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A272063 a(n) = largest k such that A004431(n) +/- k are both positive squares. 0

%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 40-24 = 4^2.

%Y Cf. A001844, A004431, A055096, A270835.

%K nonn

%O 1,1

%A _Bob Selcoe_, Apr 19 2016

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Last modified August 9 18:55 EDT 2022. Contains 356026 sequences. (Running on oeis4.)