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A085514
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Integers n representable as the product of the sum of three nonzero integers with the sum of their reciprocals: n=(x+y+z)*(1/x+1/y+1/z).
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5
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1, 9, 10, 11, 14, 15, 18, 26, 29, 30, 31, 34, 35, 37, 38, 42, 43, 44, 48, 52, 53, 54, 55, 57, 59, 62, 63, 64, 67, 69, 70, 71, 73, 74, 75, 76, 82, 84, 85, 86, 90, 92, 93, 94, 95, 96, 98, 100, 101, 102, 103, 105, 106, 108, 111, 112, 116, 117, 122, 125, 126, 127, 128
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| See under A086446 for comments and references.
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REFERENCES
| A. Bremner, R. K. Guy and R. Nowakowski, Which integers are representable as the product of the sum of three integers with the sum of their reciprocals?, Math. Comp. 61 (1993) 117-130.
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LINKS
| Allan J. MacLeod, Knight's Problem
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EXAMPLE
| a(1)=1 because (1+1-1)*(1/1+1/1-1/1)=1.
a(2)=(1+1+1)*(1/1+1/1+1/1)=9.
a(9)=(2-15+78)*(1/2-1/15+1/78)=29.
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CROSSREFS
| Cf. A086446 (representation by positive x, y, z).
See A102774, A102775, A102777 for values of x, y, z corresponding to values of n >= 11.
See also A102535.
Sequence in context: A120193 A134534 A125004 * A086446 A168042 A045522
Adjacent sequences: A085511 A085512 A085513 * A085515 A085516 A085517
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KEYWORD
| nonn
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AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Jul 19 2003
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EXTENSIONS
| Corrected and extended by Dave Rusin (rusin(at)math.niu.edu), Jul 30 2003
More terms from the MacLeod web site, Mar 17 2005
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