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Search: id:A085705
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| A085705 |
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Integers expressible as (x^3 + y^3 + z^3)/(x*y*z) with nonzero integers x, y, and z. Alternatively, integers expressible as a/b + b/c + c/a with nonzero integers a, b, and c. |
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+0
2
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| 3, 5, 6, 9, 10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 26, 29, 30, 31, 35, 36, 38, 40, 41, 44, 47, 51, 53, 54, 57, 62, 63, 64, 66, 67, 69, 70, 71, 72, 73, 74, 76, 77, 83, 84, 86, 87, 92, 94, 96, 98, 99, 101, 102, 103, 105, 106, 107, 108, 109, 110, 112, 113, 116, 117, 119, 120, 122, 123, 124, 126, 127, 128, 129, 130, 132, 133, 136, 142, 143, 145, 147, 148, 149, 151, 154, 155, 156, 158, 159, 160, 161, 162, 164, 166, 167, 172, 174, 175, 177, 178, 181, 185, 186, 187, 189, 190, 191, 192, 195, 196, 197
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A representation n=(x^3+y^3+z^3)/(x*y*z) is equivalent to 2 representations n=a/b+b/c+c/a, given by a=y^2*z,b=z^2*x,c=x^2*y and a=y*z^2,b=x*y^2,c=z*x^2. Dean Hickerson (dean(AT)math.ucdavis.edu), Jul 14 2003. For each a(n)>5 there are infinitely many representations. Dave Rusin (rusin(AT)math.niu.edu), Jul 15 2003.
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LINKS
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Dave Rusin, For which values of n is a/b + b/c + c/a = n solvable?
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EXAMPLE
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15 is in the sequence because 15=(7^3-3^3-1^3)/(7*3*1)=(343-27-1)/21=15. This is equivalent to 15=-9/7-7/147+147/9 or 15=-3/63-63/49+49/3.
16=(70^3-31^3-9^3)/(70*31*9)=(343000-29791-729)/19530=16.
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CROSSREFS
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Cf. A072716 (representation by positive x, y, z).
Sequence in context: A018900 A126590 A140584 this_sequence A072716 A112649 A050083
Adjacent sequences: A085702 A085703 A085704 this_sequence A085706 A085707 A085708
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KEYWORD
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nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Jul 18 2003
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EXTENSIONS
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More terms from Dave Rusin, Jul 26, 2003
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