A366604 Number of distinct prime divisors of 4^n - 1.

1, 2, 2, 3, 3, 4, 3, 4, 4, 5, 4, 6, 3, 6, 6, 5, 3, 8, 3, 7, 6, 7, 4, 9, 7, 7, 6, 8, 6, 11, 3, 7, 8, 7, 9, 12, 5, 7, 7, 9, 5, 12, 5, 10, 11, 9, 6, 12, 5, 12, 10, 10, 6, 12, 11, 11, 8, 9, 6, 15, 3, 8, 11, 9, 9, 14, 5, 10, 8, 15, 6, 17, 6, 10, 13, 11, 10, 16, 5

Offset: 1

Author

Sean A. Irvine, Oct 14 2023

Keywords

• nonn

Links

• Max Alekseyev, Table of n, a(n) for n = 1..1128

Crossrefs

Cf. A024036, A001221, A057957, A133801, A366602, A366603.

Cf. A046800, A133801, A366611, A366620, A366632, A366651, A366660, A102347, A366681, A366707.

Programs

Mathematica

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

PARI

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

Python

from sympy import primenu
def A366604(n): return primenu((1<<(n<<1))-1) # Chai Wah Wu, Oct 15 2023

Formula

a(n) = omega(4^n-1) = A001221(A024036(n)).

a(n) = A046800(2*n) = A046799(n) + A046800(n). - Max Alekseyev, Jan 07 2024