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Triangle read by rows: A051731 * A143239.
2

%I #14 Jun 05 2023 07:08:14

%S 1,3,-1,4,0,-1,7,-3,0,0,6,0,0,0,-1,12,-4,-3,0,0,1,8,0,0,0,0,0,-1,15,

%T -7,0,0,0,0,0,0,13,0,-4,0,0,0,0,0,0,18,-6,0,0,-3,0,0,0,0,1,12,0,0,0,0,

%U 0,0,0,0,0,-1,28,-12,-7,0,0,3,0,0,0,0,0,0,14,0,0,0,0,0,0,0,0,0,0,0,-1

%N Triangle read by rows: A051731 * A143239.

%C Left border = sigma(n), A000203.

%C Right border = mu(n), A008683.

%C Row sums = n.

%C It appears that T(n,k) = Sum_{d|n} mu(d)*sigma(n/d). - _Joerg Arndt_, Jul 31 2011

%e First few rows of the triangle:

%e 1;

%e 3, -1;

%e 4, 0, -1;

%e 7, -3, 0, 0;

%e 6, 0, 0, 0, -1;

%e 12, -4, -3, 0, 0, 1;

%e 8, 0, 0, 0, 0, 0, -1;

%e 15, -7, 0, 0, 0, 0, 0, 0;

%e 13, 0, -4, 0, 0, 0, 0, 0, 0;

%e 18, -6, 0, 0, -3, 0, 0, 0, 0, 1;

%e ...

%Y Cf. A000203, A008683, A051731, A143239.

%K tabl,sign

%O 1,2

%A _Gary W. Adamson_, Aug 07 2008

%E a(68) = -12 corrected by _Georg Fischer_, Jun 05 2023