A067753 Number of primitive solutions in nonnegative integers of x*y+x*z+y*z = n.
3, 6, 7, 6, 9, 12, 9, 9, 9, 12, 15, 12, 9, 18, 18, 9, 15, 12, 15, 18, 18, 12, 21, 18, 9, 24, 15, 12, 21, 24, 21, 15, 18, 18, 30, 18, 9, 24, 30, 18, 27, 24, 15, 24, 18, 18, 33, 18, 15, 24, 30, 18, 21, 24, 30, 30, 18, 12, 39, 24, 21, 30, 30, 15, 30, 36, 15, 30, 30, 24, 45, 18, 15, 36
Offset: 1
Examples
a(9)=9 because of permutations of (0,1,9) and (1,1,4) (but not (0,3,3)).
Links
- T. D. Noe, Table of n, a(n) for n = 1..10000
Programs
-
Mathematica
CntFunc[s_List] := Module[{len=Length[Union[s]]}, If[len==3,6,If[len==2,3,1]]]; Table[cnt=0; Do[z=(n-x*y)/(x+y); If[IntegerQ[z] && GCD[x,y,z]==1, cnt=cnt+CntFunc[{x,y,z}]], {x,0,Sqrt[n/3]}, {y, Max[1,x],Sqrt[x^2+n]-x}]; cnt, {n,100}] (* T. D. Noe, Jun 14 2006 *)
Extensions
Corrected and extended by T. D. Noe, Jun 14 2006
Comments