

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
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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



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



KEYWORD

nonn,hard,more


AUTHOR



EXTENSIONS

a(11)a(17) from Hugo Pfoertner based on data from squaring.net website, Nov 17 2020


STATUS

approved



