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A206292 Numbers a(n) such that cyclotomic polynomial Phi(a(n),-m) < Phi(j,-m) for any j > a(n) and m >= 2. 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 (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 those values of k that make 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 those values of k (k > 2) that make 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(3, -m) <  Phi(4, -m) <  Phi(6, -m)

So a(3) = 3, a(4) = 4, and a(5) = 6;

For those values of k (k > 6) that make 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(12, -m) <  Phi(8, -m) <  Phi(10, -m),

So a(6) = 12

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A037393 A048330 A118651 * A129297 A221846 A018343

Adjacent sequences:  A206289 A206290 A206291 * A206293 A206294 A206295

KEYWORD

nonn

AUTHOR

Lei Zhou, Feb 13 2012

STATUS

approved

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Last modified July 5 21:00 EDT 2020. Contains 335473 sequences. (Running on oeis4.)