A201643 John Leech's example of a set of eleven distinct odd numbers the sum of whose reciprocals is 1.

3, 5, 7, 9, 15, 21, 27, 35, 63, 105, 135

Offset: 1

Author

N. J. A. Sloane, Dec 03 2011

Keywords

• nonn
• fini
• full

Comments

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

References

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

Links

• 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

Crossrefs

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