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A159936 Triangle read by rows, A051731 * A054533 * transpose(A101688), provided A101688 is read as a square array.

%I A159936 #16 Jul 31 2019 03:53:44
%S A159936 1,1,1,1,1,2,1,1,2,2,1,1,2,3,4,1,1,2,2,3,2,1,1,2,3,4,5,6,1,1,2,2,4,4,
%T A159936 4,4,1,1,2,3,3,3,6,6,6,1,1,2,2,4,4,5,4,5,4,1,1,2,3,4,5,6,7,8,9,10,1,1,
%U A159936 2,2,3,2,4,4,6,6,4,4,1,1,2,3,4,5,6,7,8,9,10,11,12,1,1,2,2,4,4,6,6,7,6,7,6,7,6
%N A159936 Triangle read by rows, A051731 * A054533 * transpose(A101688), provided A101688 is read as a square array.
%C A159936 Row sums = A057661: (1, 2, 4, 6, 11, 11, 22,...). Right border = A000010, phi(n).
%F A159936 Triangle read by rows, A051731 * A054533 * A000012. A051731 = the inverse Mobius transform. A054533 = the lower left half of the Ramanujan sum table. The operation (* transpose(A101688)) takes partial sums of (A051731 * A054533) starting from the right. [Edited by _Petros Hadjicostas_, Jul 30 2019]
%e A159936 First few rows of the triangle are as follows:
%e A159936   1;
%e A159936   1, 1;
%e A159936   1, 1, 2;
%e A159936   1, 1, 2, 2;
%e A159936   1, 1, 2, 3, 4;
%e A159936   1, 1, 2, 2, 3, 2;
%e A159936   1, 1, 2, 3, 4, 5, 6;
%e A159936   1, 1, 2, 2, 4, 4, 4, 4;
%e A159936   1, 1, 2, 3, 3, 3, 6, 6, 6;
%e A159936   1, 1, 2, 2, 4, 4, 5, 4, 5, 4;
%e A159936   1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10;
%e A159936   1, 1, 2, 2, 3, 2, 4, 4, 6, 6,  4,  4;
%e A159936   1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12;
%e A159936   1, 1, 2, 2, 4, 4, 6, 6, 7, 6,  7,  6,  7, 6;
%e A159936   1, 1, 2, 3, 3, 3, 5, 4, 3, 5,  9,  8, 10, 9, 8;
%e A159936   1, 1, 2, 2, 4, 4, 4, 4, 8, 8,  8,  8,  8, 8, 8, 8;
%e A159936   ...
%Y A159936 Cf. A000010, A051731, A054532, A054533, A054534, A054535, A057661, A101688.
%K A159936 nonn,tabl
%O A159936 1,6
%A A159936 _Gary W. Adamson_, Apr 26 2009
%E A159936 Name edited by _Petros Hadjicostas_, Jul 30 2019