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Search: id:A002967
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| A002967 |
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Egyptian fractions: number of solutions of 1 = 1/x_1 + ... 1/x_n, x_i positive integers.
(Formerly M4745)
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+0
5
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| 1, 1, 10, 215, 12231, 2025462, 1351857641, 6255560531733
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Solutions differing only in the order of the x_i are counted as distinct.
All denominators in the expansion 1 = 1/x_1 + ... 1/x_n are bounded by the n-th term of Sylvester's sequence A000058(n) - Max Alekseyev (maxal(AT)cs.ucsd.edu), Dec 30 2003
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, D11.
D. Singmaster, ``The number of representations of one as a sum of unit fractions,'' unpublished manuscript, 1972.
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LINKS
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Index entries for sequences related to Egyptian fractions
58-th Putnam Mathematical Competition, 1997, Problem A-5
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EXAMPLE
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For n=3 the 10 solutions are {2,3,6} (6 ways), {2,4,4} (3 ways), {3,3,3} (1 way).
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CROSSREFS
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Cf. A002966, A006585.
Cf. A000058.
Sequence in context: A076803 A120596 A057408 this_sequence A007698 A007699 A024291
Adjacent sequences: A002964 A002965 A002966 this_sequence A002968 A002969 A002970
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KEYWORD
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nonn,nice,hard
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AUTHOR
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njas
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EXTENSIONS
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a(7) from Jud McCranie (j.mccranie(AT)comcast.net).
a(8) from John Dethridge, Jan 11, 2004
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