A222949 Numbers that are a sum of four nonzero squares where the summands have no common square factor > 1.

4, 7, 10, 12, 13, 15, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 30, 31, 33, 34, 35, 36, 37, 38, 39, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102

Offset: 1

Author

Wolfdieter Lang, Mar 25 2013

Keywords

• nonn

Comments

A representation of a(n) as a sum of four nonzero squares is denoted by [s(1),s(2),s(3),s(4)] with nondecreasing entries > 1 and Sum_{j=1..4} s(j)^2 = a(n). It is called primitive if gcd(s(1),s(2),s(3),s(4)) = 1. a(n) is the number with at least one such primitive representation for n, and the multiplicity m is given by the non-vanishing entries of A097203, that is A097203(a(n)).

Examples

			a(1) = 4 because 4 has the primitive representation [1, 1, 1, 1].
a(16) = 28, because 28 has the primitive representations [1, 1, 1, 5] and [1, 3, 3, 3] ([2, 2, 2, 4] is not primitive.).
4: [1, 1, 1, 1], 7: [1, 1, 1, 2], 10: [1, 1, 2, 2], 12: [1, 1, 1, 3], 13: [1, 2, 2, 2], 15: [1, 1, 2, 3], 18: [1, 2, 2, 3],
  19: [1, 1, 1, 4], 20: [1, 1, 3, 3], 21: [2, 2, 2, 3], 22: [1, 1, 2, 4], 23: [1, 2, 3, 3], 25: [1, 2, 2, 4],  26: [2, 2, 3, 3], 27: [1, 1, 3, 4], 28: [1, 1, 1, 5], [1, 3, 3, 3], ...
		

Crossrefs

Cf. A097203.

Formula

A097203(a(n)) is not 0.