Search: id:A064078
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%I A064078
%S A064078 1,3,7,5,31,1,127,17,73,11,2047,13,8191,43,151,257,131071,19,524287,41,
%T A064078 337,683,8388607,241,1082401,2731,262657,3277,536870911,331,2147483647,
%U A064078 65537,599479,43691,8727391,4033,137438953471,174763,9588151,61681
%N A064078 Zsigmondy numbers for a = 2, b = 1: Zs(n, 2, 1) is the greatest divisor 
               of 2^n - 1^n (A000225) that is relatively prime to 2^m - 1^m for 
               all positive integers m < n.
%C A064078 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.
%C A064078 Composite terms a(n) are the maximal overpseudoprimes to base 2 (see 
               A141232) for which the multiplicative order of 2 mod a(n) equals 
               n. - Vladimir Shevelev (shevelev(AT)bgu.ac.il), Aug 26 2008
%C A064078 a(n)=2^n-1 iff either n=1 or n is prime [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), 
               Sep 30 2008]
%D A064078 K. Zsigmondy, Zur Theorie der Potenzreste, Monatshefte fuer Mathematik 
               und Physik 3 (1882), 265 - 284
%H A064078 T. D. Noe, <a href="b064078.txt">Table of n, a(n) for n=1..1000</a>
%H A064078 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. Pub(1892)
%F A064078 Denominator of Sum_{d|n} d*moebius(n/d)/(2^d-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Apr 02 2004
%Y A064078 Cf. A000225, A064079, A064080, A064081, A064082, A064083.
%Y A064078 Cf. A019320, A063982.
%Y A064078 Sequence in context: A046561 A097406 A112927 this_sequence A048857 A005420 
               A161818
%Y A064078 Adjacent sequences: A064075 A064076 A064077 this_sequence A064079 A064080 
               A064081
%K A064078 nonn
%O A064078 1,2
%A A064078 Jens Voss (jens.voss(AT)poet.de), Sep 04 2001
%E A064078 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 02 2004
%E A064078 Definition corrected by Jerry Metzger, Nov 04 2009

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