A095877 Numbers n such that the middle coefficient of the cyclotomic polynomial Phi_n(x) has a value not obtained for any smaller n.

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

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 A339675 * A024476 A173014 A322017

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