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

1,1

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

Table of n, a(n) for n=1..29.

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