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A224770 Numbers that are the primitive sum of two squares in exactly two ways.

%I A224770 #15 Jan 15 2018 16:54:32
%S A224770 65,85,130,145,170,185,205,221,265,290,305,325,365,370,377,410,425,
%T A224770 442,445,481,485,493,505,530,533,545,565,610,629,650,685,689,697,725,
%U A224770 730,745,754,785,793,845,850,865,890,901,905,925,949,962,965,970
%N A224770 Numbers that are the primitive sum of two squares in exactly two ways.
%C A224770 These are the increasingly ordered numbers a(n) which satisfy A193138(a(n)) = 2.
%C A224770 Neither the order of the squares nor the signs of the numbers to be squared are taken into account. The two squares are necessarily distinct and each is nonzero.
%C A224770 This sequence is a proper subsequence of A000404.
%H A224770 T. D. Noe, <a href="/A224770/b224770.txt">Table of n, a(n) for n = 1..10000</a>
%F A224770 a(n) = a^2 + b^2, a and integers, 0 < a < b and gcd(a,b) = 1 in exactly two ways. These representations of a(n) are denoted by two different pairs (a,b).
%e A224770 n=1,   65:  (1, 8),  (4, 7),
%e A224770 n=2,   85:  (2, 9),  (6, 7),
%e A224770 n=3,  130:  (3, 11), (7, 9),
%e A224770 n=4,  145:  (1, 12), (8, 9),
%e A224770 n=5,  170:  (1, 13), (7, 11),
%e A224770 n=6,  185:  (4, 13), (8, 11),
%e A224770 n=7,  205:  (3, 14), (6, 13),
%e A224770 n=8,  221:  (5, 14), (10, 11),
%e A224770 n=9,  265:  (3, 16), (11, 12),
%e A224770 n=10, 290:  (1, 17), (11, 13).
%t A224770 nn = 35; t = Sort[Select[Flatten[Table[If[GCD[a, b] == 1, a^2 + b^2, 0], {a, nn}, {b, a, nn}]], 0 < # <= nn^2 &]]; Transpose[Select[Tally[t], #[[2]] == 2 &]][[1]] (* _T. D. Noe_, Apr 20 2013 *)
%Y A224770 Cf. A224450 (one way), A193138 (multiplicities), A000404, A024509.
%K A224770 nonn
%O A224770 1,1
%A A224770 _Wolfdieter Lang_, Apr 18 2013