OFFSET
1,2
COMMENTS
This set of 23 numbers, possibly with one more number a >= 5*10^10, appears in a corollary of the Halter-Koch reference (Korollar 1.(c), p. 13 with the first line of r_3(n) on p. 11). A number is representable as a^2 + b^2 + c^2 with a,b, and c integers, 0 <= a < b < c, and gcd(a,b,c) = 1 if and only if n is not congruent 0, 4, 7 (mod 8) and not one of the numbers {a(k), k = 1 .. 23}, and, if it exists at all, a further number >= 5*10^10.
For the multiplicities of these representable numbers see A224447, and for the numbers themselves see A224448.
For a similar set of numbers relevant for sums of three nonzero squares see A051952.
LINKS
F. Halter-Koch, Darstellung natürlicher Zahlen als Summe von Quadraten, Acta Arith. 42 (1982) 11-20, pp. 13 and 11.
MATHEMATICA
representableQ[n_] := Length[ Select[ PowersRepresentations[n, 3, 2], Unequal @@ # && GCD @@ # == 1 & ]] > 0; Select[ Range[1000], Not[ representableQ[#] || MatchQ[ Mod[#, 8], 0 | 4 | 7]] &] (* Jean-François Alcover, Apr 10 2013 *)
CROSSREFS
KEYWORD
nonn,fini,changed
AUTHOR
Wolfdieter Lang, Apr 09 2013
STATUS
approved