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A194712 Numbers L such that cyclotomic polynomial Phi(L,m) < Phi(j,m) for any j > L and m >= 2. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..53.

Wikipedia, Cyclotomic polynomial

EXAMPLE

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.

MATHEMATICA

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

CROSSREFS

Cf. A206225, A000010, A002202, A032447.

Sequence in context: A337687 A305634 A139710 * A057921 A095300 A097381

Adjacent sequences:  A194709 A194710 A194711 * A194713 A194714 A194715

KEYWORD

nonn

AUTHOR

Lei Zhou, Feb 13 2012

STATUS

approved

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Last modified May 28 04:02 EDT 2022. Contains 354112 sequences. (Running on oeis4.)