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Search: id:A067753
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| A067753 |
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Number of primitive solutions in nonnegative integers of xy+xz+yz=n. |
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+0
4
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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An upper bound on the number of solutions appears to be 9*sqrt(n). - T. D. Noe (noe(AT)sspectra.com), Jun 14 2006
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
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EXAMPLE
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a(9)=9 because of permutations of (0,1,9) and (1,1,4) (but not (0,3,3)).
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MATHEMATICA
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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 (noe(AT)sspectra.com), Jun 14 2006
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CROSSREFS
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Cf. A066751, A067752, A067754.
Sequence in context: A156648 A016616 A021276 this_sequence A129023 A152083 A003458
Adjacent sequences: A067750 A067751 A067752 this_sequence A067754 A067755 A067756
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KEYWORD
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easy,nonn
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AUTHOR
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Colin L. Mallows (colinm(AT)avaya.com), Jan 31 2002
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EXTENSIONS
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Corrected and extended by T. D. Noe (noe(AT)sspectra.com), Jun 14 2006
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