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Search: id:A077050
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| A077050 |
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Left Moebius transformation matrix, M, by antidiagonals. |
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+0
4
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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.
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LINKS
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C. Kimberling, Matrix Transformations of Integer Sequences, J. Integer Seqs., Vol. 6, 2003.
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FORMULA
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M=T^(-1), where T is the left summatory matrix, A077049.
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EXAMPLE
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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
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CROSSREFS
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Cf. A008683, A077049, A077051, A077052.
Sequence in context: A131372 A098457 A137161 this_sequence A128432 A039966 A089451
Adjacent sequences: A077047 A077048 A077049 this_sequence A077051 A077052 A077053
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KEYWORD
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sign,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Oct 22 2002
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