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Numbers k such that the greatest residue of the congruence x^k (mod k) equals k-1 for x in [0..k-1].
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%I #19 Jul 04 2021 03:21:39

%S 1,2,3,5,7,9,10,11,13,15,17,19,21,23,25,26,27,29,31,33,34,35,37,39,41,

%T 43,45,47,49,50,51,53,55,57,58,59,61,63,65,67,69,71,73,74,75,77,79,81,

%U 82,83,85,87,89,91,93,95,97,99,101,103,105,106,107,109,111

%N Numbers k such that the greatest residue of the congruence x^k (mod k) equals k-1 for x in [0..k-1].

%C All prime numbers are in the sequence.

%H Amiram Eldar, <a href="/A196499/b196499.txt">Table of n, a(n) for n = 1..10000</a>

%e 50 is in the sequence because the residues of the congruence x^50 (mod 50) are {0, 1, 24, 25, 26, 49} and the greatest value is 50 - 1 = 49.

%t lst := {}; Do[If[Max[Union[PowerMod[Range[0, n - 1], n, n]]] == n - 1, AppendTo[lst, n]], {n, 120}]; lst

%Y Cf. A196082.

%K nonn

%O 1,2

%A _Michel Lagneau_, Oct 13 2011