A Redheffer matrix is a square -matrix with elements equal to 1 if or (divides), and 0 otherwise. For , 2, ..., the first few Redheffer matrices are
The Redheffer matrix of order 255 is illustrated above.
The determinant of the
Redheffer matrix is equal to the Mertens function. For , 2, ..., the first few values are therefore 1, 0, , , , , , , , ... (OEIS A002321).
The number of unit eigenvalues of the Redheffer matrix for is equal to
(Vaughan 1993, 1996; Trott 2004, p. 57), giving the first few values as 1, 0,
1, 1, 2, 3, 4, 4, 5, 6, 7, 8, 9, 10, 11, ... (OEIS A083058).
Sloane, N. J. A. Sequences A002321/M0102 and A083058 in "The On-Line Encyclopedia
of Integer Sequences."Trott, M. The
Mathematica GuideBook for Programming. New York: Springer-Verlag, 2004. http://www.mathematicaguidebooks.org/.Vaughan,
R. C. "On the Eigenvalues of Redheffer's Matrix. I." In Number
Theory with an Emphasis on the Markov Spectrum (Provo, UT, 1991) (Ed. A. D. Pollington
and W. Moran). New York: Dekker, pp. 283-296, 1993.Vaughan,
R. C. "On the Eigenvalues of Redheffer's Matrix. II." J. Austral.
Math. Soc.60, 260-273, 1996.
-matrix with elements 
equal to 1 if 
or 
(
divides 
), and 0 otherwise. For 
, 2, ..., the first few Redheffer matrices are
![[1],[1 1; 1 1],[1 1 1; 1 1 0; 1 0 1],[1 1 1 1; 1 1 0 1; 1 0 1 0; 1 0 0 1].](/images/equations/RedhefferMatrix/NumberedEquation1.svg)
Redheffer matrix is equal to the Mertens function 
. For 
, 2, ..., the first few values are therefore 1, 0, 
, 
, 
, 
, 
, 
, 
, ... (OEIS A002321).
Redheffer matrix for 
is equal to
