This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A103225 #16 Aug 19 2025 00:00:06
%S A103225 1,4,24,24,44,48,144,96,224,96,372,192,444,304,404,392,792,448,1124,
%T A103225 408,1200,752,1648,808,1240,896,2036,1200,2440,800,2996,1600,3008,
%U A103225 1592,2404,1808,4056,2256,3616,1600,4992,2400,5784,3008,3604,3304,6916,3224,7376
%N A103225 Number of Gaussian integers z with abs(z) < n and gcd(n,z)=1.
%C A103225 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.
%C A103225 Four of the dominant lines of the plot appear to align to k(i)*Pi*n^2, with k(i) = 1, 8/9, 1/2, and 4/9. Conjecture: a(n) < Pi*n^2. - _Bill McEachen_, Aug 14 2025
%H A103225 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 A103225 a(2)=4 because 1, -1, i and -i are relatively prime to 2 and have modulus less than 2.
%t A103225 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 A103225 Cf. A002145, A051132, A103222, A103223, A103224.
%K A103225 nice,nonn
%O A103225 1,2
%A A103225 _T. D. Noe_, Jan 26 2005