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%I #20 Dec 05 2013 06:11:20
%S 25,50,100,169,200,225,289,338,400,450,578,676,800,841,900,1156,1225,
%T 1352,1369,1521,1600,1681,1682,1800,2025,2312,2450,2601,2704,2738,
%U 2809,3025,3042,3200,3362,3364,3600,3721,4050,4624,4900,5202,5329,5408,5476
%N Squares or double-squares that are the sum of two distinct nonzero squares in exactly one way.
%C Subsequence of A004431 and A001481.
%C Numbers with exactly one prime factor of form 4k+1 with multiplicity 2, and without prime factor of form 4k+3 to an odd multiplicity.
%H Jean-Christophe Hervé and Donovan Johnson, <a href="/A232438/b232438.txt">Table of n, a(n) for n = 1..1000</a> (first 368 terms from Jean-Christophe Hervé)
%F A004018(a(n)) = 12.
%F Terms are obtained by the products A125853(k)*A002144(p)^2 for k, p > 0, ordered by increasing values.
%e 25 = 5^2 = 16+9; 50 = 2*5^2 = 49+1.
%t Select[Range[10^4], (IntegerQ[Sqrt[#]] || IntegerQ[Sqrt[#/2]]) && Count[ PowersRepresentations[#, 2, 2], {x_, y_} /; Unequal[0, x, y]] == 1 &]
%t (* or *) Select[Range[10^4], SquaresR[2, #] == 12 &] (* _Jean-François Alcover_, Dec 03 2013 *)
%Y Cf. A001481, A004431, A004018, A125853 (A004018 = 4), A230779 (A004018 = 8), A025303 (A004018 = 16).
%Y Analogs for square decompositions: A084645, A084646, A084647, A084648, A084649.
%K nonn
%O 1,1
%A _Jean-Christophe Hervé_, Dec 01 2013
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