S000002


Number of primitive prime factors of 4^n - 1.

1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 3, 2, 4, 3, 2, 1, 5, 2, 2, 2, 3, 3, 4, 2, 4, 3, 3, 1, 4, 2, 4, 2, 3, 4, 5, 2, 2, 3, 6, 2, 5, 2, 5, 2, 4, 2, 5, 1, 2, 4, 3, 2, 4, 2, 4, 2, 3, 2, 5, 2, 5, 4, 3, 3, 4, 4, 4, 2, 6, 4, 7, 2, 2, 4, 3

1

S000002

T. D. Noe, Plot of 87 terms

(Mma) pp = {}; Table[f = Transpose[FactorInteger[4^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. A129735 (primitive prime factors of 4^n - 1).
Cf. S000001-S000007, S000361 (4^n-1 has one primitive prime).
Cf.
A085021 (number of primitive prime factors of 2^n - 1).

nonn,hard

T. D. Noe, May 14 2014

© Tony D Noe 2014-2015