No subject

N. J. A. Sloane njas at
Wed Dec 15 05:17:33 CET 1999

Eyptian numbers: - request for two sequences, which will probably be new.

If we can write 1 as a sum of terms of the form 1/n,
like  1 = 1/2 + 1/3 + 1/6, 
(this is called an Egyptian fraction)
then add up the n's (getting 2+3+6 = 11),
and call this number (11) Egyptian.

If the n's are distinct, as in that example, 
call the total strictly Egyptian.

1 = 1/2 + 1/2 , so 2+2 = 4 is Egyptian, though not strictly so.

R. L. Graham showed in a paper in J. Australian Math Soc , 1963,
that every number >= 78 is strictly Egyptian

So there are two finite sequences that i would like to get:

the numbers that are not Egyptian 
the numbers that are not strictly Egyptian 

Both are a subset of {1..77}

Perhaps someone would like to compute them?

Neil Sloane

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