A071610 -id:A071610 - cp's OEIS frontend

A071609 Squared radii of the spheres around (0,0,0) that contain record numbers of lattice points.

1, 2, 5, 9, 14, 26, 41, 74, 89, 101, 146, 194, 269, 314, 341, 446, 614, 626, 689, 794, 854, 941, 1106, 1109, 1154, 1286, 1361, 1634, 1781, 1889, 2141, 2609, 2966, 3134, 3401, 3449, 3506, 4241, 4289, 4826, 5381, 5561, 6254, 7229, 7829, 8069, 8126

Offset: 1

Hugo Pfoertner, May 25 2002

nonn

The number of lattice points (i,j,k) on the sphere around (0,0,0) with i^2 + j^2 + k^2 = a(n) is given by A071611(n).

Indices of records in A005875. - Daniel Suteu, Aug 13 2021

Hugo Pfoertner, Table of n, a(n) for n = 1..189

Cf. A005875, A071342, A071343, A071344, A071610, A071611.

A071611 Number of points (i,j,k) on the surface of a sphere around (0,0,0) with squared radius A071609(n).

Original entry on oeis.org

6, 12, 24, 30, 48, 72, 96, 120, 144, 168, 192, 240, 264, 312, 336, 384, 408, 432, 480, 504, 528, 552, 576, 600, 672, 696, 720, 768, 816, 864, 936, 1008, 1032, 1056, 1104, 1200, 1248, 1296, 1344, 1440, 1512, 1584, 1680, 1704, 1752, 1848, 1920, 2016

Offset: 1

Hugo Pfoertner, May 25 2002

nonn

a(n) is the number of lattice points on a sphere around (0,0,0) with r^2 = A071609(n).

			A sphere with radius 1 has 6 lattice points on its surface, so a(1)=6. A sphere with r=sqrt(2) passes through 12 lattice points of the shape (1,1,0), so a(2)=12. A sphere with r=sqrt(5) passes through 24 lattice points with shape (2,1,0), so a(3)=24. A sphere with r=sqrt(9) passes through 6 lattice points of shape (3,0,0) and through 24 lattice points of shape (2,2,1), so a(4)=6+24=30.

Hugo Pfoertner, Table of n, a(n) for n = 1..189

Cf. A005875, A071342-A071344, A071609, A071610.

a(n) = A005875(A071609(n)). - Daniel Suteu, Aug 13 2021

cp's OEIS Frontend

A071609 Squared radii of the spheres around (0,0,0) that contain record numbers of lattice points.

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