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%I #4 Mar 30 2012 18:36:53
%S 0,1,0,1,0,0,2,1,0,0,1,0,0,0,0,0,1,1,0,0,0,1,0,0,0,0,0,0,3,2,0,1,0,0,
%T 0,0,2,0,1,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
%U 2,1,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0
%N Matrix log of triangle A051731, where nonzero elements in the matrix log are all unit fractions and represented here by the denominators, with zero elements remaining zero.
%e This triangle is defined by:
%e * T(n,k) = A100995(n/k) if k|n, 0 otherwise.
%e Sequence A100995 is defined by:
%e * A100995(n) = m if n = p^m for some prime p, 0 otherwise.
%e Triangle A054525 equals A051731^-1 and is defined by:
%e * A054525(n,k) = MoebiusMu(n/k) if k|n, 0 otherwise.
%e Triangle A051731 is defined by:
%e * A051731(n,k) = 1 if k|n, 0 otherwise.
%e The matrix log of triangle A051731 begins:
%e 0;
%e 1, 0;
%e 1, 0, 0;
%e 1/2, 1, 0, 0;
%e 1, 0, 0, 0, 0;
%e 0, 1, 1, 0, 0, 0;
%e 1, 0, 0, 0, 0, 0, 0;
%e 1/3, 1/2, 0, 1, 0, 0, 0, 0;
%e 1/2, 0, 1, 0, 0, 0, 0, 0, 0;
%e 0, 1, 0, 0, 1, 0, 0, 0, 0, 0;
%e 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e 0, 0, 1/2, 1, 0, 1, 0, 0, 0, 0, 0, 0;
%e 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0;
%e 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e 1/4, 1/3, 0, 1/2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0; ...
%e where all nonzero elements are positive unit fractions.
%o (PARI) T(n,k)=if(n%k==0,if(#(factor(n/k)~)==1,factor(n/k)[1,2],0),0)
%Y Cf. A051731, A100995, A054525.
%K nonn,tabl
%O 1,7
%A _Paul D. Hanna_, Jan 13 2006
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