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A136418 Smallest order of the cyclotomic polynomial whose maximal coefficient in absolute value is n.

%I A136418 #10 Apr 14 2017 02:59:45
%S A136418 0,105,385,1365,1785,2805,3135,10353,6545,12155,21385,11165,21505,
%T A136418 10465,16555,19285,37961,35105,18445,24395,23205,53669,11305,28595,
%U A136418 17255,36465,20615,42315,123585,31535,49335,39585,61295,35805,72709,54285
%N A136418 Smallest order of the cyclotomic polynomial whose maximal coefficient in absolute value is n.
%C A136418 This differs from A013594.
%C A136418 For squarefree k, are there an infinite number of cyclotomic polynomials Phi(k,x) of height n? This is true for n=1 because it is known that there are an infinite number of flat cyclotomic polynomials with k the product of three distinct primes. See A117223. - _T. D. Noe_, Apr 22 2008
%C A136418 There are an infinite number of cyclotomic polynomials of height n if the following generalization of Kaplan's theorem 2 is true: Let N be the product of distinct odd primes and let p be one of those primes. Let q any prime such that q = p (mod N/p), then the height of Phi(Nq/p,x) is the same as the height of Phi(N,x). By Dirichlet's theorem, there are an infinite number of primes q. [From _T. D. Noe_, Apr 13 2010]
%H A136418 T. D. Noe, <a href="/A136418/b136418.txt">Table of n, a(n) for n=1..1000</a>
%H A136418 Nathan Kaplan, <a href="https://doi.org/10.1016/j.jnt.2007.01.008">Flat cyclotomic polynomials of order three</a>, J. Number Theory 127 (2007), 118-126.
%t A136418 f[n_] := f[n] = Max@ Abs@ CoefficientList[ Cyclotomic[n, x], x]; Do[ f@n, {n, 100000}]; t = Array[f, 31000]; Table[ Position[t, n, 1, 1], {n, 25}]//Flatten
%Y A136418 Cf. A013594, A046887, A134518.
%K A136418 nonn
%O A136418 1,2
%A A136418 _Robert G. Wilson v_, Mar 31 2008
%E A136418 More terms from _T. D. Noe_, Apr 22 2008