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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D. H. Lehmer, unpublished work, cited in Graham 1963.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 A059543 A160542
KEYWORD
nonn,fini,full,nice
AUTHOR
Jud McCranie, Dec 15 1999
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)