The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A002967 Egyptian fractions: number of solutions of 1 = 1/x_1 + ... + 1/x_n in positive integers.
(Formerly M4745)
8
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). - Max Alekseyev, 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D. Singmaster, "The number of representations of one as a sum of unit fractions," unpublished manuscript, 1972.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Zachary Harris and Joel Louwsma, On Arithmetical Structures on Complete Graphs, arXiv:1909.02022 [math.NT], 2019. See also Involve (2020) Vol. 13, No. 2, 345-355.
Claire Levaillant, On arithmetical structures on K9, arXiv:2311.03668 [math.NT], 2023.
Carlos E. Valencia and R. R. Villagrán, Algorithmic aspects of arithmetical structures, arXiv:2101.05238 [math.NT], 2021.
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. A000058.
Sequence in context: A213788 A278125 A274763 * A243476 A305107 A294850
KEYWORD
nonn,nice,hard,more
AUTHOR
EXTENSIONS
a(7) from Jud McCranie
a(8) from John Dethridge, Jan 11 2004
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 22 06:48 EDT 2024. Contains 372743 sequences. (Running on oeis4.)