A347224 Irregular triangle whose n-th row lists the integers m such that the n-th necklace polynomial is divisible by the m-th cyclotomic polynomial.

1, 1, 2, 1, 2, 1, 2, 4, 1, 2, 1, 2, 3, 6, 1, 2, 4, 1, 2, 3, 6, 1, 2, 4, 6, 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, 12, 1, 2, 3, 6, 8, 1, 2, 5, 6, 10, 1, 2, 11, 22, 1, 2, 4, 8

Offset

2,3

Links

Table of n, a(n) for n=2..88.

Trevor Hyde, Cyclotomic factors of necklace polynomials, arXiv:1811.08601 [math.CO], 2018.

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, 6]
  [1, 2, 5, 10]
  [1, 2, 4]
  ...

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/polcyclo(k)) == "t_POL", listput(list, k))); Vec(list);

Crossrefs

Cf. A013595, A054525, A347223.

Sequence in context: A182063 A135990 A347256 * A339270 A345226 A140715

Adjacent sequences: A347221 A347222 A347223 * A347225 A347226 A347227

Keyword

nonn,tabf

Author

Michel Marcus, Aug 24 2021

Status

approved