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One half of the even numbers that are a primitive sum of four nonzero squares at least once.
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%I #4 May 09 2013 22:44:36

%S 2,5,6,9,10,11,13,14,15,17,18,19,21,22,23,25,26,27,29,30,31,33,34,35,

%T 37,38,39,41,42,43,45,46,47,49,50,51,53,54,55,57,58,59,61,62,63,65,66,

%U 67,69,70,71,73,74,75,77,78,79,81,82,83,85,86,87,89,90,91,93,94,95,97,98,99

%N One half of the even numbers that are a primitive sum of four nonzero squares at least once.

%C These are the even numbers of A222949 divided by 2.

%C Compare with A224778 where also imprimitive sums are included. Numbers from there, not appearing here, are 8, 20, 24, 32, 36, 40, 44, 52, 56, 60, 68, 72, 76, ...

%F a(n) is one half of the n-th even number of the sequence A222949.

%e a(1) = A222949(1)/2 = 2. The primitive representation of 4 is denoted by [1, 1, 1, 1], standing for 1^2 + 1^2 + 1^2 + 1^2.

%e a(8) = A222949(18)/2 =14, with two primitive representations for 28, namely [1, 1, 1, 5] and [1, 3, 3, 3]. There is also the imprimitive representation [2, 2, 2, 4].

%e 8 does not appear because the only representation of 16 comes from [2, 2, 2, 2] which is imprimitive.

%Y Cf. A224778 (imprimitive case).

%K nonn

%O 1,1

%A _Wolfdieter Lang_, May 09 2013