

A083357


Numbers n such that A083356(n) (the total area of all incongruent integersided rectangles of area <= n) is a square.


2



0, 1, 43, 169, 227, 735, 10664, 14702, 78159, 5431210, 8350707565
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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

Table of n, a(n) for n=1..11.
Nick MacKinnon, Problem 10883, Amer. Math. Monthly, 108 (2001) 565; solution by John C. Cock, 110 (2003) 343344.


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

Cf. A083356, A083358.
Sequence in context: A123040 A142016 A140640 * A158604 A057816 A162295
Adjacent sequences: A083354 A083355 A083356 * A083358 A083359 A083360


KEYWORD

nonn,more


AUTHOR

Dean Hickerson, Apr 26 2003


EXTENSIONS

a(11) from Max Alekseyev, Jan 30 2012


STATUS

approved



