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A127574 Triangle T(n,k) = k*sigma(n) if k divides n, else 0.

%I A127574 #9 Sep 18 2022 19:15:53
%S A127574 1,3,6,4,0,12,7,14,0,28,6,0,0,0,30,12,24,36,0,0,72,8,0,0,0,0,0,56,15,
%T A127574 30,0,60,0,0,0,120,13,0,39,0,0,0,0,0,117,18,36,0,0,90,0,0,0,0,180,12,
%U A127574 0,0,0,0,0,0,0,0,0,132,28,56,84,112,0,168,0,0,0,0,0,336
%N A127574 Triangle T(n,k) = k*sigma(n) if k divides n, else 0.
%F A127574 T(n,k) = Sum_{j=k..n} A130208(n,j)*A127093(j,k), product of the two infinite lower triangular matrices.
%F A127574 T(n,1) = A000203(n).
%F A127574 T(n,n) = A064987(n).
%e A127574 First few rows of the triangle are:
%e A127574    1;
%e A127574    3,  6;
%e A127574    4,  0, 12;
%e A127574    7, 14,  0, 28;
%e A127574    6,  0,  0,  0, 30;
%e A127574   12, 24, 36,  0,  0, 72;
%e A127574   ...
%Y A127574 Cf. A127093, A127573, A064987, A000203, A072861 (row sums).
%K A127574 nonn,tabl
%O A127574 1,2
%A A127574 _Gary W. Adamson_, Jan 19 2007