A347256 Irregular triangle whose n-th row lists the integers m such that the n-th necklace polynomial is divisible by x^m-1.

1, 1, 2, 1, 2, 1, 2, 4, 1, 2, 1, 2, 3, 6, 1, 2, 4, 1, 2, 3, 6, 1, 2, 4, 1, 2, 5, 10, 1, 2, 4, 1, 2, 3, 4, 6, 12, 1, 2, 3, 6, 1, 2, 4, 1, 2, 4, 8, 1, 2, 4, 8, 16, 1, 2, 3, 6, 1, 2, 3, 6, 9, 18, 1, 2, 4, 8, 1, 2, 3, 6, 1, 2, 5, 10, 1, 2, 11, 22, 1, 2, 4, 8, 1, 2, 4, 5, 10, 20

Offset

2,3

Links

Table of n, a(n) for n=2..90.

John R. Doyle, Paul Fili and Trevor Hyde, Dynatomic polynomials, necklace operators, and universal relations for dynamical units, arXiv:2108.09333 [math.NT], 2021.

Example

Triangle begins:
  [1]
  [1, 2]
  [1, 2]
  [1, 2, 4]
  [1, 2]
  [1, 2, 3, 6]
  [1, 2, 4]
  [1, 2, 3, 6]
  [1, 2, 4]
  [1, 2, 5, 10]

Prog

(PARI) M(n) = sumdiv(n, d, moebius(d)*x^(n/d));
row(n) = my(list=List(), pol=M(n)); for (k=1, n, if (type(pol/(x^k-1)) == "t_POL", listput(list, k))); Vec(list);

Crossrefs

Cf. A054525, A347224.

Sequence in context: A071622 A182063 A135990 * A347224 A339270 A345226

Adjacent sequences: A347253 A347254 A347255 * A347257 A347258 A347259

Keyword

nonn,tabf

Author

Michel Marcus, Aug 24 2021

Status

approved