A223728 Multiplicities for A223727: primitive sums of four distinct nonzero squares.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 3, 2, 1, 1, 1, 3, 2, 1, 3, 1, 1, 1, 2, 1, 1, 2, 1, 5, 1, 2, 3, 1, 1, 2, 3, 1, 2, 1, 1, 2, 4, 2, 1, 2, 3, 1, 5, 2, 2, 2, 2, 2, 4, 3, 1, 4, 1, 1, 4, 2, 2, 2, 5, 3, 1, 6, 3, 3, 1, 2, 1, 1, 4, 4, 2, 5, 1, 3, 7, 3, 2

Offset

1,16

Comments

A223728(n) has a(n) different primitive representations as sum of four distinct nonzero squares, n>=1.

Links

Table of n, a(n) for n=1..100.

Formula

a(n) = k if there are k different solutions for A223728(n) = sum(s(j)^2, j=1..4), with 0 < s(1) < s(2) < s(3) < s(4) and gcd(s(1),s(2),s(3),s(4)) = 1.

Example

a(16) = 3 because A223727(16) = 78 has three s-quadruples, namely [1, 2, 3, 8], [1, 4, 5, 6] and [2, 3, 4, 7].
a(23) = 2 from A223727(23) =  90 with s-quadruples [1, 2, 6, 7] and [1, 3, 4, 8].

Crossrefs

Cf. A223727, A223726.

Sequence in context: A031243 A030394 A223726 * A030596 A031277 A001165

Adjacent sequences: A223725 A223726 A223727 * A223729 A223730 A223731

Keyword

nonn

Author

Wolfdieter Lang, Mar 27 2013

Status

approved