A231772 Smallest positive number which has exactly n primitive roots, or 0 if no such number exists.

8, 1, 5, 0, 11, 0, 19, 0, 17, 0, 23, 0, 29, 0, 0, 0, 41, 0, 81, 0, 67, 0, 47, 0, 53, 0, 0, 0, 59, 0, 0, 0, 97, 0, 0, 0, 109, 0, 0, 0, 83, 0, 0, 0, 139, 0, 0, 0, 113, 0, 0, 0, 107, 0, 163, 0, 0, 0, 0, 0, 199, 0, 0, 0, 137, 0, 0, 0, 0, 0, 0, 0, 149, 0, 0, 0, 0, 0

Offset: 0

Author

Arkadiusz Wesolowski, Nov 13 2013

Keywords

• nonn

Comments

If n >= 3 and n is odd, then a(n) = 0.

Links

• T. D. Noe, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Primitive Root

Crossrefs

Cf. A007617, A010554, A046144, A231773.

Programs

Mathematica

nn = 100; t = Join[{1}, Table[p = PrimitiveRoot[n]; If[IntegerQ[p], EulerPhi[EulerPhi[n]], 0], {n, 2, 2*nn}]]; Table[s = Position[t, n, 1, 1]; If[s == {}, 0, s[[1, 1]]], {n, 0, nn}] (* T. D. Noe, Nov 14 2013 *)

PARI

r=77; print1(8, ", ", 1, ", "); for(n=2, r, m=0; for(c=2*n+1, n^2+1, if(n%2==1, break); e=eulerphi(c); if(e==lcm(znstar(c)[2])&&eulerphi(e)==n, m=1; print1(c, ", "); break)); if(m==0, print1(0, ", ")));