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A260238 Denominators of the characteristic polynomials of the von Mangoldt function matrix.

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%I A260238 #9 Aug 16 2015 23:23:40
%S A260238 1,1,1,2,1,1,6,6,1,1,2,4,12,1,1,2,20,3,60,1,1,2,60,360,360,60,1,1,2,
%T A260238 420,2520,1260,504,420,1,1,1,4,120,5040,2520,5040,840,1,1,1,1,3,360,
%U A260238 15120,7560,15120,2520,1
%N A260238 Denominators of the characteristic polynomials of the von Mangoldt function matrix.
%C A260238 The von Mangoldt function matrix is the symmetric Greatest Common Divisor (GCD) type matrix A191898 divided by either the row index or the column index.
%C A260238 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.
%C A260238 The second diagonal appears to be A003418.
%e A260238 {
%e A260238 {0},
%e A260238 {1, 1},
%e A260238 {1, 2, 1},
%e A260238 {1, 6, 6, 1},
%e A260238 {1, 2, 4, 12, 1},
%e A260238 {1, 2, 20, 3, 60, 1},
%e A260238 {1, 2, 60, 360, 360, 60, 1},
%e A260238 {1, 2, 420, 2520, 1260, 504, 420, 1},
%e A260238 {1, 1, 4, 120, 5040, 2520, 5040, 840, 1},
%e A260238 {1, 1, 1, 3, 360, 15120, 7560, 15120, 2520, 1}
%e A260238 }
%t A260238 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[Denominator[b]]
%Y A260238 Cf. A191898, A003418. Numerators in A260237.
%K A260238 tabl,nonn,frac
%O A260238 1,4
%A A260238 _Mats Granvik_, Jul 20 2015