%I A118107
%S A118107 1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,2,1,1,2,4,1,1,1,2,1,2,1,1,1,1,4,1,2,
%T A118107 2,1,6,2,1,1,2,1,4,2,10,1,1,1,4,1,2,1,6,4,2,6,3,1,1,1,4,2,1,1,4,1,1,10,
%U A118107 2,1,2,1,6,4,6,4,2,1,1,1,4,1,2,1,3,3,4,1,2,2,10,4,11,6,1,1,6,4,4
%N A118107 Period of the vector sequence d(n)^2^k mod n for k=1,2,3,..., where d(n) 
               is the vector of divisors of n.
%C A118107 This sequence is related to the period of sigma_(2^k)(n) mod n, which 
               is important in verifying the n dividing sigma_(2^k)(n) for all k>
               0. See A066292 and A118076. Note that a(n)=1 if n is a power of a 
               prime.
%e A118107 See A118106 for an example involving d(n)^k.
%t A118107 Table[d=Divisors[n]; k=0; found=False; While[i=0; While[i<k-1 && !found, 
               i++; found=(dk[i]==dk[k])]; !found, k++; dk[k]=PowerMod[d,2^k,n]]; 
               k-i, {n,100}]
%Y A118107 Cf. A118106 (period of the vector sequence d(n)^k mod n).
%Y A118107 Sequence in context: A144379 A107435 A161095 this_sequence A155798 A055652 
               A154844
%Y A118107 Adjacent sequences: A118104 A118105 A118106 this_sequence A118108 A118109 
               A118110
%K A118107 nonn
%O A118107 1,14
%A A118107 T. D. Noe (noe(AT)sspectra.com), Apr 13 2006