A070309 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.

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, 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, 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

Offset: 1

Author

Benoit Cloitre, May 10 2002

Keywords

• easy
• nonn

Comments

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).

Crossrefs

Cf. A060679, A001747, A003277.

Programs

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)),",")))