This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A102095 Greatest edge length of a cuboid having integer edge lengths, volume n and minimal surface area under those restrictions. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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 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[]]; 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}] CROSSREFS Cf. A102096, A102097. Sequence in context: A162325 A197862 A006530 * A109395 A145254 A163457 Adjacent sequences:  A102092 A102093 A102094 * A102096 A102097 A102098 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 19 06:03 EST 2018. Contains 318245 sequences. (Running on oeis4.)