proposed

approved

editing

proposed

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Cuboid.html">"Cuboid."</a>

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SampleVariance.html">"Sample Variance."</a>

Wikipedia, <a href="http://en.wikipedia.org/wiki/Nonlinear_programming">"Nonlinear Programming."</a>

approved

editing

Greatest edge length of a cuboid having integer edge lengths, volume n, and minimal surface area under those restrictions.

a(16) = 4 because the cuboid of integer edge lengths, volume = 16, and minimal possible surface area under those restrictions has edge lengths {4,2,2}

nonn,new

nonn

Eric W. Weisstein, 's World of Mathematics, <a href="http://mathworld.wolfram.com/Cuboid.html">"Cuboid."</a>

Eric W. Weisstein, 's World of Mathematics, <a href="http://mathworld.wolfram.com/SampleVariance.html">"Sample Variance."</a>

nonn,new

nonn

Greatest edge length of a cuboid having integer edge lengths, volume n, and minimal surface area under those restrictions.

1, 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 3, 13, 7, 5, 4, 17, 3, 19, 5, 7, 11, 23, 4, 5, 13, 3, 7, 29, 5, 31, 4, 11, 17, 7, 4, 37, 19, 13, 5, 41, 7, 43, 11, 5, 23, 47, 4, 7, 5, 17, 13, 53, 6, 11, 7, 19, 29, 59, 5, 61, 31, 7, 4, 13, 11, 67, 17, 23, 7, 71, 6, 73, 37, 5, 19, 11, 13, 79, 5, 9, 41, 83, 7

1,2

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 for all n>1 a(n) <= n for all n. a(n) = n iff n is prime (a(1)=1).

Eric W. Weisstein, <a href="http://mathworld.wolfram.com/Cuboid.html">"Cuboid."</a>

Eric W. Weisstein, <a href="http://mathworld.wolfram.com/SampleVariance.html">"Sample Variance."</a>

Wikipedia, <a href="http://en.wikipedia.org/wiki/Nonlinear_programming">"Nonlinear Programming."</a>

a(16) = 4 because the cuboid of integer edge lengths, volume = 16, and minimal possible surface area under those restrictions has edge lengths {4,2,2}

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][[1]], {k, 1, 84}]

Cf. A102096, A102097.

nonn

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

approved