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

1,1

Links

Table of n, a(n) for n=1..29.

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

Prog

(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

Crossrefs

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

Sequence in context: A255856 A037056 A358857 * A054210 A225778 A271442

Adjacent sequences: A109344 A109345 A109346 * A109348 A109349 A109350

Keyword

nonn

Author

Jonathan Vos Post, Aug 21 2005

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

Status

approved