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%I #38 Jan 05 2024 12:56:52
%S 1,2,-1,3,0,-1,4,0,0,0,5,0,0,0,-1,6,3,2,0,0,1,7,0,0,0,0,0,-1,8,0,0,0,
%T 0,0,0,0,9,0,0,0,0,0,0,0,0,10,5,0,0,2,0,0,0,0,1,11,0,0,0,0,0,0,0,0,0,
%U -1,12,0,0,0,0,0,0,0,0,0,0,0,13,0,0,0,0,0,0,0,0,0,0,0,-1
%N Triangle T(n,m) read by rows: T(n,1) = n; T(n,m) = A008683(n)*n/m if m is a divisor of n, where m = 2..n, otherwise T(n,m) = 0.
%C The function here is _Mats Granvik_'s idea: my effort is coding it and entering it in the OEIS. All of it is based on _Gary W. Adamson_'s A126988.
%H G. C. Greubel, <a href="/A141673/b141673.txt">Rows n=1..100 of triangle, flattened</a>
%e Triangle begins
%e { 1},
%e { 2, -1},
%e { 3, 0, -1},
%e { 4, 0, 0, 0},
%e { 5, 0, 0, 0, -1},
%e { 6, 3, 2, 0, 0, 1},
%e { 7, 0, 0, 0, 0, 0, -1},
%e { 8, 0, 0, 0, 0, 0, 0, 0},
%e { 9, 0, 0, 0, 0, 0, 0, 0, 0},
%e {10, 5, 0, 0, 2, 0, 0, 0, 0, 1}
%t t[n_, m_] = If[m == 1, n, If[Mod[n, m] == 0, MoebiusMu[n]*n/m, 0]]; Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%]
%o (PARI) T(n,m) = if (m==1, n, if (n % m, 0, moebius(n)*n/m));
%o tabl(nn) = for (n=1, nn, for (m=1, n, print1(T(n,m), ", ")); print); \\ _Michel Marcus_, Jun 10 2018
%Y Cf. A008683, A055615, A126988.
%K sign,tabl,easy
%O 1,2
%A _Roger L. Bagula_, _Gary W. Adamson_ and _Mats Granvik_, Sep 06 2008
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