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 A373041 #19 May 22 2024 15:12:22
%S A373041 1,2,3,4,6,7,10,10,15,15,20,20,28,24,36,32,42,40,55,44,65,57,72,66,91,
%T A373041 68,105,88,110,100,132,102,153,126,156,136,190,138,210,170,204,187,
%U A373041 253,184,273,215,272,240,325,234,340,276,342,301,406,280,435,345,414,368,480
%N A373041 2*a(n) is the number of triangles with integer sides (x, y, n), x < y < n, and gcd(x, y, n) = 1.
%C A373041 Offset 5 is chosen to exclude the only count not divisible by 2, which represents the triangle with sides (2,3,4).
%H A373041 David A. Corneth, <a href="/A373041/b373041.txt">Table of n, a(n) for n = 5..10000</a>
%F A373041 a(n) = (A373051(n) - A373051(n-1))/2 for n >= 5.
%F A373041 a(n) = (A123323(n) - 3*A023022(n))/2 for n >= 5.
%o A373041 (PARI) a(n) = {if(isprime(n), n\=2; return(n*(n-1)/2)); my(res = 0, g, sn = vecprod(factor(n)[,1])); for(b = (n + 3)\2, n-1, g = gcd(b, sn); if(g == 1, res+=(2*b - n - 1);, my(d, e); d = divisors(g); for(i = 1, #d, e = (-1)^(omega(d[i])); t = ((b-1)\d[i])*e; t-= ((n-b)\d[i])*e; res+=t))); res>>1} \\ _David A. Corneth_, May 22 2024
%Y A373041 Cf. A023022, A123323, A373051.
%K A373041 nonn
%O A373041 5,2
%A A373041 _Andrés Sancho_ and _Hugo Pfoertner_, May 21 2024