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

%I A366604 #27 Mar 15 2025 14:12:35
%S A366604 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,
%T A366604 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,
%U A366604 11,9,9,14,5,10,8,15,6,17,6,10,13,11,10,16,5
%N A366604 Number of distinct prime divisors of 4^n - 1.
%H A366604 Max Alekseyev, <a href="/A366604/b366604.txt">Table of n, a(n) for n = 1..1128</a>
%F A366604 a(n) = omega(4^n-1) = A001221(A024036(n)).
%F A366604 a(n) = A046800(2*n) = A046799(n) + A046800(n). - _Max Alekseyev_, Jan 07 2024
%t A366604 PrimeNu[4^Range[100]-1] (* _Paolo Xausa_, Oct 14 2023 *)
%o A366604 (PARI) for(n = 1, 100, print1(omega(4^n - 1), ", "))
%o A366604 (Python)
%o A366604 from sympy import primenu
%o A366604 def A366604(n): return primenu((1<<(n<<1))-1) # _Chai Wah Wu_, Oct 15 2023
%Y A366604 Cf. A024036, A001221, A057957, A133801, A366602, A366603.
%Y A366604 Cf. A046800, A133801, A366611, A366620, A366632, A366651, A366660, A102347, A366681, A366707.
%K A366604 nonn
%O A366604 1,2
%A A366604 _Sean A. Irvine_, Oct 14 2023