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 A051882 Call m strict-sense Egyptian if we can partition m = x_1+x_2+...+x_k into distinct positive integers x_i such that Sum_{i=1..k} 1/x_i = 1; sequence gives all numbers that are not strict-sense Egyptian. 6
 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 33, 34, 35, 36, 39, 40, 41, 42, 44, 46, 47, 48, 49, 51, 56, 58, 63, 68, 70, 72, 77 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Lehmer shows that 77 is in this sequence. Graham shows that it is the last member of the sequence. REFERENCES D. H. Lehmer, unpublished work, cited in Graham 1963. 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. [Alternate link] Eric Weisstein's World of Mathematics, Egyptian Number EXAMPLE 1=1/2+1/3+1/6, so 2+3+6=11 is strict-sense Egyptian. MATHEMATICA strictEgyptianQ[m_] := Length[ Select[ IntegerPartitions[m, Ceiling[(Sqrt[8*m + 1] - 1)/2]], Length[#] == Length[ Union[#]] && 1 == Plus @@ (1/#) & , 1]] > 0; Reap[ Do[ If[ !strictEgyptianQ[m], Print[m]; Sow[m]], {m, 1, 77}]][[2, 1]] (* Jean-François Alcover, Jul 30 2012 *) CROSSREFS Cf. A028229. Sequence in context: A101947 A183223 A167520 * A136002 A043096 A160542 Adjacent sequences:  A051879 A051880 A051881 * A051883 A051884 A051885 KEYWORD nonn,fini,full,nice AUTHOR Jud McCranie, Dec 15 1999 STATUS approved

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Last modified September 19 18:38 EDT 2018. Contains 315210 sequences. (Running on oeis4.)