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%I #13 Feb 21 2020 05:21:12
%S 1,4,24,24,44,48,144,96,224,96,372,192,444,304,404,392,792,448,1124,
%T 408,1200,752,1648,808,1240,896,2036,1200,2440,800,2996,1600,3008,
%U 1592,2404,1808,4056,2256,3616,1600,4992,2400,5784,3008,3604,3304,6916,3224,7376
%N Number of Gaussian integers z with abs(z) < n and gcd(n,z)=1.
%C This sequence is much like the usual totient function. That is, it gives the number of Gaussian integers that are relatively prime to n and whose modulus is less than n. When n is a Gaussian prime, A002145, then a(n) = A051132(n)-1.
%H Amiram Eldar, <a href="/A103225/b103225.txt">Table of n, a(n) for n = 1..1000</a> (terms 1..200 from T. D. Noe)
%e a(2)=4 because 1, -1, i and -i are relatively prime to 2 and have modulus less than 2.
%t Table[cnt=0; Do[z=a+ b*I; If[Abs[z]<n && GCD[n, z]==1, cnt++ ], {a, -n+1, n-1}, {b, -n+1, n-1}]; cnt, {n, 60}]
%Y Cf. A002145, A051132, A103222, A103223, A103224.
%K nice,nonn
%O 1,2
%A _T. D. Noe_, Jan 26 2005
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