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

1,1

Links

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

Wikipedia, Parallelepiped

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A063655, A033676.

Sequence in context: A061146 A332065 A082514 * A229445 A323743 A261017

Adjacent sequences: A227212 A227213 A227214 * A227216 A227217 A227218

Keyword

nonn

Author

Carmine Suriano, Sep 19 2013

Status

approved