

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 nonEgyptian numbers.


5



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

1,1


COMMENTS

Graham showed that every number >=78 is strictsense 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

Table of n, a(n) for n=1..13.
R. L. Graham, A theorem on partitions, J. Austral. Math. Soc. 3:4 (1963), pp. 435441. doi:10.1017/S1446788700039045
Eric Weisstein's World of Mathematics, Egyptian Number.
Index entries for sequences related to Egyptian fractions


EXAMPLE

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


MATHEMATICA

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


CROSSREFS

Cf. A051882. Complement gives A125726.
Sequence in context: A006431 A285528 A151894 * A104452 A335073 A344514
Adjacent sequences: A028226 A028227 A028228 * A028230 A028231 A028232


KEYWORD

nonn,fini,full,nice


AUTHOR

N. J. A. Sloane, Jud McCranie


STATUS

approved



