A109347 Zsigmondy numbers for a = 5, b = 3: Zs(n, 5, 3) is the greatest divisor of 5^n - 3^n (A005058) that is relatively prime to 5^m - 3^m for all positive integers m < n.

2, 1, 49, 17, 1441, 19, 37969, 353, 19729, 421, 24325489, 481, 609554401, 10039, 216001, 198593, 381405156481, 12979, 9536162033329, 288961, 18306583, 6125659, 5960417405949649, 346561, 103408180634401, 152787181, 3853528045489, 179655841, 93132223146359169121

Offset: 1

Author

Jonathan Vos Post, Aug 21 2005

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Zsigmondy's Theorem

Crossrefs

Cf. A064078, A064079, A064080, A064081, A064082, A064083, A109325, A109348, A109349.

Programs

PARI

rad(n) = factorback(factor(n)[, 1])
lista(nn) = {prad = 1; for (n=1, nn, val = 5^n-3^n; d = divisors(val); gd = 1; forstep(k=#d, 1, -1, if (gcd(d[k], prad) == 1, g = d[k]; break)); print1(g, ", "); prad = ra(prad*val););} \\ Michel Marcus, Nov 15 2016

Extensions

Edited, corrected and extended by Ray Chandler, Aug 26 2005

Definition corrected by Jerry Metzger, Nov 04 2009

More terms from Michel Marcus, Nov 14 2016