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A260238 Denominators of the characteristic polynomials of the von Mangoldt function matrix. 2
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, 420, 2520, 1260, 504, 420, 1, 1, 1, 4, 120, 5040, 2520, 5040, 840, 1, 1, 1, 1, 3, 360, 15120, 7560, 15120, 2520, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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.

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.

The second diagonal appears to be A003418.

LINKS

Table of n, a(n) for n=1..54.

EXAMPLE

{

{0},

{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, 420, 2520, 1260, 504, 420, 1},

{1, 1, 4, 120, 5040, 2520, 5040, 840, 1},

{1, 1, 1, 3, 360, 15120, 7560, 15120, 2520, 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[Denominator[b]]

CROSSREFS

Cf. A191898, A003418. Numerators in A260237.

Sequence in context: A199063 A140956 A166919 * A283795 A168641 A255914

Adjacent sequences:  A260235 A260236 A260237 * A260239 A260240 A260241

KEYWORD

tabl,nonn,frac

AUTHOR

Mats Granvik, Jul 20 2015

STATUS

approved

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Last modified September 30 17:12 EDT 2020. Contains 337440 sequences. (Running on oeis4.)