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%I #24 Sep 24 2013 12:19:37
%S 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,
%T 31,10,33,10,15,20,13,10,39,22,17,11,43,12,45,15,11,26,49,11,15,12,21,
%U 17,55,12,17,13,23,32,61,12,63,34,13,12,19,16,69,21,27,14,73,13,75,40,13
%N Smallest sum of the three perpendicular integer sides of a rectangular parallelepiped of volume n.
%H Charles R Greathouse IV, <a href="/A227215/b227215.txt">Table of n, a(n) for n = 1..10000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Parallelepiped">Parallelepiped</a>
%e a(24)=9 since 9=2+3+4 is the smallest sum of all possible parallelepipeds having 24=2*3*4 as volume.
%t 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 *)
%o (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
%o (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
%Y Cf. A063655, A033676.
%K nonn
%O 1,1
%A _Carmine Suriano_, Sep 19 2013
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