A366605 Number of distinct prime divisors of 4^n + 1.

1, 1, 1, 2, 1, 2, 2, 3, 1, 4, 2, 3, 3, 4, 2, 5, 2, 4, 4, 4, 2, 6, 3, 5, 3, 5, 3, 6, 3, 3, 4, 5, 2, 6, 3, 6, 5, 5, 4, 9, 3, 5, 5, 5, 4, 10, 2, 4, 3, 6, 6, 9, 2, 4, 6, 6, 5, 8, 3, 7, 6, 6, 4, 10, 2, 9, 7, 6, 4, 8, 4, 6, 7, 5, 2, 12, 4, 9, 5, 4, 4, 10, 4, 6, 8, 10

Offset: 0

Author

Sean A. Irvine, Oct 14 2023

Keywords

• nonn

Links

• Max Alekseyev, Table of n, a(n) for n = 0..583

Crossrefs

Cf. A001221, A052539, A057940, A274903, A366604, A366606, A366607, A366608, A366609.

Cf. A046799, A366580, A366615, A366627, A366636, A366655, A366664, A119704, A366686, A366712.

Programs

Mathematica

PrimeNu[4^Range[0,100]+1] (* Paolo Xausa, Oct 14 2023 *)

PARI

for(n = 0, 100, print1(omega(4^n + 1), ", "))

Python

from sympy import primenu
def A366605(n): return primenu((1<<(n<<1))+1) # Chai Wah Wu, Oct 14 2023

Formula

a(n) = omega(4^n+1) = A001221(A052539(n)).

a(n) = A046799(2*n). - Max Alekseyev, Jan 08 2024