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

1,1

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

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

Crossrefs

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

Sequence in context: A211134 A211132 A211131 * A018388 A100866 A327823

Adjacent sequences: A201640 A201641 A201642 * A201644 A201645 A201646

Keyword

nonn,fini,full

Author

N. J. A. Sloane, Dec 03 2011

Status

approved