A227215 Smallest sum of the three perpendicular integer sides of a rectangular parallelepiped of volume n.

3, 4, 5, 5, 7, 6, 9, 6, 7, 8, 13, 7, 15, 10, 9, 8, 19, 8, 21, 9, 11, 14, 25, 9, 11, 16, 9, 11, 31, 10, 33, 10, 15, 20, 13, 10, 39, 22, 17, 11, 43, 12, 45, 15, 11, 26, 49, 11, 15, 12, 21, 17, 55, 12, 17, 13, 23, 32, 61, 12, 63, 34, 13, 12, 19, 16, 69, 21, 27, 14, 73, 13, 75, 40, 13

Offset: 1

Author

Carmine Suriano, Sep 19 2013

Keywords

• nonn

Examples

			a(24)=9 since 9=2+3+4 is the smallest sum of all possible parallelepipeds having 24=2*3*4 as volume.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Wikipedia, Parallelepiped

Crossrefs

Cf. A063655, A033676.

Programs

Mathematica

a[n_] := Block[{x,y,z}, Min[Total /@ ({x, y, z} /. List@ ToRules@ Reduce[ x*y*z == n && x >= y >= z > 0, {x, y, z}, Integers])]]; Array[a, 75] (* Giovanni Resta, Sep 19 2013 *)

PARI

a(n) = {smin = 3*n; for (i = 1, n, for (j = 1, i, for (k = 1, j, if (i*j*k == n, smin = min (smin, i+j+k));););); return (smin);} \\ Michel Marcus, Sep 23 2013

PARI

a(n)=my(m=n+2,d); fordiv(n,x,d=divisors(n/x); m=min(m, d[(#d+1)\2]+d[#d\2+1]+x)); m \\ Charles R Greathouse IV, Sep 23 2013