A064079 - OEIS

A064079

Zsigmondy numbers for a = 3, b = 1: Zs(n, 3, 1) is the greatest divisor of 3^n - 1^n (A024023) that is relatively prime to 3^m - 1^m for all positive integers m < n.

2, 1, 13, 5, 121, 7, 1093, 41, 757, 61, 88573, 73, 797161, 547, 4561, 3281, 64570081, 703, 581130733, 1181, 368089, 44287, 47071589413, 6481, 3501192601, 398581, 387440173, 478297, 34315188682441, 8401, 308836698141973, 21523361

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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..32.

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

CROSSREFS

Cf. A024023, A064078, A064080, A064081, A064082, A064083.

Sequence in context: A245625 A292947 A143663 * A167584 A112226 A192795

Adjacent sequences: A064076 A064077 A064078 * A064080 A064081 A064082

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