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A081258 Numbers k > 1 such that k^3 - 1 (or equivalently k^2 + k + 1) has no prime factor greater than k.

%I A081258 #25 Oct 29 2023 14:09:08
%S A081258 16,18,22,30,49,67,68,74,79,81,87,100,102,121,135,137,146,149,154,158,
%T A081258 159,163,165,169,172,178,181,191,211,221,229,230,235,256,262,263,269,
%U A081258 273,277,291,292,301,305,313,315,324,326,334,352,361,372,373,380,393
%N A081258 Numbers k > 1 such that k^3 - 1 (or equivalently k^2 + k + 1) has no prime factor greater than k.
%C A081258 One might also include 1 as a term here. - _R. J. Mathar_, Oct 11 2011
%H A081258 Robert Israel, <a href="/A081258/b081258.txt">Table of n, a(n) for n = 1..10000</a>
%e A081258 16 is a term: 16^3 - 1 = 4095 = 3*3*5*7*13.
%p A081258 isA081258 := proc(n)
%p A081258         numtheory[factorset](n^3-1) ;
%p A081258         if max(op(%)) <= n then
%p A081258                 true;
%p A081258         else
%p A081258                 false;
%p A081258         end if;
%p A081258 end proc;
%p A081258 for n from 1 to 400 do
%p A081258         if isA081258(n) then
%p A081258                 printf("%d,",n);
%p A081258         end if;
%p A081258 end do: # _R. J. Mathar_, Oct 11 2011
%t A081258 Select[Range[2, 1000], FactorInteger[#^3 - 1][[-1, 1]] <= #&] (* _Jean-François Alcover_, Jun 15 2020 *)
%Y A081258 Cf. A081256, A081257.
%K A081258 easy,nonn
%O A081258 1,1
%A A081258 _Jan Fricke_, Mar 14 2003
%E A081258 Name changed by _Robert Israel_, Nov 11 2016