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A224772 Multiplicities for representations of numbers as primitive sums of three distinct nonzero squares.

%I A224772 #8 Jan 19 2019 04:15:43
%S A224772 0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,0,0,0,
%T A224772 1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,0,1,2,0,0,1,1,0,0,
%U A224772 2,1,0,0,0,2,1,0,2,1,0,0,1,0,1,0,0,2,0,0,2,2,1,0,1,2,0,0,0,2,0,0,3,0,0,0,2,1,1,0,1,3,0,0,1,1,1,0,2,1,0,0,1,2,0,0,2,2,0,0,2,0,2,0,1,3,0,0,1,2,1,0,2
%N A224772 Multiplicities for representations of numbers as primitive sums of three distinct nonzero squares.
%C A224772 a(n) = k, for n >= 1, if there are exactly k representations of n as a primitive sum of three distinct nonzero squares. If a(n) = 0 then n has no such representation.
%C A224772 The increasingly ordered numbers with a(n) > 0 are given in A224771.
%H A224772 T. D. Noe, <a href="/A224772/b224772.txt">Table of n, a(n) for n = 1..10000</a>
%F A224772 a(n) = k if n = a^2 + b^2 + c^2, a, b, and c integers, 0 < a <  b < c and gcd(a,b,c) = 1, for exactly k different triples (a, b, c). If there is no such triple then a(n) = 0.
%e A224772 a(14) = 1 because the first number with a representation in question, denoted by a triple (a, b, c), is 14, with the unique triple (1, 2, 3).
%e A224772 a(62) = 2 for the first number 62 which has two representations, denoted by (1, 5, 6) and (2, 3, 7).
%e A224772 a(101) = 3 for the first number 101 with three triples, namely (1, 6, 8), (2, 4, 9) and (4, 6, 7).
%t A224772 nn = 10; t = Table[0, {nn^2}]; Do[If[GCD[a, b, c] == 1, n = a^2 + b^2 + c^2; If[n <= nn^2, t[[n]]++]], {a, nn}, {b, a + 1, nn}, {c, b + 1, nn}]; t (* _T. D. Noe_, Apr 20 2013 *)
%Y A224772 Cf. A224771, A025442 (multiplicities for sums of three distinct nonzero squares).
%K A224772 nonn
%O A224772 1,62
%A A224772 _Wolfdieter Lang_, Apr 19 2013