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

1,1

Comments

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

Links

Table of n, a(n) for n=1..60.

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A063655 (semiperimeter).

Two-dimensional equivalent of A075777.

Sequence in context: A196358 A079775 A247654 * A104173 A023991 A373042

Adjacent sequences: A262764 A262765 A262766 * A262768 A262769 A262770

Keyword

nonn,easy

Author

Tim Cieplowski, Sep 30 2015

Status

approved