Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #7 Apr 23 2016 10:12:03
%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 40-24 = 4^2.
%Y Cf. A001844, A004431, A055096, A270835.
%K nonn
%O 1,1
%A _Bob Selcoe_, Apr 19 2016