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A384487 Numbers k such that there exist two integers 0 such that i/sigma(i) + j/sigma(j) + k/sigma(k) = 1.

%I A384487 #57 Jul 03 2025 09:29:48
%S A384487 396,504,600,756,840,924,1056,1080,1140,1170,1260,1320,1428,1440,1488,
%T A384487 1512,1540,1560,1596,1638,1650,1656,1680,1704,1710,1740,1800,1820,
%U A384487 1840,1848,1872,1932,1980,2016,2040,2100,2160,2184,2232,2244,2256,2280,2340,2352,2380,2400,2430,2436,2448,2460,2484
%N A384487 Numbers k such that there exist two integers 0<i<j<k such that i/sigma(i) + j/sigma(j) + k/sigma(k) = 1.
%C A384487 The numbers i, j and k form a WHM(1)-amicable triple (WHM =  weighted harmonic mean). See Dimitrov link.
%H A384487 Robert Israel, <a href="/A384487/b384487.txt">Table of n, a(n) for n = 1..600</a>
%H A384487 S. I. Dimitrov, <a href="https://arxiv.org/abs/2408.07387">Generalizations of amicable numbers</a>, arXiv:2408.07387 [math.NT], 2024.
%e A384487 504 is a term because (72, 360, 504) is a triple with 72/sigma(72) + 360/sigma(360) + 504/sigma(504) = 1.
%e A384487 420 is not a term because the corresponding triple is (84, 420, 420).
%p A384487 S:= {}: S2:= {}: R:= NULL: count:= 0:
%p A384487 for k from 1 while count < 100 do
%p A384487   v:= k/numtheory:-sigma(k);
%p A384487   if member(1-v,S2) then
%p A384487     R:= R, k; count:= count+1;
%p A384487  fi;
%p A384487   S2:= S2 union map(t -> `if`(t+v<1,t+v,NULL),S);
%p A384487   S:= S union {v};
%p A384487 od:
%p A384487 R; # _Robert Israel_, Jul 01 2025
%o A384487 (PARI) isok(k) = for (i=1, k-1, for (j=i+1, k-1, if (i/sigma(i) + j/sigma(j) + k/sigma(k) == 1, /* print([i,j,k]); */ return(1)););); \\ _Michel Marcus_, Jun 02 2025
%Y A384487 Cf. A000203, A125490, A125491, A125492, A253534, A253535, A383964.
%K A384487 nonn
%O A384487 1,1
%A A384487 _S. I. Dimitrov_, Jun 01 2025
%E A384487 More terms from _Michel Marcus_, Jun 02 2025