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A002967 Egyptian fractions: number of solutions of 1 = 1/x_1 + ... 1/x_n, x_i positive integers.
(Formerly M4745)
+0
5
1, 1, 10, 215, 12231, 2025462, 1351857641, 6255560531733 (list; graph; listen)
OFFSET

1,3

COMMENT

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

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D. Singmaster, ``The number of representations of one as a sum of unit fractions,'' unpublished manuscript, 1972.

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: A076803 A120596 A057408 this_sequence A007698 A007699 A024291

Adjacent sequences: A002964 A002965 A002966 this_sequence A002968 A002969 A002970

KEYWORD

nonn,nice,hard

AUTHOR

njas

EXTENSIONS

a(7) from Jud McCranie (j.mccranie(AT)comcast.net).

a(8) from John Dethridge, Jan 11, 2004

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.


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