A297207 3d-congruent numbers: positive integers n for which there exists a trirectangular tetrahedron having volume n and rational areas and sides.

13, 85, 104, 175, 308, 351, 490, 680, 832, 1400, 1625, 2295, 2464, 2808, 3179, 3920, 4459, 4725, 5440, 6656, 8316, 9295, 9477, 9724, 10625, 11200, 13000, 13230, 13475, 17303, 18360, 19712, 19760, 21875, 22464, 25432, 28561, 29155, 31360, 35672, 37800, 38500, 43520, 43875

Offset

1,1

Comments

Ordered list of numbers A295507(i)*j^3 with i,j positive integers.

Links

Table of n, a(n) for n=1..44.

Eric Weisstein's World of Mathematics, Trirectangular Tetrahedron

Example

a(1) = 13 = 13*1^3 = A295507(1)*A000578(1) is the volume of the trirectangular tetrahedron with sides: {240, 117, 44, 125, 244, 267}*1^3/15840.
a(3) = 104 = 13*2^3 = A295507(1)*A000578(2) is the volume of the trirectangular tetrahedron with sides: {240, 117, 44, 125, 244, 267}*2^3/15840.

Crossrefs

Cf. A295507, A000578 (cubes).

Sequence in context: A301953 A321589 A225129 * A222491 A010025 A001848

Adjacent sequences: A297204 A297205 A297206 * A297208 A297209 A297210

Keyword

nonn

Author

Ralf Steiner, Dec 27 2017

Status

approved