A167794 Numbers with primitive root 6.

11, 13, 17, 41, 59, 61, 79, 83, 89, 103, 107, 109, 113, 121, 127, 131, 137, 151, 157, 169, 179, 199, 223, 227, 229, 233, 251, 257, 271, 277, 289, 347, 367, 373, 397, 401, 419, 443, 449, 467, 487, 491, 521, 563, 569, 587, 593, 613, 641, 659, 661, 683, 709, 733

Offset: 1

Author

T. D. Noe, Nov 12 2009

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

Maple

A167794 := proc(n)
    option remember;
    if n =1 then
        11;
    else
        for a from procname(n-1)+1 do
            if numtheory[order](6,a) = numtheory[phi](a) then
                return a;
            end if;
        end do:
    end if;
end proc:
seq(A167794(n),n=1..80) ; # R. J. Mathar, Sep 15 2021

Mathematica

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

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