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A366606 Number of divisors of 4^n+1.

%I A366606 #23 Mar 15 2025 14:13:26
%S A366606 2,2,2,4,2,6,4,8,2,16,4,8,8,16,4,48,4,16,16,16,4,64,8,32,8,64,8,64,8,
%T A366606 8,16,32,4,64,12,96,32,32,16,768,8,32,32,32,16,1536,4,16,8,64,64,512,
%U A366606 4,16,64,96,32,256,8,128,64,64,16,1024,4,768,128,64,16
%N A366606 Number of divisors of 4^n+1.
%H A366606 Max Alekseyev, <a href="/A366606/b366606.txt">Table of n, a(n) for n = 0..583</a>
%F A366606 a(n) = sigma0(4^n+1) = A000005(A052539(n)).
%F A366606 a(n) = A046798(2*n). - _Max Alekseyev_, Jan 08 2024
%e A366606 a(3)=4 because 4^3+1 has divisors {1, 5, 13, 65}.
%p A366606 a:=n->numtheory[tau](4^n+1):
%p A366606 seq(a(n), n=0..100);
%t A366606 DivisorSigma[0,4^Range[0,100]+1] (* _Paolo Xausa_, Oct 14 2023 *)
%o A366606 (PARI) a(n) = numdiv(4^n+1);
%o A366606 (Python)
%o A366606 from sympy import divisor_count
%o A366606 def A366606(n): return divisor_count((1<<(n<<1))+1) # _Chai Wah Wu_, Oct 14 2023
%Y A366606 Cf. A000005, A052539, A057940, A274903, A366602, A366605, A366607, A366608, A366609.
%Y A366606 Cf. A046798, A366577, A366616, A366628, A366637, A366656, A366665, A344897, A366688, A366714.
%K A366606 nonn
%O A366606 0,1
%A A366606 _Sean A. Irvine_, Oct 14 2023