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A063520
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Sum divides product: number of solutions (r,s,t), r>=s>=t>0, to the equation rst = n(r+s+t).
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6
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1, 3, 6, 5, 8, 8, 8, 14, 13, 9, 14, 17, 8, 18, 23, 18, 14, 17, 13, 33, 23, 10, 19, 36, 15, 22, 32, 22, 19, 26, 17, 39, 24, 18, 50, 45, 8, 22, 39, 38, 22, 27, 13, 50, 45, 16, 27, 52, 24, 39, 38, 27, 20, 50, 45, 72, 24, 12, 31, 58, 15, 28, 69, 45, 49, 39, 12, 52, 40, 33, 33, 66, 12, 33, 64
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Number of solutions (r,s) in positive integers to the equation rs = n(r+s) is tau(n^2), cf. A048691. Number of solutions (r,s), r>=s>0, to the equation rs = n(r+s) is (tau(n^2)+1)/2, cf. A018892.
Conjecturally, includes all positive integers except 2, 4, 7 and 11 - David W. Wilson (davidwwilson(AT)comcast.net)
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REFERENCES
| M. J. Pelling, "The Sum Divides the Product", Problem 10745, Amer. Math. Monthly, vol. 106 (1999), p. 587; vol. 108, (no. 7, Aug. 2001), pp. 668-669. [Gives upper bound]
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EXAMPLE
| There are 8 such solutions to rst = 5(r+s+t): (5, 4, 3), (7, 5, 2), (10, 4, 2), (11, 10, 1), (15, 8, 1), (20, 7, 1), (25, 3, 2), (35, 6, 1).
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CROSSREFS
| Cf. A018892, A004194, A063525.
More terms from David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001
Sequence in context: A201418 A123688 A082284 * A078677 A059770 A019690
Adjacent sequences: A063517 A063518 A063519 * A063521 A063522 A063523
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KEYWORD
| nonn
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AUTHOR
| Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu) and Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 01 2001
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