Hajos Group

Author

Eric W. Weisstein
January 14, 2005

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GroupTheory/HajosGroup.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/HajosGroup.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Code

HajosGroupQ[n_]:=MatchQ[Split[Sort[FactorInteger[n],#1[[2]]>#2[[2]]&],#1[[2]]==#2[[2]]&],{}|{{{p_,a_}}}|{{{p_,a_}},{{q_,1}}}|{{{p_,1},{q_,1}}}|{{{p_,2}},{{q_,1},{r_,1}}}|{{{p_,2},{q_,2}}}|{{{p_,1},{q_,1},{r_,1}}}|{{{p_,1},{q_,1},{r_,1},{s_,1}}}]

Enumeration

Select[Range[300],!HajosGroupQ[#]&]

<<Utilities`Plot`

Show[PixelPerfect[NaryPlot[Select[Range[2500],!HajosGroupQ[#]&]],BlockSize->2]]