A084550 Numbers n that have a primitive root less than n that are nonnegative perfect eleventh powers.

2053, 2083, 2099, 2131, 2141, 2187, 2197, 2213, 2221, 2237, 2243, 2269, 2293, 2309, 2339, 2357, 2371, 2389, 2437, 2459, 2467, 2477, 2539, 2549, 2557, 2579, 2621, 2659, 2677, 2683, 2693, 2699, 2741, 2789, 2797, 2803, 2809, 2819, 2837, 2843, 2851

Offset: 1

Author

Hauke Worpel (hw1(AT)email.com), May 30 2003

Keywords

• nonn

Comments

Includes n if n is in A167791 with n > 2048 and phi(n) not divisible by 11.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A167791.

Programs

Maple

filter:= proc(n) local i,t,s;
  s:= numtheory:-phi(n);
  for i from 2 do
    t:= i^11;
    if t >= n then return false fi;
    if numtheory:-order(t,n) = s then return true fi;
  od
end proc:
select(filter, [$2..10000]); # Robert Israel, Mar 02 2021

Mathematica

filterQ[n_] := Module[{i, t, s}, s = EulerPhi[n]; For[i = 2, True, i++, t = i^11; If[t >= n, Return[False]]; If[MultiplicativeOrder[t, n] == s, Return[True]]]];
Select[Range[2, 10000], filterQ] (* Jean-François Alcover, Feb 02 2023, after Robert Israel *)