|
| |
|
|
A002967
|
|
Egyptian fractions: number of solutions of 1 = 1/x_1 + ... 1/x_n, x_i positive integers.
(Formerly M4745)
|
|
4
| | |
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| 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 (maxale(AT)gmail.com), Dec 30 2003
|
|
|
REFERENCES
| 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D. Singmaster, ``The number of representations of one as a sum of unit fractions,'' unpublished manuscript, 1972.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| Index entries for sequences related to Egyptian fractions
58-th Putnam Mathematical Competition, 1997, Problem A-5
|
|
|
EXAMPLE
| For n=3 the 10 solutions are {2,3,6} (6 ways), {2,4,4} (3 ways), {3,3,3} (1 way).
|
|
|
CROSSREFS
| Cf. A002966, A006585.
Cf. A000058.
Sequence in context: A112364 A201621 A057408 * A007698 A007699 A024291
Adjacent sequences: A002964 A002965 A002966 * A002968 A002969 A002970
|
|
|
KEYWORD
| nonn,nice,hard
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| a(7) from Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu).
a(8) from John Dethridge, Jan 11, 2004
|
| |
|
|
