

A194712


Numbers a(n) such that cyclotomic polynomial Phi(a(n),m) < Phi(j,m) for any j > a(n) 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
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OFFSET

1,2


LINKS

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


EXAMPLE

For those ks 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 ks (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(6,m) < Phi(4,m) < Phi(3,m)
So a(3)=6;
For those ks (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(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: A214586 A305634 A139710 * A057921 A095300 A097381
Adjacent sequences: A194709 A194710 A194711 * A194713 A194714 A194715


KEYWORD

nonn


AUTHOR

Lei Zhou, Feb 13 2012


STATUS

approved



