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

0,1

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

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 *)

Prog

(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, ", ")));

Crossrefs

Cf. A007617, A010554, A046144, A231773.

Sequence in context: A163898 A280040 A202284 * A338935 A200120 A154861

Adjacent sequences: A231769 A231770 A231771 * A231773 A231774 A231775

Keyword

nonn

Author

Arkadiusz Wesolowski, Nov 13 2013

Status

approved