login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A102097 Least edge length of a cuboid having integer edge lengths, volume n and minimal surface area under those restrictions. 4
1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 3, 2, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 1, 3, 1, 1, 3, 4, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 3, 2, 1, 2, 1, 4, 3, 1, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

Finding a(n) given n is a fundamental problem from integer nonlinear programming, equivalent to minimizing the sum a+b+c when a*b*c=n and a,b,c are integers. a(n) is not strictly prime. a(n) = 1 iff n is prime or n is semiprime (a(1)=1). a(n) <= n^(1/3) for all n.

LINKS

Hans Havermann, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Cuboid

Eric Weisstein's World of Mathematics, Sample Variance

Wikipedia, Nonlinear programming

EXAMPLE

a(10) = 1 because the cuboid of integer edge lengths, volume = 10 and minimal possible surface area under those restrictions has edge lengths {5,2,1}

MATHEMATICA

Clear[fac, faclist, red, bool, n, a, b, c, i, ai, bi, ci]

red[n_] := Reduce[{a*b*c == n, a >= b >= c > 0}, {a, b, c}, Integers];

faclist[n_] := (

If[PrimeQ[n] || n == 1, Return[{n + 1 + 1, {n, 1, 1}}]; Abort[]];

bool = red[n];

Reap[For[i = 1, i <= Length[bool], i++,

ai = bool[[i]][[1]][[2]];

bi = bool[[i]][[2]][[2]];

ci = bool[[i]][[3]][[2]];

Sow[{ai + bi + ci, {ai, bi, ci}}]]][[2]][[1]])

fac[n_] := (

If[PrimeQ[n] || n == 1, Return[{n, 1, 1}]; Abort[]];

faclist[n][[1]][[2]])

Table[fac[k][[3]], {k, 1, 84}]

CROSSREFS

Cf. A102095, A102096.

Sequence in context: A118663 A205119 A293234 * A318749 A050330 A205788

Adjacent sequences:  A102094 A102095 A102096 * A102098 A102099 A102100

KEYWORD

nonn

AUTHOR

Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 29 2004

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 22 21:05 EDT 2018. Contains 316502 sequences. (Running on oeis4.)