Redheffer Matrix
Definition
A Redheffer matrix is a square (0, 1)-matrix with elements a_(i j) equal to 1 if j = 1 or i|j (i divides j), and 0 otherwise. For n = 1, 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]. The Redheffer matrix of order 255 is illustrated above. The determinant of the n×n Redheffer matrix is equal to the Mertens function M(n). For n = 1, 2, ..., the first few values are therefore 1, 0, -1, -1, -2, -1, -2, -2, -2, ... (OEIS A002321).
Related terms
