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

1,1

Comments

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

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Example

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

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

Crossrefs

Cf. A066751, A067752, A067754.

Sequence in context: A021276 A329516 A290943 * A129023 A188883 A336086

Adjacent sequences: A067750 A067751 A067752 * A067754 A067755 A067756

Keyword

easy,nonn

Author

Colin Mallows, Jan 31 2002

Extensions

Corrected and extended by T. D. Noe, Jun 14 2006

Status

approved