A046146 Largest primitive root modulo n, or 0 if no root exists.

0, 0, 1, 2, 3, 3, 5, 5, 0, 5, 7, 8, 0, 11, 5, 0, 0, 14, 11, 15, 0, 0, 19, 21, 0, 23, 19, 23, 0, 27, 0, 24, 0, 0, 31, 0, 0, 35, 33, 0, 0, 35, 0, 34, 0, 0, 43, 45, 0, 47, 47, 0, 0, 51, 47, 0, 0, 0, 55, 56, 0, 59, 55, 0, 0, 0, 0, 63, 0, 0, 0, 69, 0, 68, 69, 0, 0, 0, 0, 77, 0, 77, 75, 80, 0, 0

Offset

0,4

Comments

The value 0 at index 0 says 0 has no primitive roots, but the 0 at index 1 says 1 has a primitive root of 0, the only real 0 in the sequence. - Initial terms corrected by Harry J. Smith, Jan 27 2005

a(n) is nonzero if and only if n is 2, 4, or of the form p^k, or 2*p^k where p is an odd prime and k>0. - Tom Edgar, Jun 02 2014

Links

T. D. Noe, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Primitive Root.

Mathematica

f[n_] := Block[{pr = PrimitiveRootList[n]}, If[pr == {}, 0, pr[[-1]]]]; Array[f, 86, 0] (* Robert G. Wilson v, Nov 03 2014 *)

Prog

(PARI) for(i=0, 100, p=0; for(q=1, i-1, if(gcd(q, i)==1&&znorder(Mod(q, i))==eulerphi(i), p=q)); print1(p", ")) /* V. Raman, Nov 22 2012 */

Crossrefs

Cf. A001918, A046144, A046145, A002233, A071894, A219027, A008330, A010554.

Sequence in context: A175108 A265145 A103310 * A081768 A273493 A193404

Adjacent sequences: A046143 A046144 A046145 * A046147 A046148 A046149

Keyword

nonn

Author

Eric W. Weisstein

Extensions

Initial terms corrected by Harry J. Smith, Jan 27 2005

Status

approved