A077050 Left Moebius transformation matrix, M, by antidiagonals.

1, -1, 0, -1, 1, 0, 0, 0, 0, 0, -1, -1, 1, 0, 0, 1, 0, 0, 0, 0, 0, -1, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1

Offset: 1

Author

Clark Kimberling, Oct 22 2002

Keywords

• sign
• tabl

Comments

If S=(s(1),s(2),...) is a sequence written as a column vector, then M*S is the Moebius transform of S; i.e. its n-th term is Sum{mu(k)*s(k): k|n}. If s(n)=n, then M*S(n)=phi(n), the Euler totient function, A000010. Row sums: 0 for n>=2.

Examples

			Northwest corner:
1 0 0 0 0 0
-1 1 0 0 0 0
-1 0 1 0 0 0
0 -1 0 1 0 0
-1 0 0 0 1 0
1 -1 -1 0 0 1
		

Links

• C. Kimberling, Matrix Transformations of Integer Sequences, J. Integer Seqs., Vol. 6, 2003.

Crossrefs

Cf. A008683, A054525, A077049, A077051, A077052.

Programs

PARI

nn=10; matrix(nn, nn, n, k, if (n % k, 0, 1))^(-1) \\ Michel Marcus, May 21 2015

Formula

M = T^(-1), where T is the left summatory matrix, A077049.