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Minimal number of rectangles with integer sides that will form any rectangle with area n.
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%I #22 Oct 22 2024 09:47:38

%S 1,1,1,2,1,2,1,2,3,2,1,4,1,2,3,4,1,4,1,4,3,2,1,5,5,2,3,4,1,6,1,4,3,2,

%T 5,8,1,2,3,6,1,6,1,4,7,2,1,8,7,6,3,4,1,6,5,8,3,2,1,8,1,2,9,8,5,6,1,4,

%U 3,9,1,10,1,2,7,4,7,6,1,11,9,2,1,10,5,2

%N Minimal number of rectangles with integer sides that will form any rectangle with area n.

%C A033676(n) <= a(n) <= A052126(n). - _Charlie Neder_, Oct 06 2018

%H Nicholas John Bizzell-Browning, <a href="https://bura.brunel.ac.uk/handle/2438/29960">LIE scales: Composing with scales of linear intervallic expansion</a>, Ph. D. Thesis, Brunel Univ. (UK, 2024). See p. 147.

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a034/A034880.java">Java program</a> (github)

%F a(prime) = 1. - _Sean A. Irvine_, Sep 10 2020

%e a(24) = 5 because the five rectangles 1 X 3, 1 X 3, 1 X 6, 1 X 6, 1 X 6 can form each of the rectangles 1 X 24, 2 X 12, 3 X 8, and 4 X 6. - _Sean A. Irvine_, Sep 10 2020

%Y Cf. A070966. [_R. J. Mathar_, Sep 25 2008]

%K nonn

%O 1,4

%A _Erich Friedman_

%E a(24)-a(59) from _Charlie Neder_, Oct 06 2018

%E More terms from _Sean A. Irvine_, Sep 10 2020