A160338 Height (maximum absolute value of coefficients) of the n-th cyclotomic polynomial.

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

Offset: 1

Author

Max Alekseyev, May 13 2009

Keywords

• nonn
• nice

Comments

Different from A137979: first time these sequence disagree is at n=14235 with a(14235)=2 and A137979(14235)=3.

Examples

			a(4) = 1 because the 4th cyclotomic polynomial x^2 + 1 has height 1.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..100000
• Alexandre Kosyak, Pieter Moree, Efthymios Sofos and Bin Zhang, Cyclotomic polynomials with prescribed height and prime number theory, arXiv:1910.01039 [math.NT], 2019.
• Emma Lehmer, On the magnitude of the coefficients of the cyclotomic polynomial, Bull. Amer. Math. Soc. 42 (1936), 389-392.
• H. Maier, The coefficients of cyclotomic polynomials, Analytic number theory, Vol. 2 (1995), pp. 633-639, Progr. Math., 139.
• Lola Thompson, Heights of divisors of x^n-1, arXiv:1111.5404 [math.NT], 2011.
• R. C. Vaughan, Bounds for the coefficients of cyclotomic polynomials, Michigan Math. J. 21 (1974), 289-295 (1975).

Crossrefs

Cf. A160339 (records), A160340 (indices of records), A160341.

Programs

Mathematica

Table[Max@Abs@CoefficientList[Cyclotomic[n,x],x],{n,1,105}] (* from Jean-François Alcover, Apr 02 2011 *)

PARI

a(n) = vecmax(abs(Vec(polcyclo(n))))