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

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%I A223728 #4 Mar 27 2013 11:26:52
%S A223728 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,
%T A223728 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,
%U A223728 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
%N A223728 Multiplicities for A223727: primitive sums of four distinct nonzero squares.
%C A223728 A223728(n) has a(n) different primitive representations as sum of four distinct nonzero squares, n>=1.
%F A223728 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.
%e A223728 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].
%e A223728 a(23) = 2 from A223727(23) =  90 with s-quadruples [1, 2, 6, 7] and [1, 3, 4, 8].
%Y A223728 Cf. A223727, A223726.
%K A223728 nonn
%O A223728 1,16
%A A223728 _Wolfdieter Lang_, Mar 27 2013