%I A097406
%S A097406 0,3,7,5,31,0,127,17,73,11,89,13,8191,43,151,257,131071,19,524287,41,
%T A097406 337,683,178481,241,1801,2731,262657,113,2089,331,2147483647,65537,
%U A097406 599479,43691,122921,109,616318177,174763,121369,61681,164511353,5419
%N A097406 Largest primitive prime factor of 2^n-1.
%C A097406 Except for a(6) where 2^6-1 = 1*63; 3*21; 7*9. 9, 21 and 63 are composite.
%C A097406 Prime factors 3 & 7 first appear when n=2 & n=3 so neither of them is 
               unique.
%C A097406 Conjectures: (1) For every n the highest unique prime factor is of the 
               form kn+1. The values for k are in A097407. (2) For each composite 
               n many factors of the form kn+1 occur intermittently but always singly 
               in any cofactor pair. (3) For each prime n every factor is of the 
               form kn+1.
%C A097406 A prime factor of 2^n-1 is called primitive if it does not divide 2^r-1 
               for any r<n, cf. A086251.
%Y A097406 Cf. A064078, A097407.
%Y A097406 Sequence in context: A115765 A112071 A046561 this_sequence A112927 A064078 
               A048857
%Y A097406 Adjacent sequences: A097403 A097404 A097405 this_sequence A097407 A097408 
               A097409
%K A097406 nonn,easy
%O A097406 1,2
%A A097406 Marco Matosic (marcomatosic(AT)hotmail.com), Aug 16 2004
%E A097406 More terms and better description from Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Sep 03 2004