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A051882
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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.
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6
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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
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OFFSET
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1,1
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COMMENTS
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Lehmer shows that 77 is in this sequence. Graham shows that it is the last member of the sequence.
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REFERENCES
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D. H. Lehmer, unpublished work, cited in Graham 1963.
See also R. K. Guy, Unsolved Problems Number Theory, Sect. D11.
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LINKS
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EXAMPLE
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1=1/2+1/3+1/6, so 2+3+6=11 is strict-sense Egyptian.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,fini,full,nice
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AUTHOR
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STATUS
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approved
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