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A002967 Egyptian fractions: number of solutions of 1 = 1/x_1 + ... + 1/x_n in positive integers.
(Formerly M4745)
4
1, 1, 10, 215, 12231, 2025462, 1351857641, 6255560531733 (list; graph; refs; listen; history; text; internal format)
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 A000058(n-1)=A129871(n). [From Max Alekseyev, Dec 30 2003]

REFERENCES

Mohammad K. Azarian, Diophantine Pair, Problem B-881, Fibonacci Quarterly, Vol. 37, No. 3, August 1999, pp. 277-278.  Solution published in Vol. 38, No. 2, May 2000, pp. 183-184.

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D. Singmaster, ``The number of representations of one as a sum of unit fractions,'' unpublished manuscript, 1972.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

Table of n, a(n) for n=1..8.

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: A245985 A211912 A213788 * A243476 A007698 A007699

Adjacent sequences:  A002964 A002965 A002966 * A002968 A002969 A002970

KEYWORD

nonn,nice,hard

AUTHOR

N. J. A. Sloane.

EXTENSIONS

a(7) from Jud McCranie.

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

STATUS

approved

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Last modified October 31 14:42 EDT 2014. Contains 248868 sequences.