A262767 - OEIS

%I #18 Jun 08 2024 15:43:53

%S 4,6,8,8,12,10,16,12,12,14,24,14,28,18,16,16,36,18,40,18,20,26,48,20,

%T 20,30,24,22,60,22,64,24,28,38,24,24,76,42,32,26,84,26,88,30,28,50,96,

%U 28,28,30,40,34,108,30,32,30,44,62,120,32

%N Minimum perimeter of a rectangle with area n and integer sides.

%C a(n) >= A027709(n) = 2*ceiling(2*sqrt(n)). - _Dmitry Kamenetsky_, Feb 27 2017

%F a(n) = 2*A063655(n). - _Michel Marcus_, Oct 01 2015

%e Since 2 * (2 + 3) < 2 * (1+6), a(6) = 10.

%t f[n_] := Block[{w = Round@ Sqrt@ n}, While[Mod[n, w] != 0, w--]; 2 (w + Round[n/w])]; Array[f, {60}] (* _Michael De Vlieger_, Oct 01 2015 *)

%o (Python)

%o def perimeter(area):

%o     width = round(area ** (1/2))

%o     while area % width != 0:

%o         width -= 1

%o     return 2*(width + round(area/width))

%o (PARI) a(n) = {local(d); d=divisors(n); 2*(d[(length(d)+1)\2] + d[length(d)\2+1])}

%o vector(50, n, a(n)) \\ _Altug Alkan_, Oct 16 2015

%Y Cf. A063655 (semiperimeter).

%Y Two-dimensional equivalent of A075777.

%K nonn,easy

%O 1,1

%A _Tim Cieplowski_, Sep 30 2015