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%I #33 Dec 01 2019 17:09:49
%S 2,3,5,6,7,8,12,13,14,15,19,21,23
%N 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.
%C Graham showed that every number >=78 is strict-sense Egyptian.
%D J. D. E. Konhauser et al., Which Way Did the Bicycle Go?, MAA 1996, p. 147.
%D See also R. K. Guy, Unsolved Problems Number Theory, Sect. D11.
%H R. L. Graham, <a href="https://www.math.ucsd.edu/~ronspubs/63_02_partitions.pdf">A theorem on partitions</a>, J. Austral. Math. Soc. 3:4 (1963), pp. 435-441. <a href="https://doi.org/10.1017/S1446788700039045">doi:10.1017/S1446788700039045</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EgyptianNumber.html">Egyptian Number.</a>
%H <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>
%e 1=1/3+1/3+1/3, so 3+3+3=9 is Egyptian.
%t 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 *)
%Y Cf. A051882. Complement gives A125726.
%K nonn,fini,full,nice
%O 1,1
%A _N. J. A. Sloane_, _Jud McCranie_
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