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

0,4

Links

Max Alekseyev, Table of n, a(n) for n = 0..561

Formula

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

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

Mathematica

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

Prog

(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

Crossrefs

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

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

Sequence in context: A359587 A336471 A357975 * A133755 A357853 A336470

Adjacent sequences: A366602 A366603 A366604 * A366606 A366607 A366608

Keyword

nonn

Author

Sean A. Irvine, Oct 14 2023

Status

approved