cp's OEIS Frontend

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.

%I A064080 #14 Apr 28 2022 18:46:27
%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,
%U A064080 23456248059221,65281,1100586419201,13421773,22906579627,15790321,96076792050570581
%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.
%H A064080 K. Zsigmondy, <a href="http://dx.doi.org/ 10.1007/BF01692444">Zur Theorie der Potenzreste</a>, Monatshefte für Mathematik und Physik, 3 (1892) 265-284.
%F A064080 For even n, a(n) = A064078(2*n); for odd n, a(n) = A064078(n) * A064078(2*n). - _Max Alekseyev_, Apr 28 2022
%Y A064080 Cf. A024036, A064078, A064079, A064081, A064082, A064083.
%K A064080 nonn
%O A064080 1,1
%A A064080 _Jens Voß_, Sep 04 2001
%E A064080 Corrected and extended by _Vladeta Jovovic_, Sep 05 2001
%E A064080 Definition corrected by _Jerry Metzger_, Nov 04 2009