Search: id:A064080
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%I A064080
%S A064080 3,5,7,17,341,13,5461,257,1387,41,1398101,241,22369621,3277,49981,
%T A064080 65537,5726623061,4033,91625968981,61681,1826203,838861,23456248059221,
%U A064080 65281,1100586419201,13421773,22906579627,15790321,96076792050570581
%N A064080 Zsigmondy numbers for a = 4, b = 1: Zs(n, 4, 1) is the greatest divisor 
               of 4^n - 1^n (A024036) that is relatively prime to 4^m - 1^m for 
               all positive integers m < n.
%C A064080 By Zsigmondy's theorem, the n-th Zsigmondy number for bases a and b is 
               not 1 except in the three cases (1) a = 2, b = 1, n = 1, (2) a = 
               2, b = 1, n = 6, (3) n = 2 and a+b is a power of 2.
%D A064080 K. Zsigmondy, Zur Theorie der Potenzreste, Monatshefte fuer Mathematik 
               und Physik 3 (1882), 265 - 284
%H A064080 K. Zsigmondy, <a href="http://dieper.aib.uni-linz.ac.at/cgi-bin/project2/
               showstruct.pl?PE_ID=2&VO_ID=3&NUM=22">Zur Theorie der Potenzreste</
               a>, Monatsh. f. Math. III. 265-284. Published 1892.
%Y A064080 Cf. A024036, A064078, A064079, A064081, A064082, A064083.
%Y A064080 Sequence in context: A140797 A038893 A075227 this_sequence A112986 A088732 
               A052333
%Y A064080 Adjacent sequences: A064077 A064078 A064079 this_sequence A064081 A064082 
               A064083
%K A064080 nonn
%O A064080 1,1
%A A064080 Jens Voss (jens.voss(AT)poet.de), Sep 04 2001
%E A064080 Corrected and extended by Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 
               05 2001
%E A064080 Definition corrected by Jerry Metzger, Nov 04 2009

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