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A224449 A finite set of numbers relevant for the representation of numbers as primitive distinct sums of three squares (0 square allowed). 1
1, 2, 3, 6, 9, 11, 18, 19, 22, 27, 33, 43, 51, 57, 67, 99, 102, 123, 163, 177, 187, 267, 627 (list; graph; refs; listen; history; text; internal format)
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.

REFERENCES

F. Halter-Koch, Darstellung natuerlicher Zahlen als Summe von Quadraten, Acta Arith. 42 (1982) 11-20, pp. 13 and 11.

LINKS

Table of n, a(n) for n=1..23.

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-Fran├žois Alcover, Apr 10 2013 *)

CROSSREFS

Cf. A224447, A224448, A051952.

Sequence in context: A338546 A176189 A057127 * A007780 A018537 A018331

Adjacent sequences:  A224446 A224447 A224448 * A224450 A224451 A224452

KEYWORD

nonn,fini

AUTHOR

Wolfdieter Lang, Apr 09 2013

STATUS

approved

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Last modified September 27 02:43 EDT 2021. Contains 347673 sequences. (Running on oeis4.)