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 A306841 Number of rectangles of integer sides whose area or perimeter is n. 0

%I

%S 1,1,1,3,1,3,1,4,2,4,1,6,1,5,2,7,1,7,1,8,2,7,1,10,2,8,2,10,1,11,1,11,

%T 2,10,2,14,1,11,2,14,1,14,1,14,3,13,1,17,2,15,2,16,1,17,2,18,2,16,1,

%U 21,1,17,3,20,2,20,1,20,2,21,1,24,1,20,3,22,2,23

%N Number of rectangles of integer sides whose area or perimeter is n.

%H MathOverflow, <a href="https://mathoverflow.net/q/324654">Tiling a square with rectangles whose areas or perimeters are 1, 2, 3, ..., N</a>

%F a(n) = ceiling(d(n)/2) + floor(n/4) if n is even, a(n) = ceiling(d(n)/2) otherwise, where d(n) is the number of divisors of n.

%e a(4) = 3 because there are two rectangles of integer sides of area 4 (2 X 2 and 1 X 4) and one rectangle of integer sides of perimeter 4 (1 X 1).

%Y Cf. A038548 (area n), A004526 (perimeter 2n).

%K nonn

%O 1,4

%A _Freddy Barrera_, Mar 12 2019

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Last modified March 24 17:52 EDT 2023. Contains 361505 sequences. (Running on oeis4.)