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A084550
Numbers n that have a primitive root less than n that are nonnegative perfect eleventh powers.
4
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
1,1
COMMENTS
Includes n if n is in A167791 with n > 2048 and phi(n) not divisible by 11.
LINKS
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 *)
CROSSREFS
Cf. A167791.
Sequence in context: A280021 A168190 A238934 * A020400 A068723 A252187
KEYWORD
nonn
AUTHOR
Hauke Worpel (hw1(AT)email.com), May 30 2003
STATUS
approved