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A335558 Positive integers that cannot be expressed as the sum of at most 5 pairwise coprime squares. 0
21, 22, 23, 24, 33, 45, 46, 47, 48, 57, 69, 70, 71, 72, 81, 93, 94, 95, 96, 105, 117, 118, 119, 120, 129, 141, 142, 143, 144, 153, 154, 161, 165, 166, 167, 168, 177, 189, 190, 191, 192, 201, 209, 213, 214, 215, 216, 217, 225, 237, 238, 239, 240, 246, 249, 261 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, C20.

LINKS

Table of n, a(n) for n=1..56.

MATHEMATICA

n = 261;

a1 = Prime[Range[6]]^2; a2 = a3 = a4 = a5 = {};

Do[If[GCD[x, y] == 1, AppendTo[a2, x^2 + y^2]], {x, 0, (n/2)^(1/2)}, {y, x, (n - x^2)^(1/2)}];

Do[If[GCD[x, y] == GCD[x, z] == GCD[y, z] == 1, AppendTo[a3, x^2 + y^2 + z^2]], {x, 0, (n/3)^(1/2)}, {y, x, ((n - x^2)/2)^(1/2)}, {z, y, (n - x^2 - y^2)^(1/2)}];

Do[If[GCD[x, y] == GCD[x, z] == GCD[x, t] == GCD[y, z] == GCD[y, t] == GCD[z, t] == 1, AppendTo[a4, x^2 + y^2 + z^2 + t^2]], {x, 0, (n/4)^(1/2)}, {y, x, ((n - x^2)/3)^(1/2)}, {z, y, ((n - x^2 - y^2)/2)^(1/2)}, {t, z, (n - x^2 - y^2 - z^2)^(1/2)}];

Do[If[GCD[x, y] == GCD[x, z] == GCD[x, t] == GCD[x, w] == GCD[y, z] == GCD[y, t] == GCD[y, w] == GCD[z, t] == GCD[z, w] == GCD[t, w] == 1, AppendTo[a5, x^2 + y^2 + z^2 + t^2 + w^2]], {x, 0, (n/5)^(1/2)}, {y, x, ((n - x^2)/4)^(1/2)}, {z, y, ((n - x^2 - y^2)/3)^(1/2)}, {t, z, ((n - x^2 - y^2 - z^2)/2)^(1/2)}, {w, t, (n - x^2 - y^2 - z^2 - t^2)^(1/2)}];

Complement[Range[n], Union@Join[a1, a2, a3, a4, a5]]

CROSSREFS

Cf. A008784, A280991.

Sequence in context: A183738 A004510 A199934 * A141439 A323419 A333908

Adjacent sequences:  A335555 A335556 A335557 * A335559 A335560 A335561

KEYWORD

nonn

AUTHOR

XU Pingya, Jun 14 2020

STATUS

approved

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Last modified January 17 06:12 EST 2022. Contains 350378 sequences. (Running on oeis4.)