This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A028229 #34 Feb 16 2025 08:32:35
%S A028229 2,3,5,6,7,8,12,13,14,15,19,21,23
%N 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.
%C A028229 Graham showed that every number >=78 is strict-sense Egyptian.
%D A028229 J. D. E. Konhauser et al., Which Way Did the Bicycle Go?, MAA 1996, p. 147.
%D A028229 See also R. K. Guy, Unsolved Problems Number Theory, Sect. D11.
%H A028229 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 A028229 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EgyptianNumber.html">Egyptian Number.</a>
%H A028229 <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>
%e A028229 1=1/3+1/3+1/3, so 3+3+3=9 is Egyptian.
%t A028229 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 A028229 Cf. A051882. Complement gives A125726.
%K A028229 nonn,fini,full,nice
%O A028229 1,1
%A A028229 _N. J. A. Sloane_, _Jud McCranie_