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z-value of the solution (x,y,z) to 5/n = 1/x + 1/y + 1/z satisfying 0 < x < y < z and having the largest z-value. The x and y components are in A075249 and A075250.
3

%I #4 Mar 30 2012 17:22:26

%S 6,20,6,12,70,72,342,42,99,156,780,1806,156,272,1564,1332,5852,420,

%T 945,4070,6670,14520,930,1560,2970,7140,30450,1806,1736,16800,26796,

%U 56882,3192,5256,29304,23256,97656,5256,11439,16002,75078,157212,8190,13340

%N z-value of the solution (x,y,z) to 5/n = 1/x + 1/y + 1/z satisfying 0 < x < y < z and having the largest z-value. The x and y components are in A075249 and A075250.

%C See A075248 for more details.

%t For[xLst={}; yLst={}; zLst={}; n=3, n<=100, n++, cnt=0; xr=n/5; If[IntegerQ[xr], x=xr+1, x=Ceiling[xr]]; While[yr=1/(5/n-1/x); If[IntegerQ[yr], y=yr+1, y=Ceiling[yr]]; cnt==0&&y>x, While[zr=1/(5/n-1/x-1/y); cnt==0&&zr>y, If[IntegerQ[zr], z=zr; cnt++; AppendTo[xLst, x]; AppendTo[yLst, y]; AppendTo[zLst, z]]; y++ ]; x++ ]]; zLst

%Y Cf. A075248, A075249, A075250.

%K hard,nice,nonn

%O 3,1

%A _T. D. Noe_, Sep 10 2002