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%I #10 Feb 09 2021 02:05:24
%S 2,8,18,20,32,50,72,80,90,98,128,144,162,180,200,242,272,288,320,338,
%T 360,392,450,468,500,512,576,578,648,650,720,722,800,810,882,968,980,
%U 1058,1088,1152,1250,1280,1296,1332,1352,1440,1458,1568,1620,1682,1800
%N Numbers whose reciprocal is the sum of two reciprocals of squares.
%C These are numbers which can be written either as b^2*c^2*(b^2+c^2)*d^2 or if (b^2+c^2) is a square then as b^2*c^2*d^2, since 1/(b*(b^2+c^2)*d)^2+1/(c*(b^2+c^2)*d)^2 =1/(b^2*c^2*(b^2+c^2)*d^2) and 1/(b*sqrt(b^2+c^2)*d)^2+1/(c*sqrt(b^2+c^2)*d)^2 = 1/(b^2*c^2*d^2).
%e 98 is in the sequence since 1/98=1/10^2+1/70^2 (also 1/98=1/14^2+1/14^2).
%o (Python)
%o from fractions import Fraction
%o def aupto(lim):
%o sqr_recips = [Fraction(1, i*i) for i in range(1, lim+2)]
%o ssr = set(f + g for i, f in enumerate(sqr_recips) for g in sqr_recips[i:])
%o representable = [f.denominator for f in ssr if f.numerator == 1]
%o return sorted(r for r in representable if r <= lim)
%o print(aupto(1800)) # _Michael S. Branicky_, Feb 08 2021
%Y Either products of terms in A063663 and A000290, or squares of A008594.
%Y Cf. A001481, A000404, A063665, A063669.
%K nonn
%O 1,1
%A _Henry Bottomley_, Jul 28 2001
%E Offset changed to 1 by _Derek Orr_, Jun 23 2015