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 A260237 Numerators of the characteristic polynomials of the von Mangoldt function matrix. 3
 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, -1183, 53, 1, 0, -3, -1231, 5251, 8989, 1451, -731, -1, 0, 0, 7, 397, -12491, -19877, -15047, 1567, 1, 0, 0, 0, -7, -1483, 50111, 69761, 45959, -5261, -1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS The von Mangoldt function matrix is the symmetric matrix A191898 divided by either the row index or the column index. 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. LINKS EXAMPLE The first term set to zero is not part of the characteristic polynomials. It is only there for the formatting of the table. { {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, -1183, 53, 1}, {0, -3, -1231, 5251, 8989, 1451, -731, -1}, {0, 0, 7, 397, -12491, -19877, -15047, 1567, 1}, {0, 0, 0, -7, -1483, 50111, 69761, 45959, -5261,-1} } MATHEMATICA 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]}] CROSSREFS Denominators in A260238. Sequence in context: A158215 A294254 A216792 * A118135 A318671 A109014 Adjacent sequences:  A260234 A260235 A260236 * A260238 A260239 A260240 KEYWORD tabl,sign,frac AUTHOR Mats Granvik, Jul 20 2015 STATUS approved

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Last modified April 18 11:20 EDT 2019. Contains 322209 sequences. (Running on oeis4.)