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%I #18 Aug 06 2015 11:03:53
%S 12,18,48,72,108,147,150,162,180,192,225,240,288,300,400,405,432,448,
%T 450,578,588,600,648,720,768,882,900,960,972,980,1008,1100,1152,1200,
%U 1260,1323,1350,1452,1458,1600,1620,1728,1792,1800,2025,2028,2100,2160,2178,2312,2352,2400,2592,2700,2880,3042,3072,3150
%N Numbers of the form (m*k)^2/(m^2-k^2) for distinct integers m and k.
%C The odd numbers are much more rare than even numbers: 147, 225, 405, 1323, 2025, 3645, 3675, ... For 1 <= m <= 10^4 and 1 <= k <= m, there are 9217 total solutions. Of these solutions, only 679 are odd. See A259288.
%C Similarly, the reciprocals of these numbers can be represented as the difference in the reciprocals of two squares (i.e., there exists two distinct integers m and k satisfying 1/a(n) = 1/m^2 - 1/k^2).
%C If a(n) is a square, its square root is in A111200.
%e (3*6)^2/(6^2-3^2) = 18^2/(3*9) = 12. So 12 is a member of this sequence.
%o (PARI) v=[];for(m=1,7500,for(n=1,m-1,if(type(s=(m*n)^2/(m^2-n^2))=="t_INT",v=concat(v,s))));vecsort(v,,8)
%Y Cf. A063664, A111200, A259288.
%K nonn
%O 1,1
%A _Derek Orr_, Jun 22 2015
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