A013590 Numbers k such that Phi(k,x) is a cyclotomic polynomial containing a coefficient with an absolute value greater than one.

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

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