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%I #2 Mar 30 2012 17:25:28
%S 0,0,1,0,0,1,0,1,0,2,0,0,0,0,1,0,1,1,0,0,4,0,0,0,0,0,0,1,0,1,0,2,0,0,
%T 0,4,0,0,1,0,0,0,0,0,3,0,1,0,0,1,0,0,0,0,6,0,0,0,0,0,0,0,0,0,0,1,0,1,
%U 1,2,0,4,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,8
%N Triangle read by rows: A051731 * A051953^(n-k) * 0^(n-k), 1 <= k <= n.
%C Row sums = A001065: (0, 1, 1, 3, 1, 6, 1, 7, 4, 8,...).
%C n-th row = (p-1) zeros followed by 1, iff n is prime.
%C For T(n,k), k divides n if k not = 0.
%F Triangle read by rows, A051731 * A051953^(n-k); where A051953^(n-k) = an infinite lower triangular matrix with A051953 (0, 1, 1, 2, 1, 4, 1, 4, 3, 6, 1, 8,...) in the main diagonal and the rest zeros. A051731 = inverse Mobius transform.
%e First few rows of the triangle =
%e 0;
%e 0, 1;
%e 0, 0, 1;
%e 0, 1, 0, 2;
%e 0, 0, 0, 0, 1;
%e 0, 1, 1, 0, 0, 4;
%e 0, 0, 0, 0, 0, 0, 1;
%e 0, 1, 0, 2, 0, 0, 0, 4;
%e 0, 0, 1, 0, 0, 0, 0, 0, 3;
%e 0, 1, 0, 0, 1, 0, 0, 0, 0, 6;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e 0, 1, 1, 2, 0, 4, 0, 0, 0, 0, 0, 8;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 8;
%e ...
%Y Cf. A051953, A001065.
%K nonn,tabl
%O 1,10
%A _Gary W. Adamson_, Jul 11 2008
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