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A260237 Numerators of the characteristic polynomials of the von Mangoldt function matrix.

%I A260237 #11 Aug 18 2015 13:51:41
%S A260237 0,1,-1,-1,-1,1,1,11,-1,-1,0,-3,-9,5,1,0,3,81,7,-73,-1,0,3,73,-1261,
%T A260237 -1183,53,1,0,-3,-1231,5251,8989,1451,-731,-1,0,0,7,397,-12491,-19877,
%U A260237 -15047,1567,1,0,0,0,-7,-1483,50111,69761,45959,-5261,-1
%N A260237 Numerators of the characteristic polynomials of the von Mangoldt function matrix.
%C A260237 The von Mangoldt function matrix is the symmetric matrix A191898 divided by either the row index or the column index.
%C A260237 Every eigenvalue of a smaller von Mangoldt function matrix appears to be common to infinitely many larger von Mangoldt matrices. The eigenvalues of smaller von Mangoldt function matrices also repeat within larger von Mangoldt function matrices.
%e A260237 The first term set to zero is not part of the characteristic polynomials. It is only there for the formatting of the table.
%e A260237 {
%e A260237 {0},
%e A260237 {1, -1},
%e A260237 {-1, -1, 1},
%e A260237 {1, 11, -1, -1},
%e A260237 {0, -3, -9, 5, 1},
%e A260237 {0, 3, 81, 7, -73, -1},
%e A260237 {0, 3, 73, -1261, -1183, 53, 1},
%e A260237 {0, -3, -1231, 5251, 8989, 1451, -731, -1},
%e A260237 {0, 0, 7, 397, -12491, -19877, -15047, 1567, 1},
%e A260237 {0, 0, 0, -7, -1483, 50111, 69761, 45959, -5261,-1}
%e A260237 }
%t A260237 Clear[nnn, nn, T, n, k, x]; nnn = 9; T[n_, k_] := T[n, k] = Which[n < 1 || k < 1, 0, n == 1 || k == 1, 1, k > n, T[k, n], n > k, T[k, Mod[n, k, 1]], True, -Sum[T[n, i], {i, n - 1}]]; b = Table[CoefficientList[CharacteristicPolynomial[Table[Table[T[n, k]/n, {k, 1, nn}], {n, 1, nn}], x], x], {nn, 1, nnn}]; Flatten[{0,Numerator[b]}]
%Y A260237 Denominators in A260238.
%K A260237 tabl,sign,frac
%O A260237 1,8
%A A260237 _Mats Granvik_, Jul 20 2015