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Numbers with primitive root 6.
20

%I #12 Jan 04 2025 00:34:23

%S 11,13,17,41,59,61,79,83,89,103,107,109,113,121,127,131,137,151,157,

%T 169,179,199,223,227,229,233,251,257,271,277,289,347,367,373,397,401,

%U 419,443,449,467,487,491,521,563,569,587,593,613,641,659,661,683,709,733

%N Numbers with primitive root 6.

%H Vincenzo Librandi, <a href="/A167794/b167794.txt">Table of n, a(n) for n = 1..1000</a>

%p A167794 := proc(n)

%p option remember;

%p if n =1 then

%p 11;

%p else

%p for a from procname(n-1)+1 do

%p if numtheory[order](6,a) = numtheory[phi](a) then

%p return a;

%p end if;

%p end do:

%p end if;

%p end proc:

%p seq(A167794(n),n=1..80) ; # _R. J. Mathar_, Sep 15 2021

%t pr=6; Select[Range[2,2000], MultiplicativeOrder[pr,# ] == EulerPhi[ # ] &]

%o (PARI) is(n)=if(gcd(n, 6)>1, return(0)); my(p=eulerphi(n)); znorder(Mod(6, n), p)==p \\ _Charles R Greathouse IV_, Jan 04 2025

%Y Cf. A019336 (primes with primitive root 6). Subsequence of A033948.

%K nonn

%O 1,1

%A _T. D. Noe_, Nov 12 2009