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 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

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