%I A103223
%S A103223 0,1,0,2,2,2,0,4,0,4,0,4,4,6,4,8,4,6,0,8,0,10,0,8,10,12,0,12,6,8,0,16,
               0,
%T A103223 16,12,12,6,18,8,16,8,12,0,20,12,22,0,16,0,20,8,24,8,18,20,24,0,28,0,16,
%U A103223 10,30,0,32,24,20,0,32,0,24,0,24,10,36,20,36,0,24,0,32,0,40,0,24,32,42
%N A103223 Imaginary part of the totient function phi(n) for Gaussian integers. 
               See A103222 for the real part and A103224 for the norm.
%C A103223 Note that a(n)=0 when n is in A004614, the product of real Gaussian primes. 
               It appears that all terms are nonnegative.
%H A103223 T. D. Noe, <a href="b103223.txt">Table of n, a(n) for n=1..1000</a>
%t A103223 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]]; Im[Table[phi[n], 
               {n, 100}]]
%Y A103223 Sequence in context: A071442 A124759 A071295 this_sequence A091399 A000091 
               A155123
%Y A103223 Adjacent sequences: A103220 A103221 A103222 this_sequence A103224 A103225 
               A103226
%K A103223 nonn
%O A103223 1,4
%A A103223 T. D. Noe (noe(AT)sspectra.com), Jan 26 2005