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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. 5
2, 3, 5, 6, 7, 8, 12, 13, 14, 15, 19, 21, 23 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Graham showed that every number >=78 is strict-sense 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. 435-441.

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]] (* Jean-Fran├žois Alcover, Feb 23 2012 *)

CROSSREFS

Cf. A051882. Complement gives A125726.

Sequence in context: A006431 A285528 A151894 * A104452 A062877 A068526

Adjacent sequences:  A028226 A028227 A028228 * A028230 A028231 A028232

KEYWORD

nonn,fini,full,nice

AUTHOR

N. J. A. Sloane, Jud McCranie

STATUS

approved

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Last modified November 16 17:04 EST 2019. Contains 329201 sequences. (Running on oeis4.)