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 A317272 Numbers k such that Phi(k,x) is a cyclotomic polynomial with middle coefficient different from -1, 0, 1. 1
 385, 770, 1155, 1365, 1540, 1925, 2065, 2145, 2310, 2415, 2465, 2695, 2717, 2730, 2737, 2821, 2849, 3003, 3080, 3255, 3315, 3465, 3619, 3850, 4095, 4130, 4199, 4235, 4277, 4290, 4543, 4620, 4785, 4830, 4845, 4879, 4930, 4991 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS n is in the sequence if and only if A204455(n) is in the sequence. - Robert Israel, Apr 17 2019 LINKS Robert Israel, Table of n, a(n) for n = 1..2000 M. Beiter, The midterm coefficient of the cyclotomic polynomial F_{pq}(x), Amer. Math. Monthly 71 (1964), 769-770. G. Dresden, On the Middle Coefficient of a Cyclotomic Polynomial, Amer. Math. Monthly 111 (2004), 531-533. EXAMPLE 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) MAPLE filter:= proc(n) local p, d;    p:= numtheory:-cyclotomic(n, x);    d:= degree(p, x);    abs(coeff(p, x, d/2))>1 end proc: select(filter, [\$3..5000]); # Robert Israel, Apr 17 2019 MATHEMATICA Select[Range[3, 4000], Abs[Coefficient[Cyclotomic[#, x], x, EulerPhi[#]/2]] > 1 &] PROG (PARI) isok(n) = (n > 2) && (abs(polcoeff(polcyclo(n), eulerphi(n)/2)) > 1); \\ Michel Marcus, Aug 02 2018 CROSSREFS Cf. A013590, A023022 (phi(n)/2), A204455. Sequence in context: A013591 A152941 A229853 * A157354 A065110 A200525 Adjacent sequences:  A317269 A317270 A317271 * A317273 A317274 A317275 KEYWORD nonn AUTHOR Greg Dresden, Jul 25 2018 STATUS approved

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Last modified June 6 17:20 EDT 2020. Contains 334829 sequences. (Running on oeis4.)