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

%I A084550 #10 Feb 02 2023 11:11:39
%S A084550 2053,2083,2099,2131,2141,2187,2197,2213,2221,2237,2243,2269,2293,
%T A084550 2309,2339,2357,2371,2389,2437,2459,2467,2477,2539,2549,2557,2579,
%U A084550 2621,2659,2677,2683,2693,2699,2741,2789,2797,2803,2809,2819,2837,2843,2851
%N A084550 Numbers n that have a primitive root less than n that are nonnegative perfect eleventh powers.
%C A084550 Includes n if n is in A167791 with n > 2048 and phi(n) not divisible by 11.
%H A084550 Robert Israel, <a href="/A084550/b084550.txt">Table of n, a(n) for n = 1..10000</a>
%p A084550 filter:= proc(n) local i,t,s;
%p A084550   s:= numtheory:-phi(n);
%p A084550   for i from 2 do
%p A084550     t:= i^11;
%p A084550     if t >= n then return false fi;
%p A084550     if numtheory:-order(t,n) = s then return true fi;
%p A084550   od
%p A084550 end proc:
%p A084550 select(filter, [$2..10000]); # _Robert Israel_, Mar 02 2021
%t A084550 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]]]];
%t A084550 Select[Range[2, 10000], filterQ] (* _Jean-François Alcover_, Feb 02 2023, after _Robert Israel_ *)
%Y A084550 Cf. A167791.
%K A084550 nonn
%O A084550 1,1
%A A084550 Hauke Worpel (hw1(AT)email.com), May 30 2003