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A262767 Minimum perimeter of a rectangle with area n and integer sides. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A183005

Adjacent sequences:  A262764 A262765 A262766 * A262768 A262769 A262770

KEYWORD

nonn,easy

AUTHOR

Tim Cieplowski, Sep 30 2015

STATUS

approved

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Last modified April 25 10:11 EDT 2017. Contains 285379 sequences.