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A262767
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Minimum perimeter of a rectangle with area n and integer sides.
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1
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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
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OFFSET
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1,1
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COMMENTS
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a(n) >= A027709(n) = 2*ceiling(2*sqrt(n)). - Dmitry Kamenetsky, Feb 27 2017
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LINKS
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Table of n, a(n) for n=1..60.
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FORMULA
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a(n) = 2*A063655(n). - Michel Marcus, Oct 01 2015
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EXAMPLE
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Since 2 * (2 + 3) < 2 * (1+6), a(6) = 10.
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MATHEMATICA
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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 *)
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PROG
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#(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
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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Tim Cieplowski, Sep 30 2015
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STATUS
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approved
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