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A067753 Number of primitive solutions in nonnegative integers of xy+xz+yz=n. 4

%I #8 Sep 21 2013 13:11:28

%S 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,

%T 15,12,21,24,21,15,18,18,30,18,9,24,30,18,27,24,15,24,18,18,33,18,15,

%U 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

%N Number of primitive solutions in nonnegative integers of xy+xz+yz=n.

%C An upper bound on the number of solutions appears to be 9*sqrt(n). - _T. D. Noe_, Jun 14 2006

%H T. D. Noe, <a href="/A067753/b067753.txt">Table of n, a(n) for n = 1..10000</a>

%e a(9)=9 because of permutations of (0,1,9) and (1,1,4) (but not (0,3,3)).

%t 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

%Y Cf. A066751, A067752, A067754.

%K easy,nonn

%O 1,1

%A _Colin Mallows_, Jan 31 2002

%E Corrected and extended by _T. D. Noe_, Jun 14 2006

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Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)