The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A102889 Square of the minimal space diagonal of an integral cuboid having volume n. 1
 3, 6, 11, 9, 27, 14, 51, 12, 19, 30, 123, 17, 171, 54, 35, 24, 291, 22, 363, 33, 59, 126, 531, 29, 51, 174, 27, 57, 843, 38, 963, 36, 131, 294, 75, 34, 1371, 366, 179, 45, 1683, 62, 1851, 129, 43, 534, 2211, 41, 99, 54, 299, 177, 2811, 54, 147, 69, 371, 846, 3483 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) = A102095(n)^2 + A102096(n)^2 + A102097(n)^2. Ceiling(3*n^(2/3)) <= a(n) <= 2 + n^2 a(n) = 3*n^(2/3) iff n is a cube. a(n) = 2 + n^2 iff n is prime. LINKS Eric Weisstein's World of Mathematics, "Cuboid." EXAMPLE a(4)=9 because the minimal-space-diagonal integral cuboid of volume 4 has dimensions 2 by 2 by 1 and 2^2 + 2^2 + 1^2 = 9. MATHEMATICA Clear[surfarea, sumprint, temp, 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]][][]; bi = bool[[i]][][]; ci = bool[[i]][][]; Sow[{ai + bi + ci, {ai, bi, ci}}]]][][]) fac[n_] := ( If[PrimeQ[n] || n == 1, Return[{n, 1, 1}]; Abort[]]; faclist[n][][]) surfarea[n_] := (Clear[temp]; temp = fac[n]; 2*temp[]^2 + 2*temp[]^2 + 2*temp[]^2) Table[surfarea[n]/2, {n, 1, 85}] CROSSREFS Cf. A102890. Sequence in context: A325551 A258928 A144562 * A183543 A256108 A028744 Adjacent sequences:  A102886 A102887 A102888 * A102890 A102891 A102892 KEYWORD nonn AUTHOR Joseph Biberstine (jrbibers(AT)indiana.edu), Jan 16 2005 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 July 11 23:53 EDT 2020. Contains 335654 sequences. (Running on oeis4.)