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 A385749 #19 Jul 18 2025 21:42:24 %S A385749 120,672,1740,2556,4680,11556,27312,32136,41412,41952,42168 %N A385749 Numbers z such that there exist two integers 0<x<=y<=z such that (x^2/sigma(x)^2 + y^2/sigma(y)^2 + z^2/sigma(z)^2) * (x + y + z)^2 = x^2 + y^2 + z^2. %C A385749 The numbers x, y and z form a WHM(2)-amicable triple (WHM = weighted harmonic mean). An amicable triple forms a WHM(2)-amicable triple, so the larger member of an amicable triple A125492 is a term of this sequence. %H A385749 S. I. Dimitrov, <a href="https://arxiv.org/abs/2408.07387">Generalizations of amicable numbers</a>, arXiv:2408.07387 [math.NT], 2024. %e A385749 (1980, 2016, 2556) is such a triple because (1980^2/sigma(1980)^2 + 2016^2/sigma(2016)^2 + 2556^2/sigma(2556)^2)*(1980 + 2016 + 2556)^2 = 1980^2 + 2016^2 + 2556^2. %e A385749 Other kinds of triples are: (120,120,120), (1560, 1740, 1740) and (117, 117, 4680). %e A385749 Note that (117, 117, 4680) is the only known WHM(2)-amicable triple that is not an amicable triple. %Y A385749 Cf. A000203, A125492, A384487. %Y A385749 Cf. A005820 (a subsequence, for (x,x,x) triples). %K A385749 nonn,hard,more %O A385749 1,1 %A A385749 _S. I. Dimitrov_, Jul 08 2025