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%I #11 Jul 28 2015 05:49:23
%S 147,225,405,1323,2025,3645,3675,4225,5625,7203,7623,10125,11025,
%T 11907,14415,17457,17787,18225,18513,19845,24375,24843,27225,30625,
%U 32805,33075,38025,42483,49005,50625,53067,61347,64827,65025,68445,68607,77763,81225,91125,91875,98397,99225,105625,107163,117045,119025
%N Odd numbers of the form (m*k)^2/(m^2-k^2) for distinct integers m and k.
%C The first term ending in a 9 seems to be 1225449, and the first term ending in a 1 is 136161.
%C For 1 <= m <= 10^4 and 1 <= k <= m, there are 9217 numbers of the form (m*k)^2/(m^2-k^2). Of these numbers, only 679 are odd.
%C If a(n) is not a square, then m = 9*k or m = 7*k. If a(n) is a square, m does not appear to be a multiple of k.
%C Let a(n) be a square generated by m_1 and k_1. If a(n-1) is generated by m_2 and k_2, then k_1 = k_2 and m_1 < m_2.
%C 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).
%e (84*12)^2/(84^2-12^2) = 84^2/48 = 147. So 147 is a member of this sequence. (Note that k=12 and m=84 and so m=7*k.)
%o (PARI) v=[]; for(m=1, 7500, for(n=1, m-1, if(type(s=(m*n)^2/(m^2-n^2))=="t_INT"&&(s%2), v=concat(v, s)))); vecsort(v, , 8)
%Y Cf. A259263, A111200.
%K nonn
%O 1,1
%A _Derek Orr_, Jun 23 2015
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