A262767 Minimum perimeter of a rectangle with area n and integer sides.

4, 6, 8, 8, 12, 10, 16, 12, 12, 14, 24, 14, 28, 18, 16, 16, 36, 18, 40, 18, 20, 26, 48, 20, 20, 30, 24, 22, 60, 22, 64, 24, 28, 38, 24, 24, 76, 42, 32, 26, 84, 26, 88, 30, 28, 50, 96, 28, 28, 30, 40, 34, 108, 30, 32, 30, 44, 62, 120, 32

Offset: 1

Author

Tim Cieplowski, Sep 30 2015

Keywords

• nonn
• easy

Comments

a(n) >= A027709(n) = 2*ceiling(2*sqrt(n)). - Dmitry Kamenetsky, Feb 27 2017

Examples

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

Crossrefs

Cf. A063655 (semiperimeter).

Two-dimensional equivalent of A075777.

Programs

Mathematica

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 *)

PARI

a(n) = {local(d); d=divisors(n); 2*(d[(length(d)+1)\2] + d[length(d)\2+1])}
vector(50, n, a(n)) \\ Altug Alkan, Oct 16 2015

Python

def perimeter(area):
    width = round(area ** (1/2))
    while area % width != 0:
        width -= 1
    return 2*(width + round(area/width))

Formula

a(n) = 2*A063655(n). - Michel Marcus, Oct 01 2015