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3d-congruent numbers: positive integers n for which there exists a trirectangular tetrahedron having volume n and rational areas and sides.
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%I #22 Jan 10 2018 15:23:36

%S 13,85,104,175,308,351,490,680,832,1400,1625,2295,2464,2808,3179,3920,

%T 4459,4725,5440,6656,8316,9295,9477,9724,10625,11200,13000,13230,

%U 13475,17303,18360,19712,19760,21875,22464,25432,28561,29155,31360,35672,37800,38500,43520,43875

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

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TrirectangularTetrahedron.html">Trirectangular Tetrahedron</a>

%e 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.

%e 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.

%Y Cf. A295507, A000578 (cubes).

%K nonn

%O 1,1

%A _Ralf Steiner_, Dec 27 2017