A075251 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.

6, 20, 6, 12, 70, 72, 342, 42, 99, 156, 780, 1806, 156, 272, 1564, 1332, 5852, 420, 945, 4070, 6670, 14520, 930, 1560, 2970, 7140, 30450, 1806, 1736, 16800, 26796, 56882, 3192, 5256, 29304, 23256, 97656, 5256, 11439, 16002, 75078, 157212, 8190, 13340

Offset: 3

Author

T. D. Noe, Sep 10 2002

Keywords

• hard
• nice
• nonn

Comments

See A075248 for more details.

Crossrefs

Cf. A075248, A075249, A075250.

Programs

Mathematica

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