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

1,1

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, ...

Links

Table of n, a(n) for n=1..72.

Formula

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

Example

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).

Sequence in context: A143909 A284507 A284492 * A171888 A286905 A028946

Adjacent sequences: A224776 A224777 A224778 * A224780 A224781 A224782

Keyword

nonn

Author

Wolfdieter Lang, May 09 2013

Status

approved