OFFSET
1,3
COMMENTS
The reference asks "Let R(n) be the set of all rectangles whose side lengths are natural numbers and whose area is at most n. Find an integer n>1 such that the members of R(n), each used exactly once, tile a square.". It shows that n=43 is the smallest solution. A necessary condition is that n be in this sequence. Is this also a sufficient condition?
A heuristic argument suggests that the sequence is infinite and has about 2*sqrt(log(n)) terms <= n.
No other terms below 10^10.
LINKS
Nick MacKinnon, Problem 10883, Amer. Math. Monthly, 108 (2001) 565; solution by John C. Cock, 110 (2003) 343-344.
EXAMPLE
A083356(43)=2116=46^2, so 43 is in this sequence.
MATHEMATICA
For[n=area=0, True, n++; area+=n*Ceiling[DivisorSigma[0, n]/2], If[IntegerQ[s=Sqrt[area]], Print[{n, s}]]]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Dean Hickerson, Apr 26 2003
EXTENSIONS
a(11) from Max Alekseyev, Jan 30 2012
STATUS
approved