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A347223
Irregular triangle whose n-th row lists the integers m such that Phi_n(x)-1 is divisible by Phi_m(x), where Phi_m(x) is the m-th cyclotomic polynomial, or 0 if not divisible by any cyclotomic polynomials.
1
0, 2, 0, 2, 4, 1, 2, 3, 6, 0, 2, 6, 1, 4, 2, 5, 10, 1, 2, 2, 3, 4, 6, 12, 1, 3, 6, 1, 2, 4, 0, 2, 4, 8, 16, 1, 3, 2, 3, 6, 9, 18, 1, 2, 8, 1, 2, 6, 1, 5, 10, 2, 11, 22, 1, 2, 4, 2, 4, 10, 20, 1, 3, 4, 6, 12, 2, 6, 18, 1, 2, 3, 6, 12, 2, 4, 7, 14, 28, 1, 2, 4
OFFSET
2,2
COMMENTS
It appears that row(2^m) is empty for m>=1.
LINKS
Trevor Hyde, Cyclotomic factors of necklace polynomials, arXiv:1811.08601 [math.CO], 2018.
EXAMPLE
Triangle begins:
[0]
[2]
[0]
[2, 4]
[1]
[2, 3, 6]
[0]
[2, 6]
[1, 4]
[2, 5, 10]
[1, 2]
...
PROG
(PARI) row(n) = my(list=List(), pol=polcyclo(n)-1); for (k=1, n, if (type(pol/polcyclo(k)) == "t_POL", listput(list, k))); if (#list, Vec(list), [0]);
CROSSREFS
Sequence in context: A120557 A092594 A092741 * A338227 A350861 A144182
KEYWORD
nonn,tabf
AUTHOR
Michel Marcus, Aug 24 2021
STATUS
approved