
COMMENTS

Given on p. 8 of Dixon, with "coincidence" involving Fibonacci numbers.
Since there is no indication of how the sequence 1,2,8,24 might be extended, I have marked this as "fini" and "full".  N. J. A. Sloane, Nov 12 2010
Let x = {1, 2, 8, 24}. Then (Lambda_x/x + 1)^2  1 = {8, 15, 960, 67092480} and is either a cake number (A000125) or the product of consecutive cake numbers. For instance, 960 = 1 * 2 * 4 * 8 * 15 = (Lambda_8/8 + 1)^2  1 and 67092480 = 1 * 2 * 4 * 8 * 15 * 26 * 42 * 64 = (Lambda_24/24 + 1)^2  1. This is interesting, at least in part, since x^2 = {1, 4, 64, 576} is also a cake number.  Raphie Frank, Dec 06 2012


REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", SpringerVerlag, Chap. 6.
