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

Author

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

Keywords

• nonn

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

Crossrefs

Cf. A013594, A117223, A117318, A137979.

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

Programs

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, j1 ]; 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 *)

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

Extensions

Definition clarified by Harvey P. Dale, Mar 13 2013

New name from Michel Marcus, Apr 29 2018