A102095 - OEIS

A102095

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

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OFFSET

1,2

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

LINKS

Table of n, a(n) for n=1..84.

Eric Weisstein's World of Mathematics, Cuboid

Eric Weisstein's World of Mathematics, Sample Variance

Wikipedia, Nonlinear Programming

EXAMPLE

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}

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[]];