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

1,3

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).

Links

Table of n, a(n) for n=1..89.

Prog

(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)), ", ")))

Crossrefs

Cf. A060679, A001747, A003277.

Sequence in context: A164848 A213514 A130827 * A287556 A353748 A236966

Adjacent sequences: A070306 A070307 A070308 * A070310 A070311 A070312

Keyword

easy,nonn

Author

Benoit Cloitre, May 10 2002

Status

approved