login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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: A166919 A338874 A338876 * A283795 A168641 A255914
KEYWORD
tabl,nonn,frac
AUTHOR
Mats Granvik, Jul 20 2015
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)