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A317272 Numbers k such that Phi(k,x) is a cyclotomic polynomial with middle coefficient different from -1, 0, 1.

%I A317272 #19 Apr 17 2019 08:02:50
%S A317272 385,770,1155,1365,1540,1925,2065,2145,2310,2415,2465,2695,2717,2730,
%T A317272 2737,2821,2849,3003,3080,3255,3315,3465,3619,3850,4095,4130,4199,
%U A317272 4235,4277,4290,4543,4620,4785,4830,4845,4879,4930,4991
%N A317272 Numbers k such that Phi(k,x) is a cyclotomic polynomial with middle coefficient different from -1, 0, 1.
%C A317272 n is in the sequence if and only if A204455(n) is in the sequence. - _Robert Israel_, Apr 17 2019
%H A317272 Robert Israel, <a href="/A317272/b317272.txt">Table of n, a(n) for n = 1..2000</a>
%H A317272 M. Beiter, <a href="https://www.jstor.org/stable/2310894">The midterm coefficient of the cyclotomic polynomial F_{pq}(x)</a>, Amer. Math. Monthly 71 (1964), 769-770.
%H A317272 G. Dresden, <a href="https://www.jstor.org/stable/4145075">On the Middle Coefficient of a Cyclotomic Polynomial</a>, Amer. Math. Monthly 111 (2004), 531-533.
%e A317272 385 is the first item in the list because Phi(385,x) is the first cyclotomic polynomial with middle coefficient different from -1,0,1 (the middle term is -3x^120)
%p A317272 filter:= proc(n) local p,d;
%p A317272    p:= numtheory:-cyclotomic(n,x);
%p A317272    d:= degree(p,x);
%p A317272    abs(coeff(p, x, d/2))>1
%p A317272 end proc:
%p A317272 select(filter, [$3..5000]); # _Robert Israel_, Apr 17 2019
%t A317272 Select[Range[3, 4000],
%t A317272 Abs[Coefficient[Cyclotomic[#, x], x, EulerPhi[#]/2]] > 1 &]
%o A317272 (PARI) isok(n) = (n > 2) && (abs(polcoeff(polcyclo(n), eulerphi(n)/2)) > 1); \\ _Michel Marcus_, Aug 02 2018
%Y A317272 Cf. A013590, A023022 (phi(n)/2), A204455.
%K A317272 nonn
%O A317272 1,1
%A A317272 _Greg Dresden_, Jul 25 2018