Number of primitive prime factors of 8^n - 1.
1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 3, 2, 3, 2, 2, 3, 4, 1, 3, 3, 2, 3, 3, 2, 4, 2, 3, 4, 5, 1, 2, 3, 3, 4, 5, 2, 5, 3, 4, 2, 4, 1, 4, 4, 3, 3, 5, 2, 2, 3, 2, 7, 7, 3, 4, 3, 2, 3, 5, 3, 4, 3, 2, 3, 2, 2, 5, 7, 4, 5, 6, 2, 6, 5, 4, 6, 3, 1, 7, 3, 4, 5, 4, 2, 4, 4, 1
1
T. D. Noe, Plot of 87 terms
(Mma) pp = {}; Table[f = Transpose[FactorInteger[8^n - 1]][[1]]; p = Complement[f, pp]; pp = Union[pp, p]; Length[p], {n, 87}]
Cf. A112505 (number of primitive prime factors of 10^n - 1).
Cf. S000001-S000007, S000043 (primitive prime factors of 8^n - 1), S000365 (one primitive prime).
Cf. A085021 (number of primitive prime factors of 2^n - 1).
nonn,hard
T. D. Noe, May 14 2014