

A051882


Call m strictsense 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 strictsense 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
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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D. H. Lehmer, unpublished work, cited in Graham 1963.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

Table of n, a(n) for n=1..47.
R. L. Graham, A theorem on partitions, J. Austral. Math. Soc. 3:4 (1963), pp. 435441. [Alternate link]
Eric Weisstein's World of Mathematics, Egyptian Number
Index entries for sequences related to Egyptian fractions


EXAMPLE

1=1/2+1/3+1/6, so 2+3+6=11 is strictsense 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]] (* JeanFrançois 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



