A064081 - OEIS

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

(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

Table of n, a(n) for n=1..26.

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

AUTHOR

Jens Voß, Sep 04 2001

EXTENSIONS

More terms from Vladeta Jovovic, Sep 06 2001

Definition corrected by Jerry Metzger, Nov 04 2009

STATUS

approved