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%I #8 Feb 20 2022 01:27:50
%S 1,-1,1,-2,0,1,-1,-1,0,1,-4,0,0,0,1,2,-2,-1,0,0,1,-6,0,0,0,0,0,1,-1,
%T -1,0,-1,0,0,0,1,-2,0,-2,0,0,0,0,0,1,4,-4,0,0,-1,0,0,0,0,1,-10,0,0,0,
%U 0,0,0,0,0,0,1,2,2,-1,-2,0,-1,0,0,0,0,0,1
%N Inverse of A054523.
%C Row sums = A130054, (1, -1, -1, -3, 0, -5, -2, -3, 0, ...). A129691 * A126988 = A051731. Left column = A023900: (1, -1, -2, -1, -4, 2, -6, ...).
%H Andrew Howroyd, <a href="/A129691/b129691.txt">Table of n, a(n) for n = 1..1275</a>
%F A054523^(-1), as an infinite lower triangular matrix.
%F T(n,k) = A023900(n/k) for k | n, T(n,k) = 0 otherwise. - _Andrew Howroyd_, Aug 03 2018
%e First few rows of the triangle:
%e 1;
%e -1, 1;
%e -2, 0, 1;
%e -1, -1, 0, 1;
%e -4, 0, 0, 0, 1;
%e 2, -2, -1, 0, 0, 1;
%e ...
%o (PARI) T(n,k)={if(n%k, 0, sumdivmult(n/k, d, d*moebius(d)))} \\ _Andrew Howroyd_, Aug 03 2018
%Y Cf. A054523, A130055, A023900, A126988, A051731.
%K tabl,sign
%O 1,4
%A _Gary W. Adamson_, May 04 2007
%E Terms a(56) and beyond from _Andrew Howroyd_, Aug 03 2018
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