A335558 Positive integers that cannot be expressed as the sum of at most 5 pairwise coprime squares.

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

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