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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
MathOverflow, tiling a rectangle with the smallest number of squares, answer by Ed Pegg Jr, Jul 09 2017.
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
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.)