A197930 Numbers n such that the number of distinct residues in x^(n-1) (mod n), x=0..n-1, equals n.

1, 2, 6, 10, 14, 22, 26, 30, 34, 38, 42, 46, 58, 62, 74, 78, 82, 86, 94, 102, 106, 110, 114, 118, 122, 134, 138, 142, 146, 158, 166, 170, 174, 178, 182, 194, 202, 206, 210, 214, 218, 222, 226, 230, 254, 258, 262, 266, 274, 278, 282, 290, 298, 302, 314, 318

Offset: 1

Author

Michel Lagneau, Oct 19 2011

Keywords

• nonn

Comments

a(n) = n if n = 2p, p prime > 2, or n = 2q with q nonprime such that q = 1, 15, 21, 39, 51, 55, 57, 69, 85, 87, 91,…

Examples

			a(8) = 30 because x^29  == 0,1,2, …,28,29  (mod 30) with 30 distinct residues.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A197929, A195637.

Programs

Mathematica

lst={}; Table[If[Length[Union[PowerMod[Range[0,n-1],n-1,n]]]==n, AppendTo[lst,n]], {n,320}]; lst
Select[Range[400],Length[Union[PowerMod[Range[0,#-1],#-1,#]]]==#&] (* Harvey P. Dale, Nov 06 2016 *)

Formula

n such that A197929(n) = n.