Redheffer Matrix

Author

Eric W. Weisstein
November 2, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/LinearAlgebra/RedhefferMatrix.nb.

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

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

Code

Redheffer[d_]:=SparseArray[{{i_,1}->1,{i_,j_}/;Mod[j,i]==0->1},{d,d}]

Redheffer2[d_]:=Table[If[j==1||IntegerQ[j/i],1,0],{i,d},{j,d}]

Check

Table[Redheffer[n]==Redheffer2[n],{n,10}]

Enumeration

MatrixForm/@Redheffer/@Range[5]

Visualization

<<Utilities`Plot`

Show[PixelPerfect[Redheffer[255]//Normal]]

Determinants

Det/@Redheffer/@Range[35]

FindSequenceFunction[%]

Det/@Redheffer/@Range[50]==Rest[FoldList[Plus,0,MoebiusMu/@Range[50]]]

Eigenvalues

Count[#,1]&/@Eigenvalues/@Redheffer/@Range[30]

Table[n-Floor[Log[2,n]]-1,{n,30}]

A083058