A064083 - OEIS

A064083

Zsigmondy numbers for a = 7, b = 1: Zs(n, 7, 1) is the greatest divisor of 7^n - 1^n (A024075) that is relatively prime to 7^m - 1^m for all positive integers m < n.

6, 1, 19, 25, 2801, 43, 137257, 1201, 39331, 2101, 329554457, 2353, 16148168401, 102943, 4956001, 2882401, 38771752331201, 117307, 1899815864228857, 1129901, 11898664849, 247165843, 4561457890013486057, 5762401, 79797014141614001

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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..25.

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

CROSSREFS

Cf. A024075, A064078, A064079, A064080, A064081, A064082.

Sequence in context: A157386 A157396 A019430 * A152249 A167580 A080213

Adjacent sequences: A064080 A064081 A064082 * A064084 A064085 A064086

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