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.

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

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D. H. Lehmer, unpublished work, cited in Graham 1963.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. 435-441. [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 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

Adjacent sequences: A051879 A051880 A051881 * A051883 A051884 A051885

Keyword

nonn,fini,full,nice

Author

Jud McCranie, Dec 15 1999

Status

approved