%I
%S 4,6,12,8,16,24,10,20,30,12,24,40,36,14,48,28,42,60,56,32,48,70,64,18,
%T 84,80,54,72,96,20,40,90,60,112,80,108,22,100,126,120,88,144,110,48,
%U 140,72,132,96,160,120,154,52,78,144,180
%N a(n) = largest k such that A004431(n) +/ k are both positive squares.
%C There can be more than one value of k such that A004431(n) +/ k are both positive squares; i.e., when there are multiple ways to express A004431(n) as the sum of positive squares. These are the terms which appear more than once in A055096. For example A004431(19) = 65 = {(1^2 + 8^2), (4^2 + 7^2)}: 65 +/ 16 = {7^2, 9^2} and 65 +/ 56 = {3^2, 11^2}. So a(19) = 56 rather than 16.
%C Similar to A270835; differences occur for n<56 at n = {19,25,38,39,42,51}; i.e., terms A004431(n) which appear more than once in A055096.
%C Sequence contains every even number >=4 and no odd numbers.
%F a(n) = A004431(n)1 when A004431(n) = k^2 + (k+1)^2 == A001844(k), k>=1.
%e a(11)=24 because A004431(11) = 40; 40+24 = 8^2 and 4024 = 4^2.
%Y Cf. A001844, A004431, A055096, A270835.
%K nonn
%O 1,1
%A _Bob Selcoe_, Apr 19 2016
