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A077050 Left Moebius transformation matrix, M, by antidiagonals. 4
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..96.

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

FORMULA

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

EXAMPLE

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

PROG

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

CROSSREFS

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

Sequence in context: A131372 A098457 A137161 * A128432 A195198 A039966

Adjacent sequences:  A077047 A077048 A077049 * A077051 A077052 A077053

KEYWORD

sign,tabl

AUTHOR

Clark Kimberling, Oct 22 2002

STATUS

approved

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Last modified February 24 21:22 EST 2018. Contains 299628 sequences. (Running on oeis4.)