The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.



Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A201643 John Leech's example of a set of eleven distinct odd numbers the sum of whose reciprocals is 1. 22
3, 5, 7, 9, 15, 21, 27, 35, 63, 105, 135 (list; graph; refs; listen; history; text; internal format)



There are smaller sets - see for example A201644.

One of 17 possible sets of eleven numbers of the form 3^alpha 5^beta 7^gamma whose sum of reciprocals is 1. The 17 solutions are given in A211118 - A211134. N. J. A. Sloane, Apr 02 2012


R. K. Guy, Unsolved Problems in Number Theory (UPINT), Section D11.


Table of n, a(n) for n=1..11.

Burshtein, Nechemia. On distinct unit fractions whose sum equals 1. Discrete Math. 5 (1973), 201--206. MR0314738 (47 #3290)

Burshtein, Nechemia. All the solutions of the equation Sum_{i=1..11}} 1/x_i = 1 in distinct integers of the form x_i = 3^alpha 5^beta 7^gamma. Discrete Math. 308 (2008), no. 18, 4286--4292. MR2427761 (2009e:11061)

The Prime Puzzles and Problems Connection, Problem 35

Index entries for sequences related to Egyptian fractions


Cf. A201643, A201644, A201646, A201647, A201648, A201649.

Sequence in context: A211134 A211132 A211131 * A018388 A100866 A327823

Adjacent sequences:  A201640 A201641 A201642 * A201644 A201645 A201646




N. J. A. Sloane, Dec 03 2011



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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 2 08:19 EST 2021. Contains 349437 sequences. (Running on oeis4.)