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A194712
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Numbers L such that cyclotomic polynomial Phi(L,m) < Phi(j,m) for any j > L and m >= 2.
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6
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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
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OFFSET
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1,2
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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t = Select[Range[2400], EulerPhi[#] <= 480 &]; t2 = SortBy[t, Cyclotomic[#, 2] &]; DeleteDuplicates[Table[Max[Take[t2, n]], {n, Length[t2]}]]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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