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A006585 Egyptian fractions: number of solutions to 1 = 1/x_1 + ... + 1/x_n in positive integers x_1 < ... < x_n.
(Formerly M4281)
5
1, 0, 1, 6, 72, 2320, 245765, 151182379 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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). [Max Alekseyev, Oct 11 2012]

If on the other hand, x_k need not be unique, see A002966. - Robert G. Wilson v, Jul 17 2013

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.

Marc LeBrun, personal communication.

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

EXAMPLE

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.

CROSSREFS

Cf. A002966, A002967.

Cf. A000058.

Sequence in context: A009523 A009793 A132878 * A166472 A182917 A203433

Adjacent sequences:  A006582 A006583 A006584 * A006586 A006587 A006588

KEYWORD

nonn,nice,hard,more

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Enumeration confirmed by Jud McCranie

a(8) from John Dethridge (jcd(AT)ms.unimelb.edu.au), Jan 08 2004

STATUS

approved

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Last modified April 19 19:16 EDT 2014. Contains 240777 sequences.