login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 21 02:30 EST 2014. Contains 249767 sequences.