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 A351801 #32 Mar 11 2022 12:38:54
%S A351801 325,440,5016,39360,14800,70720,91200,3864,9405,30429,11704,4669,
%T A351801 250096,11704,32640,81840,203000,7208,218120,199325,99360,76760,
%U A351801 359352,342912,8184,122200,595595,621387,12600,26040,19320,137344,3108105,24955,409640,58400,1520
%N A351801 a(n) = A351477(n) * FA where F is the Fermat point of a primitive integer-sided triangle ABC with A < B < C < 2*Pi/3 and FA + FB + FC = A336329(n).
%C A351801 Inspired by Project Euler, Problem 143 (see link) where such a triangle is called a "Torricelli triangle".
%C A351801 For the corresponding primitive triples, miscellaneous properties and references, see A336328.
%C A351801 Equivalently, a(n) is the numerator of the fraction FA = a(n) / A351477(n).
%C A351801 Also, if F is the Fermat point of a triangle ABC with A < B < C < 2*Pi/3, where AB, BC, CA, FA, FB and FC are all positive integers, then, when FA + FB + FC = d = A351476(n), we have FA = a(n).
%C A351801 FA is the largest length with FC < FB < FA (remember a < b < c).
%H A351801 Project Euler, <a href="https://projecteuler.net/problem=143">Problem 143 - Investigating the Torricelli point of a triangle</a>.
%H A351801 Wikipedia, <a href="https://en.wikipedia.org/wiki/Fermat_point">Fermat point</a>.
%F A351801 a(n) = A351476(n) - A351802(n) - A351803(n).
%F A351801 FA = sqrt(((2*b*c)^2 - (b^2 + c^2 - d^2)^2)/3) / d. - _Jinyuan Wang_, Feb 19 2022
%e A351801 For the 1st triple in A336328, i.e., (57, 65, 73), we get A336329(1) = FA + FB + FC = 325/7 + 264/7 + 195/7 = 112, hence A351477(1) = 7 and a(1) = 325.
%o A351801 (PARI) lista(nn) = {my(d); for(c=4, nn, for(b=ceil(c/sqrt(3)), c-1, for(a=1+(sqrt(4*c^2-3*b^2)-b)\2, b-1, if(gcd([a, b, c])==1 && issquare(d=6*(a^2*b^2+b^2*c^2+c^2*a^2)-3*(a^4+b^4+c^4)) && issquare(d=(a^2+b^2+c^2+sqrtint(d))/2), d = sqrtint(d); print1(numerator(sqrtint(((2*b*c)^2 - (b^2 + c^2 - d^2)^2)/3)/d), ", ");););););} \\ _Michel Marcus_, Mar 02 2022
%Y A351801 Cf. A336328 (primitive triples), A336329 (FA + FB + FC), A336330 (smallest side), A336331 (middle side), A336332 (largest side), A336333 (perimeter), this sequence (FA numerator), A351802 (FB numerator), A351803 (FC numerator), A351477 (common denominator of FA, FB, FC), A351476 (other 'FA + FB + FC').
%K A351801 nonn
%O A351801 1,1
%A A351801 _Bernard Schott_, Feb 19 2022
%E A351801 More terms from _Jinyuan Wang_, Feb 19 2022