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.

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

Offset: 1

Author

Jens Voß, Sep 04 2001

Keywords

• nonn

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.

Crossrefs

Cf. A024036, A064078, A064079, A064081, A064082, A064083.

Formula

For even n, a(n) = A064078(2*n); for odd n, a(n) = A064078(n) * A064078(2*n). - Max Alekseyev, Apr 28 2022

Extensions

Corrected and extended by Vladeta Jovovic, Sep 05 2001

Definition corrected by Jerry Metzger, Nov 04 2009