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A194712 Numbers L such that cyclotomic polynomial Phi(L,m) < Phi(j,m) for any j > L and m >= 2.

%I A194712 #46 Jul 10 2021 21:01:38
%S A194712 1,2,6,10,12,14,18,20,24,30,36,42,48,60,66,72,90,96,120,126,150,210,
%T A194712 240,270,330,390,420,462,510,546,570,630,660,690,714,780,840,870,930,
%U A194712 990,1050,1110,1140,1170,1260,1320,1470,1530,1560,1680,1710,1890,1950
%N A194712 Numbers L such that cyclotomic polynomial Phi(L,m) < Phi(j,m) for any j > L and m >= 2.
%H A194712 Wikipedia, <a href="http://en.wikipedia.org/wiki/Cyclotomic_polynomial">Cyclotomic polynomial</a>
%e A194712 For k such that A000010(k) = 1,
%e A194712   Phi(1,m) = -1 + m,
%e A194712   Phi(2,m) = 1 + m,
%e A194712   Phi(1,m) < Phi(2,m),
%e A194712 so a(1) = 1, a(2) = 2.
%e A194712 For k > 2 such that A000010(k) = 2,
%e A194712   Phi(3,m) = 1 + m + m^2,
%e A194712   Phi(4,m) = 1 + m^2,
%e A194712   Phi(6,m) = 1 - m + m^2.
%e A194712 Obviously when integer m > 1, Phi(6,m) < Phi(4,m) < Phi(3,m), so a(3)=6.
%e A194712 For k > 6 such that A000010(k) = 4,
%e A194712   Phi(8,m) = 1 + m^4,
%e A194712   Phi(10,m) = 1 - m + m^2 - m^3 + m^4,
%e A194712   Phi(12,m) = 1 - m^2 + m^4.
%e A194712 Obviously when integer m > 1, Phi(10,m) < Phi(12,m) < Phi(8,m), so a(4) = 10, and a(5) = 12.
%t A194712 t = Select[Range[2400], EulerPhi[#] <= 480 &]; t2 = SortBy[t, Cyclotomic[#, 2] &]; DeleteDuplicates[Table[Max[Take[t2, n]], {n, Length[t2]}]]
%Y A194712 Cf. A206225, A000010, A002202, A032447.
%K A194712 nonn
%O A194712 1,2
%A A194712 _Lei Zhou_, Feb 13 2012