The Loeschian numbers (OEIS A003136) are numbers of the form
are integers. For example,
, with (28,2,4) as the related Loeschian triplet.
But first, something else. A different sequence is the Farey sequence, which at order 5 is
In two dimensions, the Farey sequence can make Ford circles, each with the number as a radius, centered above their number, and tangent to the zero line and each other.
Loeschian spheres can be made, each with the number as a curvature (the reciprocal of the radius). With
as a Loeschian triplet satisfying
, the sphere centers are at one of six locations.