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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 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. 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-François 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 STATUS approved

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