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%I #13 Nov 27 2019 17:27:27
%S 25,125,169,289,625,841,1369,1681,2197,2809,3125,3721,4913,5329,7921,
%T 9409,10201,11881,12769,15625,18769,22201,24389,24649,28561,29929,
%U 32761,37249,38809,50653,52441,54289,58081,66049,68921,72361,76729,78125
%N Hypotenuses of primitive Pythagorean triples which are not prime numbers and which are the hypotenuse of a unique triangle.
%C Each term is a prime power of the form p^e where p is in A002144 and e>1.
%C A proper subset of A120960 by eliminating A002144.
%C A proper subset of A120961 by eliminating A024409.
%C A proper subset of A008846 by eliminating A002144 and A024409.
%C A proper subset of A020882 by eliminating A002144, A024409 and duplicate entries.
%H Ray Chandler, <a href="/A146945/b146945.txt">Table of n, a(n) for n = 1..10000</a>
%t lst1 = {1, 1}; lst2 = {}; Do[ If[ GCD[m, n] == 1, a = 2m*n; b = m^2 - n^2; c = m^2 + n^2; If[ !PrimeQ@c, AppendTo[lst1, c]]], {m, 3, 1000}, {n, If[OddQ@m, 2, 1], m - 1, 2}]; lst1 = Sort@ lst1; Do[ If[ lst1[[n - 1]] != lst1[[n]] && lst1[[n]] != lst1[[n + 1]], AppendTo[lst2, lst1[[n]]]], {n, 2, Length@ lst1 - 1}]; Take[lst2, 50] (* _Robert G. Wilson v_, May 02 2009 *)
%Y Cf. A020882, A008846, A002144, A024409, A120960, A120961.
%K nonn
%O 1,1
%A John Harrison (harrison_uk_2000(AT)yahoo.co.uk), Apr 20 2009
%E a(7) corrected by and a(17) and further terms from _Robert G. Wilson v_, May 02 2009
%E Minor edits to comments. - _Ray Chandler_, Nov 27 2019