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A063655 Smallest semiperimeter of integral rectangle with area n. 14
2, 3, 4, 4, 6, 5, 8, 6, 6, 7, 12, 7, 14, 9, 8, 8, 18, 9, 20, 9, 10, 13, 24, 10, 10, 15, 12, 11, 30, 11, 32, 12, 14, 19, 12, 12, 38, 21, 16, 13, 42, 13, 44, 15, 14, 25, 48, 14, 14, 15, 20, 17, 54, 15, 16, 15, 22, 31, 60, 16, 62, 33, 16, 16, 18, 17, 68, 21, 26 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Similar to A027709, which is minimal perimeter of polyomino of n cells, or equivalently, minimal perimeter of rectangle of area at least n and with integer sides. Present sequence is minimal semiperimeter of rectangle with area exactly n and with integer sides. - Winston C. Yang (winston(AT)cs.wisc.edu), Feb 03 2002

Semiperimeter b+d, d >= b, of squarest (smallest d-b) integral rectangle with area bd = n. That is, b = largest divisor of n <= sqrt(n), d = smallest divisor of n >= sqrt(n). a(n) = n+1 iff n is noncomposite (1 or prime). - Daniel Forgues, Nov 22 2009

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A033676(n) + A033677(n).

a(n) = A162348(2n-1) + A162348(2n). - Daniel Forgues, Sep 29 2014

EXAMPLE

Since 15 = 1*15 = 3*5 and the 3*5 rectangle gives smallest semiperimeter 8, we have a(15)=8.

MAPLE

interface(quiet=true); for n from 1 to 100 do for i from floor(sqrt(n)) to 1 by -1 do j := floor(n / i); if (i * j = n) then printf("%d, ", i + j); break; end if; od; od; # from Winston C. Yang, Feb 03 2002

MATHEMATICA

Table[d = Divisors[n]; len = Length[d]; If[OddQ[len], 2*Sqrt[n], d[[len/2]] + d[[1 + len/2]]], {n, 100}] (* T. D. Noe, Mar 06 2012 *)

CROSSREFS

Sequence in context: A158973 A071323 A071324 * A117248 A079788 A146288

Adjacent sequences:  A063652 A063653 A063654 * A063656 A063657 A063658

KEYWORD

nonn

AUTHOR

Floor van Lamoen (fvlamoen(AT)hotmail.com), Jul 24 2001

EXTENSIONS

Corrected and extended by Larry Reeves (larryr(AT)acm.org) and Dean Hickerson, Jul 26 2001

STATUS

approved

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Last modified November 24 01:09 EST 2014. Contains 249867 sequences.