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A103224 Norm of the totient function phi(n) for Gaussian integers. See A103222 and A103223 for the real and imaginary parts.

%I A103224 #20 Feb 21 2020 07:07:23
%S A103224 1,2,4,8,8,8,36,32,36,16,100,32,80,72,32,128,160,72,324,64,144,200,
%T A103224 484,128,200,160,324,288,520,64,900,512,400,320,288,288,936,648,320,
%U A103224 256,1088,288,1764,800,288,968,2116,512,1764,400,640,640,2000,648,800,1152
%N A103224 Norm of the totient function phi(n) for Gaussian integers. See A103222 and A103223 for the real and imaginary parts.
%C A103224 See A103222 for definitions.
%C A103224 Multiplicative because the totient function on Gaussian integers is multiplicative and the norm is completely multiplicative. - _Andrew Howroyd_, Aug 03 2018
%H A103224 Amiram Eldar, <a href="/A103224/b103224.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)
%F A103224 a(n) = A103222(n)^2 + A103223(n)^2. - _Andrew Howroyd_, Aug 03 2018
%t A103224 phi[z_] := Module[{f, k, prod}, If[Abs[z]==1, z, f=FactorInteger[z, GaussianIntegers->True]; If[Abs[f[[1, 1]]]==1, k=2; prod=f[[1, 1]], k=1; prod=1]; Do[prod=prod*(f[[i, 1]]-1)f[[i, 1]]^(f[[i, 2]]-1), {i, k, Length[f]}]; prod]]; Abs[Table[phi[n], {n, 100}]]^2
%o A103224 (PARI) \\ See A103222
%o A103224 CEulerPhi(z)={my(f=factor(z,I)); prod(i=1, #f~, my([p,e]=f[i,]); if(norm(p)==1, p^e, (p-1)*p^(e-1)))}
%o A103224 a(n)=norm(CEulerPhi(n)); \\ _Andrew Howroyd_, Aug 03 2018
%Y A103224 Cf. A103222, A103223, A103230.
%K A103224 nonn,mult
%O A103224 1,2
%A A103224 _T. D. Noe_, Jan 26 2005