A028229 Call m Egyptian if we can partition m = x_1+x_2+...+x_k into positive integers x_i such that Sum_{i=1..k} 1/x_i = 1; sequence gives all non-Egyptian numbers.

2, 3, 5, 6, 7, 8, 12, 13, 14, 15, 19, 21, 23

Offset: 1

Author

N. J. A. Sloane, Jud McCranie

Keywords

• nonn
• fini
• full
• nice

Comments

Graham showed that every number >=78 is strict-sense Egyptian.

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. 3:4 (1963), pp. 435-441. doi:10.1017/S1446788700039045
• Eric Weisstein's World of Mathematics, Egyptian Number.
• Index entries for sequences related to Egyptian fractions

Crossrefs

Cf. A051882. Complement gives A125726.

Programs

Mathematica

egyptianQ[n_] := Select[ IntegerPartitions[n], Total[1/#] == 1 &, 1] =!= {}; A028229 = Reap[ Do[ If[ !egyptianQ[n], Sow[n]], {n, 1, 40}]][[2, 1]] (* Jean-François Alcover, Feb 23 2012 *)