OFFSET
1,1
COMMENTS
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]][[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]]) surfarea[n_] := (Clear[temp]; temp = fac[n]; 2*temp[[1]]^2 + 2*temp[[2]]^2 + 2*temp[[3]]^2) Table[surfarea[n]/2, {n, 1, 85}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Joseph Biberstine (jrbibers(AT)indiana.edu), Jan 16 2005
STATUS
approved