A224779 One half of the even numbers that are a primitive sum of four nonzero squares at least once.

2, 5, 6, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 46, 47, 49, 50, 51, 53, 54, 55, 57, 58, 59, 61, 62, 63, 65, 66, 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

Offset: 1

Author

Wolfdieter Lang, May 09 2013

Keywords

• nonn

Comments

These are the even numbers of A222949 divided by 2.

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, ...

Examples

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

Crossrefs

Cf. A224778 (imprimitive case).

Formula

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