A239063 Numbers k for which the equation x^x == 1 (mod k) has x=1 as its only solution such that 1 <= x <= k.

1, 2, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 32, 34, 36, 40, 42, 46, 48, 50, 54, 60, 64, 68, 72, 78, 80, 82, 84, 90, 94, 96, 98, 100, 102, 108, 110, 114, 120, 126, 128, 136, 144, 150, 156, 160, 162, 164, 168, 170, 176, 180, 186, 188, 192, 194, 198, 200, 204

Offset: 1

Author

José María Grau Ribas, Mar 09 2014

Keywords

• nonn

Comments

A number k belongs to this sequence if and only if for all primes p|k and for all primes q|p-1, q divides k. - Bernat Pagès Vives, Oct 30 2021

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000
• Art of Problem Solving, OMO Fall 2013 Solutions, problem 22

Crossrefs

Cf. A239061.

Programs

Mathematica

gg1[n_] := Sum[If[Mod[x^x, n] == Mod[1, n], 1, 0],{x,1,n}]; Select[Range[100], gg1[#] == 1 &]