S000009


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

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

0

S000009

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, 0, 86}]

Cf. A086257 (number of primitive prime factors of 2^n + 1), S000369 (4^n+1 has one primitive prime).
Cf. S000008-S000015S000046 (primitive prime factors of 4^n + 1).

nonn,hard

T. D. Noe, May 14 2014

Offset corrected. - T. D. Noe, Nov 20 2014

© Tony D Noe 2014-2015