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Greatest residue of x^(n-1) (mod n), x=0..n-1.
2

%I #14 Sep 11 2018 17:03:10

%S 0,1,1,3,1,5,1,7,7,9,1,11,1,13,10,15,1,17,1,19,18,21,1,23,21,25,25,27,

%T 1,29,1,31,31,33,30,35,1,37,36,39,1,41,1,43,40,45,1,47,43,49,49,51,1,

%U 53,49,55,55,57,1,59,1,61,58,63,61,65,1,67,64,69,1,71,1,73,69,75,71,77,1,79,79,81,1,83,81,85,82,87,1,89,78

%N Greatest residue of x^(n-1) (mod n), x=0..n-1.

%C a(n) = 1 if n prime and a(n) = n-1 if n even.

%H Antti Karttunen, <a href="/A197943/b197943.txt">Table of n, a(n) for n = 1..11111</a>

%e a(8) = 7 because x^7 == 0, 1, 3, 5, 7 (mod 8) => 7 is the greatest residue.

%t Table[Max[PowerMod[Range[0,n-1],n-1,n]], {n,100}]

%o (PARI) A197943(n) = { my(m=0); for(x=0,n-1, m = max(m,lift(Mod(x^(n-1),n)))); (m); }; \\ _Antti Karttunen_, Sep 10 2018

%Y Cf. A196082, A197929, A197930.

%K nonn,easy

%O 1,4

%A _Michel Lagneau_, Oct 19 2011

%E More terms added, incorrect PARI-program removed by _Antti Karttunen_, Sep 10 2018