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

Offset: 1

Author

Jens Voß, Sep 04 2001

Keywords

• nonn

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

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

Crossrefs

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

Extensions

More terms from Vladeta Jovovic, Sep 06 2001

Definition corrected by Jerry Metzger, Nov 04 2009