A240103 Numbers with primitive root 18.

5, 11, 29, 37, 43, 53, 59, 61, 67, 83, 101, 107, 109, 121, 139, 149, 157, 163, 173, 179, 181, 197, 227, 251, 269, 277, 283, 293, 317, 347, 349, 379, 389, 397, 419, 421, 461, 467, 491, 509, 523, 541, 547, 557, 563, 571, 587, 613, 619, 653, 659, 661, 677

Offset: 1

Author

Vincenzo Librandi, Apr 01 2014

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. numbers with positive primitive root r: A167791 (r=2), A167792 (r=3), A167793 (r=5), A167794 (r=6), A167795 (r=7), A167796 (r=8), A167797 (r=10), A240028 (r=11), A240030 (r=12), A240032 (r=13), A240094 (r=14), A240096 (r=15), A240101 (r=17).

Cf. numbers with negative primitive root r: A167798 (r=-2), A167799 (r=-3), A167800 (r=-4), A167801 (r=-5), A167802 (r=-6), A167803 (r=-7), A167804 (r=-8), A167805 (r=-9), A167806 (r=-10), A240029 (r=-11), A240031 (r=-12), A240093 (r=-13), A240095 (r=-14), A240097 (r=-15), A240100 (r=-17), A240102 (r=-18).

Programs

Mathematica

pr = 18; Select[Range[2, 800], MultiplicativeOrder[pr, #] == EulerPhi[#] &]

PARI

is(n)=if(gcd(n, 6)>1, return(0)); my(p=eulerphi(n)); znorder(Mod(18, n), p)==p \\ Charles R Greathouse IV, Nov 26 2014