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A013590 Numbers k such that Phi(k,x) is a cyclotomic polynomial containing a coefficient with an absolute value greater than one. 8
105, 165, 195, 210, 255, 273, 285, 315, 330, 345, 357, 385, 390, 420, 429, 455, 495, 510, 525, 546, 555, 561, 570, 585, 595, 609, 615, 627, 630, 645, 660, 665, 690, 705, 714, 715, 735, 759, 765, 770, 777, 780, 795, 805, 819, 825, 840, 855 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Previous name was: Orders of cyclotomic polynomials containing a coefficient with an absolute value greater than one.

First occurrence of A137979(n)=k is given in A013594.

From David A. Corneth, Apr 21 2018: (Start)

Terms are composite.

If k is a term of the sequence then so is k * m for m > 0.

Let a primitive term p of this sequence be a term of which no divisor is in the sequence. Then p is an odd squarefree number. (End)

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..1627

MAPLE

isA013590 := proc(n)

    numtheory[cyclotomic](n, x) ;

    {coeffs(%, x)} ;

    map(abs, %) ;

    if % minus {1}  = {} then

        false;

    else

        true;

    end if;

end proc:

for n from 1 do

    if isA013590(n) then

        print(n);

    end if;

end do: # R. J. Mathar, Nov 28 2016

MATHEMATICA

S[ n_ ] := For[ j=1; t=0, j<n, j++, t=Cases[ CoefficientList[ Cyclotomic[ j, x ], x ], k_ /; Abs[ k ]>1 ]; If[ Length[ t ]!=0, Print[ j ] ] ]; S[ 856 ]

f[n_] := Max@ Abs@ CoefficientList[ Cyclotomic[n, x], x]; Select[ Range@ 1000, f@# > 1 &] (* Robert G. Wilson v *)

Select[Range[900], Max[Abs[CoefficientList[Cyclotomic[#, x], x]]]>1&] (* Harvey P. Dale, Mar 13 2013 *)

PROG

(PARI) is(n)=for(k=0, n, if(abs(polcoeff(polcyclo(n), k))>1, return(n))); 0

for(n=1, 1000, if(is(n), print1(n, ", "))) \\ Derek Orr, Apr 22 2015

CROSSREFS

Cf. A013594, A117223, A117318, A137979.

Flat cyclotomic polynomial: A117223 (order 3), A117318 (order 4).

Sequence in context: A203614 A252069 A133509 * A216918 A278569 A046389

Adjacent sequences:  A013587 A013588 A013589 * A013591 A013592 A013593

KEYWORD

nonn

AUTHOR

Peter T. Wang (peterw(AT)cco.caltech.edu)

EXTENSIONS

Definition clarified by Harvey P. Dale, Mar 13 2013

New name from Michel Marcus, Apr 29 2018

STATUS

approved

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Last modified August 19 15:52 EDT 2018. Contains 313878 sequences. (Running on oeis4.)