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%I #18 Dec 30 2019 15:09:51
%S 1625,2125,3250,3625,4250,4625,4875,5125,6375,6500,6625,7250,7625,
%T 8500,9125,9250,9750,10250,10875,10985,11125,11375,12125,12625,12750,
%U 13000,13250,13625,13875,14125,14500,14625,14875,15250,15375,17000,17125
%N Numbers n that are the hypotenuse of exactly 10 distinct integer-sided right triangles, i.e., n^2 can be written as a sum of two squares in 10 ways.
%C If m is a term, then 2*m and p*m are terms where p is any prime of the form 4k+3. - _Ray Chandler_, Dec 30 2019
%H Ray Chandler, <a href="/A097225/b097225.txt">Table of n, a(n) for n = 1..10000</a>
%t r[n_] := Reduce[0 < x <= y && n^2 == x^2 + y^2, {x, y}, Integers]; Reap[For[n = 5, n <= 20000, n++, rn = r[n]; If[rn =!= False, If[Length[r[n]] == 10, Print[n]; Sow[n]]]]][[2, 1]] (* _Jean-François Alcover_, Nov 15 2016 *)
%Y Cf. A004144 (0), A084645 (1), A084646 (2), A084647 (3), A084648 (4), A084649 (5), A097219 (6), A097101 (7), A290499 (8), A290500 (9), A290501 (11), A097226 (12), A097102 (13), A290502 (14), A290503 (15), A097238 (16), A097239 (17), A290504 (18), A290505 (19), A097103 (22), A097244 (31), A097245 (37), A097282 (40), A097626 (67).
%K nonn
%O 1,1
%A _James R. Buddenhagen_, Sep 17 2004