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%I #16 Oct 15 2017 06:54:18
%S 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,
%T 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,
%U 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
%N Left Moebius transformation matrix, M, by antidiagonals.
%C 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.
%H C. Kimberling, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Kimberling/kimberling24.html">Matrix Transformations of Integer Sequences</a>, J. Integer Seqs., Vol. 6, 2003.
%F M = T^(-1), where T is the left summatory matrix, A077049.
%e Northwest corner:
%e 1 0 0 0 0 0
%e -1 1 0 0 0 0
%e -1 0 1 0 0 0
%e 0 -1 0 1 0 0
%e -1 0 0 0 1 0
%e 1 -1 -1 0 0 1
%o (PARI) nn=10; matrix(nn, nn, n, k, if (n % k, 0, 1))^(-1) \\ _Michel Marcus_, May 21 2015
%Y Cf. A008683, A054525, A077049, A077051, A077052.
%K sign,tabl
%O 1,1
%A _Clark Kimberling_, Oct 22 2002
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