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

1, 2, 6, 10, 12, 14, 18, 20, 24, 30, 36, 42, 48, 60, 66, 72, 90, 96, 120, 126, 150, 210, 240, 270, 330, 390, 420, 462, 510, 546, 570, 630, 660, 690, 714, 780, 840, 870, 930, 990, 1050, 1110, 1140, 1170, 1260, 1320, 1470, 1530, 1560, 1680, 1710, 1890, 1950

Offset: 1

Author

Lei Zhou, Feb 13 2012

Keywords

• nonn

Examples

			For k such that A000010(k) = 1,
  Phi(1,m) = -1 + m,
  Phi(2,m) = 1 + m,
  Phi(1,m) < Phi(2,m),
so a(1) = 1, a(2) = 2.
For k > 2 such that A000010(k) = 2,
  Phi(3,m) = 1 + m + m^2,
  Phi(4,m) = 1 + m^2,
  Phi(6,m) = 1 - m + m^2.
Obviously when integer m > 1, Phi(6,m) < Phi(4,m) < Phi(3,m), so a(3)=6.
For k > 6 such that A000010(k) = 4,
  Phi(8,m) = 1 + m^4,
  Phi(10,m) = 1 - m + m^2 - m^3 + m^4,
  Phi(12,m) = 1 - m^2 + m^4.
Obviously when integer m > 1, Phi(10,m) < Phi(12,m) < Phi(8,m), so a(4) = 10, and a(5) = 12.
		

Links

• Wikipedia, Cyclotomic polynomial

Crossrefs

Cf. A206225, A000010, A002202, A032447.

Programs

Mathematica

t = Select[Range[2400], EulerPhi[#] <= 480 &]; t2 = SortBy[t, Cyclotomic[#, 2] &]; DeleteDuplicates[Table[Max[Take[t2, n]], {n, Length[t2]}]]