The K-smooth integers on a generalized Ulam spiral [Les entiers K-friables sur une spirale d'Ulam généralisée ]

The K-smooth integers on a generalized Ulam spiral [Les entiers K-friables sur une spirale d'Ulam généralisée].




Starting from the center of the picture, the spheres are numbered (N=2,..., 65026) when following a square spiral. The radius of the sphere displaying the number N is an decreasing function of the logarithm of the smoothness K of N (K being the largest prime factors of N).


Nota: the logarithm of K (inside [2,11.082] and renormalized inside [2,255]) is displayed using the following palette. Then the luminance is too a decreasing function of the logarithm of K.


[Plus d'informations à propos de la spirale d'Ulam et de ses généralisations -en français/in french-]
[More information about the Ulam spiral and ist generalizations -in english/en anglais-]


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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