numbers  
The smooth integers: the prime factor sum of the integer numbers The smooth integers: the prime factor product -the radical function- of the integer numbers

The 2-smooth integers The 3-smooth integers The 5-smooth integers The 7-smooth integers  
The 2/3/5/7-smooth integers

The 2/3/5/7-smooth integers on a generalized Ulam spiral The 2/3/5/7-smooth integers on a generalized Ulam spiral  
The 2/3/5/7/11/13/17-smooth integers on a generalized Ulam spiral  
The K-smooth integers on a generalized Ulam spiral  
The K-smooth integers on a generalized Ulam spiral The K-smooth integers on a generalized Ulam spiral The K-smooth integers on a generalized Ulam spiral  
The K-smooth integers on a generalized Ulam spiral The K-smooth integers on a generalized Ulam spiral The K-smooth integers on a generalized Ulam spiral

The K-smooth integers on a Bidimensional Hilbert Curve -iteration 1- The K-smooth integers on a Bidimensional Hilbert Curve -iteration 2- The K-smooth integers on a Bidimensional Hilbert Curve -iteration 3- The K-smooth integers on a Bidimensional Hilbert Curve -iteration 4- The K-smooth integers on a Bidimensional Hilbert Curve -iteration 5-  
The K-smooth integers on a Tridimensional Hilbert Curve -iteration 1- The K-smooth integers on a Tridimensional Hilbert Curve -iteration 2- The K-smooth integers on a Tridimensional Hilbert Curve -iteration 3- The K-smooth integers on a Tridimensional Hilbert Curve -iteration 4- Empty


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