# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a013590
Showing 1-1 of 1

%I A013590 #48 Apr 29 2018 12:21:39
%S A013590 105,165,195,210,255,273,285,315,330,345,357,385,390,420,429,455,495,
%T A013590 510,525,546,555,561,570,585,595,609,615,627,630,645,660,665,690,705,
%U A013590 714,715,735,759,765,770,777,780,795,805,819,825,840,855
%N A013590 Numbers k such that Phi(k,x) is a cyclotomic polynomial containing a coefficient with an absolute value greater than one.
%C A013590 Previous name was: Orders of cyclotomic polynomials containing a coefficient with an absolute value greater than one.
%C A013590 First occurrence of A137979(n)=k is given in A013594.
%C A013590 From _David A. Corneth_, Apr 21 2018: (Start)
%C A013590 Terms are composite.
%C A013590 If k is a term of the sequence then so is k * m for m > 0.
%C A013590 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)
%H A013590 Robert G. Wilson v, <a href="/load/view.php?a=aHR0cDovL29laXMub3JnL0EwMTM1OTAvYjAxMzU5MC50eHQ">Table of n, a(n) for n = 1..1627</a>
%p A013590 isA013590 := proc(n)
%p A013590     numtheory[cyclotomic](n,x) ;
%p A013590     {coeffs(%,x)} ;
%p A013590     map(abs,%) ;
%p A013590     if % minus {1}  = {} then
%p A013590         false;
%p A013590     else
%p A013590         true;
%p A013590     end if;
%p A013590 end proc:
%p A013590 for n from 1 do
%p A013590     if isA013590(n) then
%p A013590         print(n);
%p A013590     end if;
%p A013590 end do: # _R. J. Mathar_, Nov 28 2016
%t A013590 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 ]
%t A013590 f[n_] := Max@ Abs@ CoefficientList[ Cyclotomic[n, x], x]; Select[ Range@ 1000, f@# > 1 &] (* _Robert G. Wilson v_ *)
%t A013590 Select[Range[900],Max[Abs[CoefficientList[Cyclotomic[#,x],x]]]>1&] (* _Harvey P. Dale_, Mar 13 2013 *)
%o A013590 (PARI) is(n)=for(k=0,n,if(abs(polcoeff(polcyclo(n),k))>1,return(n)));0
%o A013590 for(n=1,1000,if(is(n),print1(n,", "))) \\ _Derek Orr_, Apr 22 2015
%Y A013590 Cf. A013594, A117223, A117318, A137979.
%Y A013590 Flat cyclotomic polynomial: A117223 (order 3), A117318 (order 4).
%K A013590 nonn
%O A013590 1,1
%A A013590 Peter T. Wang (peterw(AT)cco.caltech.edu)
%E A013590 Definition clarified by _Harvey P. Dale_, Mar 13 2013
%E A013590 New name from _Michel Marcus_, Apr 29 2018

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE