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

1,2

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,…

Links

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

Formula

n such that A197929(n) = n.

Example

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

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 *)

Crossrefs

Cf. A197929, A195637.

Sequence in context: A354715 A239221 A039956 * A192109 A216090 A342641

Adjacent sequences: A197927 A197928 A197929 * A197931 A197932 A197933

Keyword

nonn

Author

Michel Lagneau, Oct 19 2011

Status

approved