A201643 - OEIS

%I #21 May 30 2026 16:40:35

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

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

%C There are smaller sets - see for example A201644.

%C 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

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

%H Burshtein, Nechemia. <a href="https://doi.org/10.1016/0012-365X(73)90136-2">On distinct unit fractions whose sum equals 1</a>. Discrete Math. 5 (1973), 201--206. MR0314738 (47 #3290)

%H Burshtein, Nechemia. <a href="https://doi.org/10.1016/j.disc.2007.08.049">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</a>. Discrete Math. 308 (2008), no. 18, 4286--4292. MR2427761 (2009e:11061)

%H The Prime Puzzles and Problems Connection, <a href="http://www.primepuzzles.net/problems/prob_035.htm">Problem 35</a>.

%H <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>

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

%K nonn,fini,full,changed

%O 1,1

%A _N. J. A. Sloane_, Dec 03 2011