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

%I A366605 #26 Mar 15 2025 14:13:00
%S A366605 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,
%T A366605 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,
%U A366605 6,4,8,4,6,7,5,2,12,4,9,5,4,4,10,4,6,8,10
%N A366605 Number of distinct prime divisors of 4^n + 1.
%H A366605 Max Alekseyev, <a href="/A366605/b366605.txt">Table of n, a(n) for n = 0..583</a>
%F A366605 a(n) = omega(4^n+1) = A001221(A052539(n)).
%F A366605 a(n) = A046799(2*n). - _Max Alekseyev_, Jan 08 2024
%t A366605 PrimeNu[4^Range[0,100]+1] (* _Paolo Xausa_, Oct 14 2023 *)
%o A366605 (PARI) for(n = 0, 100, print1(omega(4^n + 1), ", "))
%o A366605 (Python)
%o A366605 from sympy import primenu
%o A366605 def A366605(n): return primenu((1<<(n<<1))+1) # _Chai Wah Wu_, Oct 14 2023
%Y A366605 Cf. A001221, A052539, A057940, A274903, A366604, A366606, A366607, A366608, A366609.
%Y A366605 Cf. A046799, A366580, A366615, A366627, A366636, A366655, A366664, A119704, A366686, A366712.
%K A366605 nonn
%O A366605 0,4
%A A366605 _Sean A. Irvine_, Oct 14 2023