%I
%S 1,8,15,20,22,27,29,34,36,38,39,41,43,45,46,48,49,50,51,52,53,54,55,
%T 56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,
%U 79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101
%N Numbers n such that a cube can be divided into n subcubes.
%C If m and n are in the sequence, so is m+n1, since ndissecting one cube in an mdissection gives an (m+n1)dissection. 1, 8, 20, 38, 49, 51, 54 are in the sequence because of dissections corresponding to the equations 1^3=1^3, 2^3=8*1^3, 3^3=2^3+19*1^3, 4^3=3^3+37*1^3, 6^3=4*3^3+9*2^3+36*1^3, 6^3=5*3^3+5*2^3+41*1^3 and 8^3=6*4^3+2*3^3+4*2^3+42*1^3.
%C Combining these facts gives the remaining terms shown and all numbers > 47.
%C It may or may not have been shown that no other numbers occur  see Hickerson link.
%D J.P. Delahaye, Les inattendus mathematiques, pp. 93 BelinPour la science, Paris, 2004.
%D Eves, Howard, A Survey of Geometry, Vol. 1. Allyn and Bacon, Inc., Boston, Mass. 1966, see p. 271.
%D M. Gardner, Fractal Music, Hypercards and More: Mathematical Recreations from Scientific American Magazine. New York: W. H. Freeman, pp. 297298, 1992.
%H Dean Hickerson, <a href="/A014544/a014544.txt">Further comments on A014544</a>, Nov 01 2007 and Nov 10 2007
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CubeDissection.html">Cube Dissection</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HadwigerProblem.html">Hadwiger Problem</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,1).
%K easy,nonn
%O 1,2
%A _Eric W. Weisstein_
%E More terms from _Jud McCranie_, Mar 19 2001, who remarks that all integers > 47 are in the sequence.
%E Edited by _Dean Hickerson_, Jan 05 2003
