%I #15 Jan 15 2018 16:54:32

%S 65,85,130,145,170,185,205,221,265,290,305,325,365,370,377,410,425,

%T 442,445,481,485,493,505,530,533,545,565,610,629,650,685,689,697,725,

%U 730,745,754,785,793,845,850,865,890,901,905,925,949,962,965,970

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

%C These are the increasingly ordered numbers a(n) which satisfy A193138(a(n)) = 2.

%C 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 This sequence is a proper subsequence of A000404.

%H T. D. Noe, <a href="/A224770/b224770.txt">Table of n, a(n) for n = 1..10000</a>

%F 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 n=1, 65: (1, 8), (4, 7),

%e n=2, 85: (2, 9), (6, 7),

%e n=3, 130: (3, 11), (7, 9),

%e n=4, 145: (1, 12), (8, 9),

%e n=5, 170: (1, 13), (7, 11),

%e n=6, 185: (4, 13), (8, 11),

%e n=7, 205: (3, 14), (6, 13),

%e n=8, 221: (5, 14), (10, 11),

%e n=9, 265: (3, 16), (11, 12),

%e n=10, 290: (1, 17), (11, 13).

%t 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 Cf. A224450 (one way), A193138 (multiplicities), A000404, A024509.

%K nonn

%O 1,1

%A _Wolfdieter Lang_, Apr 18 2013