%I #19 Jan 08 2024 05:58:08

%S 1,1,1,1,1,2,1,1,1,12,1,10,1,1,1,60,1,10,1,1,1,18,1,2,1,1,1,660,1,66,

%T 1,1,1,1,1,10,1,1,1,4620,1,6,1,1,1,660,1,2,1,1,1,31878,1,2,1,1,1,

%U 197340,1,5742,1,1,1,1,1,52026,1,1,1,440220,1,28014,1,1,1,4,1,2610,1,1,1,28014,1,2,1,1,1,3693690,1,2,1,1,1,1,1,7590,1,1,1,1642460820

%N a(n) = period length of the sequence A020639(n^k - 1), k >= 1.

%C For n = 2, the sequence A020639(n^k - 1) is not periodic (see A049479), but it is such for any n >= 3.

%C a(n) divides A058254(A000720(A020639(n-1))).

%H Max Alekseyev, <a href="/A368811/b368811.txt">Table of n, a(n) for n = 3..10000</a>

%F For odd n >= 3, a(n) = 1.

%e a(8) = 2 is the period length of A010705.

%e a(12) = 12 is the period length of A366717.

%o (PARI) { a368811(n) = my(r=[], z); forprime(p=2, factor(n-1)[1, 1], if(n%p==0, next); z=znorder(Mod(n, p)); if(!#r || vecmin(apply(x->z%x,r)), r=concat(r,[z])) ); lcm(r); }

%Y Cf. A010705, A020639, A049479, A058254, A366717.

%K nonn

%O 3,6

%A _Max Alekseyev_, Jan 06 2024