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A102096 Second greatest (or second least) edge length of a cuboid having integer edge lengths, volume n and minimal surface area under those restrictions. 3
1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 3, 1, 2, 3, 2, 1, 3, 5, 2, 3, 2, 1, 3, 1, 4, 3, 2, 5, 3, 1, 2, 3, 4, 1, 3, 1, 2, 3, 2, 1, 4, 7, 5, 3, 2, 1, 3, 5, 4, 3, 2, 1, 4, 1, 2, 3, 4, 5, 3, 1, 2, 3, 5, 1, 4, 1, 2, 5, 2, 7, 3, 1, 4, 3, 2, 1, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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 (a(1)=1). a(n) <= n^(1/2) for all n.

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(10) = 2 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][[2]], {k, 1, 84}]

CROSSREFS

Cf. A102095, A102097.

Sequence in context: A082061 A107286 A087039 * A137866 A266161 A072203

Adjacent sequences:  A102093 A102094 A102095 * A102097 A102098 A102099

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified October 23 17:20 EDT 2018. Contains 316529 sequences. (Running on oeis4.)