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 A351802 #24 Mar 12 2022 07:57:21
%S A351802 264,325,1064,27265,6528,34200,12376,1015,8512,11520,8415,1656,116025,
%T A351802 8415,17575,56448,81928,6765,107712,106128,43953,60903,235008,311885,
%U A351802 3105,32571,571648,411320,9499,4991,1800,13875,1894144,16320,402375,42735,805,218925
%N A351802 a(n) = A351477(n) * FB 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 A351802 Inspired by Project Euler, Problem 143 (see link) where such a triangle is called a "Torricelli triangle".
%C A351802 For the corresponding primitive triples, miscellaneous properties and references, see A336328.
%C A351802 Equivalently, a(n) is the numerator of the fraction FB = a(n) / A351477(n).
%C A351802 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 FB = a(n).
%C A351802 FB is the middle length with FC < FB < FA (remember a < b < c).
%H A351802 Project Euler, <a href="https://projecteuler.net/problem=143">Problem 143 - Investigating the Torricelli point of a triangle</a>.
%F A351802 a(n) = A351476(n) - A351801(n) - A351803(n).
%F A351802 FB = sqrt(((2*a*c)^2 - (a^2+c^2-d^2)^2)/3) / d. - _Jinyuan Wang_, Feb 19 2022
%e A351802 For the 2nd triple in A336328, i.e., (73, 88, 95), we get A336329(2) = FA + FB + FC = 440/7 + 325/7 + 264/7 = 147, hence A351477(2) = 7 and a(2) = 325.
%o A351802 (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*a*c)^2 - (a^2+c^2-d^2)^2)/3)/d), ", ");););););} \\ _Michel Marcus_, Mar 01 2022
%Y A351802 Cf. A336328 (primitive triples), A336329 (FA + FB + FC), A336330 (smallest side), A336331 (middle side), A336332 (largest side), A336333 (perimeter), A351801 (FA numerator), this sequence (FB numerator), A351803 (FC numerator), A351477 (common denominator of FA, FB, FC), A351476 (other 'FA + FB + FC').
%K A351802 nonn
%O A351802 1,1
%A A351802 _Bernard Schott_, Feb 19 2022
%E A351802 More terms from _Jinyuan Wang_, Feb 19 2022