Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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