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A095877 Numbers n such that the middle coefficient of the cyclotomic polynomial Phi_n(x) has a value not obtained for any smaller n. 2
3, 4, 6, 385, 1155, 4785, 6545, 7735, 10101, 11305, 14105, 17255, 18445, 20615, 22165, 22715, 26565, 28985, 33915, 35581, 36295, 37961, 40755, 47355, 49665, 51765, 51935, 52003, 53295, 54285, 61215, 62205, 74613, 76245, 76755, 79365, 82005, 85085, 86955, 87087, 90915, 92235, 99671 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Note that for n > 6, we need examine only squarefree n having three or more factors. Sequence A095878 has the values of the middle coefficient of Phi_n(x) for the n in this sequence. Note that for n = 1 and 2, Phi_n(x) is a polynomial having no middle term.

LINKS

Table of n, a(n) for n=1..43.

G. Dresden, On the Middle Coefficient of a Cyclotomic Polynomial (MAA Monthly, 2004, 531 - 533).

EXAMPLE

385 is in this sequence because the middle coefficient of Phi_385(x) is -3, which does not occur for any n < 385.

MATHEMATICA

vals={1, 0, -1}; lst={3, 4, 6}; Do[pwrs=Transpose[FactorInteger[n]][[2]]; If[Length[pwrs]>2 && 1==Times@@pwrs, c=Coefficient[Cyclotomic[n, x], x, EulerPhi[n]/2]; If[ !MemberQ[vals, c], AppendTo[lst, n]; AppendTo[vals, c]]], {n, 7, 50000, 2}]; lst

CROSSREFS

Cf. A094754 (middle coefficient of cyclotomic polynomial Phi_n(x)).

Sequence in context: A129293 A233512 A049010 * A024476 A173014 A093087

Adjacent sequences:  A095874 A095875 A095876 * A095878 A095879 A095880

KEYWORD

hard,nonn

AUTHOR

T. D. Noe, Jun 10 2004

EXTENSIONS

More terms from Jozsef Pelikan, Dec 18 2014

STATUS

approved

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Last modified September 25 18:20 EDT 2017. Contains 292499 sequences.