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A006585
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Egyptian fractions: number of solutions to 1 = 1/x_1 + ... + 1/x_n in positive integers x_1 < ... < x_n.
(Formerly M4281)
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5
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OFFSET
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1,4
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COMMENTS
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All denominators in the expansion 1 = 1/x_1 + ... + 1/x_n are bounded by A000058(n-1), i.e., 0 < x_1 < ... < x_n < A000058(n-1). Furthermore, for a fixed n, x_i <= (n+1-i)*(A000058(i-1)-1). [From Max Alekseyev, Oct 11 2012]
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REFERENCES
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Marc LeBrun, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=1..8.
Index entries for sequences related to Egyptian fractions
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EXAMPLE
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The 6 solutions for n=4 are 2,3,7,42; 2,3,8,24; 2,3,9,18; 2,3,10,15; 2,4,5,20; 2,4,6,12.
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CROSSREFS
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Cf. A002966, A002967.
Cf. A000058.
Sequence in context: A009523 A009793 A132878 * A166472 A182917 A203433
Adjacent sequences: A006582 A006583 A006584 * A006586 A006587 A006588
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KEYWORD
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nonn,nice,hard,more
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Enumeration confirmed by Jud McCranie
a(8) from John Dethridge (jcd(AT)ms.unimelb.edu.au), Jan 08 2004
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STATUS
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approved
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