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Number of solutions 2<=x<=A060679(n) to the equation x^A060679(n)==1 (mod A060679(n)) where A060679(n) are the orders of non-cyclic groups.
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%I #5 Mar 30 2012 18:38:58

%S 1,1,3,2,1,3,1,7,5,7,2,1,7,4,1,8,3,3,15,1,11,1,2,15,11,3,2,1,15,6,9,7,

%T 17,4,7,2,1,15,1,8,31,3,7,3,23,1,4,3,11,31,26,1,23,1,7,11,3,2,1,31,13,

%U 2,39,3,15,2,1,35,19,2,15,11,7,8,1,31,10,1,3,24,35,63,2,3,7,1,8,31,3

%N Number of solutions 2<=x<=A060679(n) to the equation x^A060679(n)==1 (mod A060679(n)) where A060679(n) are the orders of non-cyclic groups.

%C If there is only one solution 2<=x<=A060679(k) to x^A060679(k)==1 (mod A060679(k)) this solution is : x=A060679(k)-1 (also solution is A060679(k)+1). In this case A060679(k) is a term of A001747(n).

%o (PARI) for(n=1,200,if(prod(i=2,n-1,(i^n-1)%n)==0,print1(sum(i=2,n-1,if((i^n-1)%n,0,1)),",")))

%Y Cf. A060679, A001747, A003277.

%K easy,nonn

%O 1,3

%A _Benoit Cloitre_, May 10 2002