

A006585


Egyptian fractions: number of solutions to 1 = 1/x_1 + ... + 1/x_n in positive integers x_1 < ... < x_n.
(Formerly M4281)


5




OFFSET

1,4


COMMENTS

All denominators in the expansion 1 = 1/x_1 + ... + 1/x_n are bounded by A000058(n1), i.e., 0 < x_1 < ... < x_n < A000058(n1). Furthermore, for a fixed n, x_i <= (n+1i)*(A000058(i1)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 B881, Fibonacci Quarterly, Vol. 37, No. 3, August 1999, pp. 277278. Solution published in Vol. 38, No. 2, May 2000, pp. 183184.
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: A009793 A259212 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



