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A160338
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Height (maximum absolute value of coefficients) of the n-th cyclotomic polynomial.
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5
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2
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OFFSET
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1,105
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COMMENTS
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Different from A137979: first time these sequence disagree is at n=14235 with a(14235)=2 and A137979(14235)=3.
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REFERENCES
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H. Maier, "The size of the coefficients of cyclotomic polynomials", Analytic number theory, Vol. 2 (1995), pp. 633-639, Progr. Math., 139.
R. C. Vaughan, "Bounds for the coefficients of cyclotomic polynomials", Michigan Math. J. 21 (1974), pp. 289-295.
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LINKS
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Max Alekseyev, Table of n, a(n) for n = 1..100000
Lola Thompson, Heights of divisors of x^n-1 (2011).
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EXAMPLE
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a(4) = 1 because the 4-th cyclotomic polynomial x^2 + 1 has height 1.
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MATHEMATICA
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Table[Max@Abs@CoefficientList[Cyclotomic[n, x], x], {n, 1, 105}] (* from Jean-François Alcover, Apr 02 2011 *)
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PROG
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(PARI) a(n) = vecmax(abs(Vec(polcyclo(n))))
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CROSSREFS
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Cf. A160339 (records), A160340 (indices of records), A160341.
Sequence in context: A112316 A112802 A137979 * A037281 A143241 A118626
Adjacent sequences: A160335 A160336 A160337 * A160339 A160340 A160341
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KEYWORD
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nonn,nice
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AUTHOR
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Max Alekseyev, May 13 2009
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STATUS
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approved
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