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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.
2
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
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
KEYWORD
nonn,tabf
AUTHOR
Michel Marcus, Aug 24 2021
STATUS
approved