A206292 Numbers k such that cyclotomic polynomial Phi(k,-m) < Phi(j,-m) for any j > k and m >= 2.

1, 2, 3, 4, 6, 12, 18, 30, 42, 48, 60, 66, 70, 78, 90, 102, 120, 126, 150, 180, 210, 240, 270, 300, 330, 420, 450, 462, 480, 510, 540, 630, 660, 690, 780, 840, 870, 924, 1050, 1092, 1140, 1260, 1320, 1470, 1560, 1680, 1890, 2310, 2730, 2940, 3150, 3570, 3990

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.
When integer m > 1, Phi(3, -m) < Phi(4, -m) < Phi(6, -m), so a(3) = 3, a(4) = 4, and a(5) = 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.
When integer m > 1, Phi(12, -m) < Phi(8, -m) < Phi(10, -m), so a(6) = 12.
		

Links

• Wikipedia, Cyclotomic polynomial

Crossrefs

Cf. A194712, A206225, A000010, A002202, A032447.

Programs

Mathematica

t = Select[Range[4000], EulerPhi[#] <= 1000 &]; t =  SortBy[t, Cyclotomic[#, -2] &]; DeleteDuplicates[Table[Max[Take[t, n]], {n, 1, Length[t]}]]