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A206292
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Numbers k such that cyclotomic polynomial Phi(k,-m) < Phi(j,-m) for any j > k and m >= 2.
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2
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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
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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.
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.
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MATHEMATICA
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t = Select[Range[4000], EulerPhi[#] <= 1000 &]; t = SortBy[t, Cyclotomic[#, -2] &]; DeleteDuplicates[Table[Max[Take[t, n]], {n, 1, Length[t]}]]
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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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