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 A373561 #24 Jun 13 2024 04:52:38
%S A373561 0,1,20,126,480,1375,3276,6860,13056,23085,38500,61226,93600,138411,
%T A373561 198940,279000,382976,515865,683316,891670,1148000,1460151,1836780,
%U A373561 2287396,2822400,3453125,4191876,5051970,6047776,7194755,8509500,10009776,11714560,13644081,15819860
%N A373561 a(n) = (1/3)*n^5 + (1/2)*n^4 + (1/6)*n^3.
%H A373561 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A373561 a(n) = n^3*(n+1)*(2*n+1)/6.
%F A373561 a(n) = n^2 * A000330(n).
%F A373561 Conjecture: a(n) = Sum_{k=1..n} Sum_{z=1..n} Sum_{y=1..n} Sum_{x=1..n} [GCD(f(x,y,z), n) = k] * f(x,y,z), where f(x,y,z) = x^2 + y^2 - z^2.
%F A373561 G.f.: x*(1 + 14*x + 21*x^2 + 4*x^3)/(1 - x)^6. - _Stefano Spezia_, Jun 10 2024
%t A373561 nn = 34; Table[+1/3 n^5 + 1/2 n^4 + 1/6 n^3, {n, 0, nn}]
%t A373561 p = 2; Table[Sum[Sum[Sum[Sum[If[GCD[x^p + y^p - z^p, n] == k, x^p + y^p - z^p, 0], {x, 1, n}], {y, 1, n}], {z, 1, n}], {k, 1, n}], {n, 0, nn}]
%t A373561 LinearRecurrence[{6,-15,20,-15,6,-1}, {0,1,20,126,480,1375}, 35] (* _Hugo Pfoertner_, Jun 10 2024 *)
%Y A373561 Cf. A368197, A000330.
%K A373561 nonn,easy
%O A373561 0,3
%A A373561 _Mats Granvik_, Jun 10 2024