OFFSET
1,1
COMMENTS
Numbers which are cubes themselves are excluded as trivial.
It appears that this sequence is infinite. For seventh powers < 10^49, only 2^7 and 3^7 are closer to cubes than squares. Note that 1/2+1/3+1/5>1, but 1/2+1/3+1/7<1. Do these inequalities determine whether there are an infinite or finite number of solutions? Mazur discusses how the ABC conjecture applies to perfect power problems. - T. D. Noe, Apr 07 2006
LINKS
B. Mazur, Questions about Number
Eric Weisstein's World of Mathematics, MathWorld: Perfect Power
EXAMPLE
The distance of 199^5 to the nearest cube is 49688. To the nearest square is 165882.
MATHEMATICA
nMax=10^6; lst={}; Do[n5=n^5; n3=Round[n5^(1/3)]^3; n2=Round[n5^(1/2)]^2; If[0 < Abs[n5-n3] < Abs[n5-n2], AppendTo[lst, n]], {n, nMax}]; lst (Noe) - T. D. Noe, Apr 07 2006
CROSSREFS
KEYWORD
nonn
AUTHOR
Ed Pegg Jr, Apr 05 2006
EXTENSIONS
More terms from T. D. Noe and Hans Havermann, Apr 08 2006
STATUS
approved