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 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. 11
 3, 5, 7, 17, 341, 13, 5461, 257, 1387, 41, 1398101, 241, 22369621, 3277, 49981, 65537, 5726623061, 4033, 91625968981, 61681, 1826203, 838861, 23456248059221, 65281, 1100586419201, 13421773, 22906579627, 15790321, 96076792050570581 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS K. Zsigmondy, Zur Theorie der Potenzreste, Monatshefte für Mathematik und Physik, 3 (1892) 265-284. FORMULA For even n, a(n) = A064078(2*n); for odd n, a(n) = A064078(n) * A064078(2*n). - Max Alekseyev, Apr 28 2022 CROSSREFS Cf. A024036, A064078, A064079, A064081, A064082, A064083. Sequence in context: A350176 A248796 A247164 * A184875 A112986 A052333 Adjacent sequences:  A064077 A064078 A064079 * A064081 A064082 A064083 KEYWORD nonn AUTHOR Jens Voß, Sep 04 2001 EXTENSIONS Corrected and extended by Vladeta Jovovic, Sep 05 2001 Definition corrected by Jerry Metzger, Nov 04 2009 STATUS approved

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Last modified May 18 22:37 EDT 2022. Contains 353826 sequences. (Running on oeis4.)