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Irregular triangle whose n-th row lists the integers m such that the n-th necklace polynomial is divisible by x^m-1.
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%I #6 Aug 25 2021 08:18:37

%S 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,

%T 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,

%U 1,2,3,6,1,2,5,10,1,2,11,22,1,2,4,8,1,2,4,5,10,20

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

%H John R. Doyle, Paul Fili and Trevor Hyde, <a href="https://arxiv.org/abs/2108.09333">Dynatomic polynomials, necklace operators, and universal relations for dynamical units</a>, arXiv:2108.09333 [math.NT], 2021.

%e Triangle begins:

%e [1]

%e [1, 2]

%e [1, 2]

%e [1, 2, 4]

%e [1, 2]

%e [1, 2, 3, 6]

%e [1, 2, 4]

%e [1, 2, 3, 6]

%e [1, 2, 4]

%e [1, 2, 5, 10]

%o (PARI) M(n) = sumdiv(n, d, moebius(d)*x^(n/d));

%o 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);

%Y Cf. A054525, A347224.

%K nonn,tabf

%O 2,3

%A _Michel Marcus_, Aug 24 2021