A125726 Call n Egyptian if we can partition n = x_1+x_2+...+x_k into positive integers x_i such that Sum_{i=1..k} 1/x_i = 1; sequence gives Egyptian numbers.

1, 4, 9, 10, 11, 16, 17, 18, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86

Offset: 1

Author

Jan RUCKA (jan_rucka(AT)hotmail.com), Feb 06 2007

Keywords

• nonn

Examples

			1=1/3+1/3+1/3, so 3+3+3=9 is Egyptian.
		

References

• J. D. E. Konhauser et al., Which Way Did the Bicycle Go?, MAA 1996, p. 147.
• See also R. K. Guy, Unsolved Problems Number Theory, Sect. D11.

Links

• R. L. Graham, A theorem on partitions, J. Austral. Math. Soc., 4 (1963), 435-441.
• Les Mathematiques.net, Nombres remarquables (French blog).
• Eric Weisstein's World of Mathematics, Egyptian Number.
• Index entries for sequences related to Egyptian fractions

Crossrefs

Complement of A028229.