A201644 The first of the five known sets of nine distinct odd numbers the sum of whose reciprocals is 1.

3, 5, 7, 9, 11, 15, 35, 45, 231

Offset: 1

Author

N. J. A. Sloane, Dec 03 2011

Keywords

• nonn
• fini
• full

Comments

John Leech showed that nine is the smallest number of odd numbers with this property.

This set was apparently discovered by S. Yamashita in 1976.

Examples

			1/3+1/5+1/7+1/9+1/11+1/15+1/35+1/45+1/231 = 1.
		

References

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

Links

• Nechemia Burshtein, The equation sum(i=1,9,1/xi)=1 in distinct odd integers has only the five known solutions, Journal of Number Theory, Volume 127, Issue 1, November 2007, Pages 136-144.
• The Prime Puzzles and Problems Connection, Problem 35
• Index entries for sequences related to Egyptian fractions

Crossrefs

There are five known sets of nine odd numbers with this property: A201644, A201646, A201647, A201648, A201649.