Zsigmondy numbers

func zsigmondy (a, b, c) {

    var aexp = (0..c -> map {|k| a**k })
    var bexp = (0..c -> map {|k| b**k })

    var z = []
    for n in (1 .. c) {
        divisors(aexp[n] - bexp[n]).flip.each {|d|
            1 ..^ n -> all {|k|
                aexp[k] - bexp[k] -> is_coprime(d)
            } && (z << d; break)
        }
    }
    return z
}

for name,a,b in ([
    'A064078: Zsigmondy(n,2,1)', 2,1,
    'A064079: Zsigmondy(n,3,1)', 3,1,
    'A064080: Zsigmondy(n,4,1)', 4,1,
    'A064081: Zsigmondy(n,5,1)', 5,1,
    'A064082: Zsigmondy(n,6,1)', 6,1,
    'A064083: Zsigmondy(n,7,1)', 7,1,
    'A109325: Zsigmondy(n,3,2)', 3,2,
    'A109347: Zsigmondy(n,5,3)', 5,3,
    'A109348: Zsigmondy(n,7,3)', 7,3,
    'A109349: Zsigmondy(n,7,5)', 7,5,
].slices(3)) {
    say ("\n#{name}:\n", zsigmondy(a, b, 20))
}

Output:

A064078: Zsigmondy(n,2,1):
[1, 3, 7, 5, 31, 1, 127, 17, 73, 11, 2047, 13, 8191, 43, 151, 257, 131071, 19, 524287, 41]

A064079: Zsigmondy(n,3,1):
[2, 1, 13, 5, 121, 7, 1093, 41, 757, 61, 88573, 73, 797161, 547, 4561, 3281, 64570081, 703, 581130733, 1181]

A064080: Zsigmondy(n,4,1):
[3, 5, 7, 17, 341, 13, 5461, 257, 1387, 41, 1398101, 241, 22369621, 3277, 49981, 65537, 5726623061, 4033, 91625968981, 61681]

A064081: Zsigmondy(n,5,1):
[4, 3, 31, 13, 781, 7, 19531, 313, 15751, 521, 12207031, 601, 305175781, 13021, 315121, 195313, 190734863281, 5167, 4768371582031, 375601]

A064082: Zsigmondy(n,6,1):
[5, 7, 43, 37, 311, 31, 55987, 1297, 46873, 1111, 72559411, 1261, 2612138803, 5713, 1406371, 1679617, 3385331888947, 46441, 121871948002099, 1634221]

A064083: Zsigmondy(n,7,1):
[6, 1, 19, 25, 2801, 43, 137257, 1201, 39331, 2101, 329554457, 2353, 16148168401, 102943, 4956001, 2882401, 38771752331201, 117307, 1899815864228857, 1129901]

A109325: Zsigmondy(n,3,2):
[1, 5, 19, 13, 211, 7, 2059, 97, 1009, 11, 175099, 61, 1586131, 463, 3571, 6817, 129009091, 577, 1161737179, 4621]

A109347: Zsigmondy(n,5,3):
[2, 1, 49, 17, 1441, 19, 37969, 353, 19729, 421, 24325489, 481, 609554401, 10039, 216001, 198593, 381405156481, 12979, 9536162033329, 288961]

A109348: Zsigmondy(n,7,3):
[4, 5, 79, 29, 4141, 37, 205339, 1241, 127639, 341, 494287399, 2041, 24221854021, 82573, 3628081, 2885681, 58157596211761, 109117, 2849723505777919, 4871281]

A109349: Zsigmondy(n,7,5):
[2, 3, 109, 37, 6841, 13, 372709, 1513, 176149, 1661, 964249309, 1801, 47834153641, 75139, 3162961, 3077713, 115933787267041, 30133, 5689910849522509, 3949201]