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 A338861 a(n) is the largest area of a rectangle which can be dissected into n squares with integer sides s_i, i = 1 .. n, and gcd(s_1,...,s_n) = 1. 3
 1, 2, 6, 15, 42, 143, 399, 1190, 4209, 10920, 37245, 109886, 339745, 1037186, 3205734, 9784263, 29837784, 93313919, 289627536 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A219158 gives the minimum number of squares to tile an i x j rectangle. a(n) is found by checking all rectangles (i,j) for which A219158 has a dissection into n squares. Due to the potential counterexamples to the minimal squaring conjecture (see MathOverflow link), terms after a(19) have to be considered only as lower bounds: a(20) >= 876696755, a(21) >= 2735106696. - Hugo Pfoertner, Nov 17 2020, Apr 02 2021 LINKS Table of n, a(n) for n=1..19. Stuart Anderson, Catalogues of Simple Perfect Squared Rectangles. Stuart Anderson, Simple Imperfect Squared Rectangles, orders 9 to 24. Bertram Felgenhauer, Filling rectangles with integer-sided squares. MathOverflow, tiling a rectangle with the smallest number of squares, answer by Ed Pegg Jr, Jul 09 2017. Rainer Rosenthal, Rectangle tiled by 19 squares with maximum area a(19) EXAMPLE a(6) = 11*13 = 143. Dissection of the 11 X 13 rectangle into 6 squares: . +-----------+-------------+ | | | | | | | 6 X 6 | 7 X 7 | | | | | | | +---------+-+ | | +-+-----+-------+ | 5 X 5 | | | | | 4 X 4 | 4 X 4 | | | | | +---------+-------+-------+ . a(19) = 16976*17061 = 289627536. Dissection of the 16976 X 17061 rectangle into 19 squares: . +----------------+-------------+ | | | | | | | | 7849 | | 9212 | | | | | | | | | |------+------| |________________| | | | | see | 4109 | | |Rosenthal| | | | link +-+------+ | 7764 |-------| | | | | 5018 | | | 4279 | | | | | | +-------------+-------+--------+ . CROSSREFS Cf. A219158, A290821 (analog with triangles), A340726, A340920. Sequence in context: A065178 A178936 A221744 * A340726 A303833 A148438 Adjacent sequences: A338858 A338859 A338860 * A338862 A338863 A338864 KEYWORD nonn,hard,more AUTHOR Rainer Rosenthal, Nov 12 2020 EXTENSIONS a(11)-a(17) from Hugo Pfoertner based on data from squaring.net website, Nov 17 2020 a(18) from Hugo Pfoertner, Feb 18 2021 a(19) from Hugo Pfoertner, Apr 02 2021 STATUS approved

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Last modified February 27 12:56 EST 2024. Contains 370375 sequences. (Running on oeis4.)