A064081 Zsigmondy numbers for a = 5, b = 1: Zs(n, 5, 1) is the greatest divisor of 5^n - 1^n (A024049) that is relatively prime to 5^m - 1^m for all positive integers m < n.

4, 3, 31, 13, 781, 7, 19531, 313, 15751, 521, 12207031, 601, 305175781, 13021, 315121, 195313, 190734863281, 5167, 4768371582031, 375601, 196890121, 8138021, 2980232238769531, 390001, 95397958987501, 203450521, 3814699218751, 234750601, 46566128730773925781, 464881, 1164153218269348144531

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

Robert Israel, Table of n, a(n) for n = 1..133

K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. f. Math. 3 (1892) 265-284.

Crossrefs

Cf. A024049, A064078, A064079, A064080, A064082, A064083.

Sequence in context: A376607 A286795 A127138 * A211364 A099438 A002178

Adjacent sequences: A064078 A064079 A064080 * A064082 A064083 A064084

Keyword

nonn,changed

Author

Jens Voß, Sep 04 2001

Extensions

More terms from Vladeta Jovovic, Sep 06 2001

Definition corrected by Jerry Metzger, Nov 04 2009

More terms from Robert Israel, Feb 21 2025

Status

approved